Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 74.3% → 80.5%

Time: 28.3s

Alternatives: 24

Speedup: 0.5×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot y - t \cdot a\\ t_2 := t \cdot i - z \cdot c\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(b, t_2, \mathsf{fma}\left(x, t_1, j \cdot \mathsf{fma}\left(y, -i, c \cdot a\right)\right)\right)\\ \mathbf{elif}\;b \leq 9800000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot y - b \cdot c, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(b \cdot t - y \cdot j\right)\right) - t \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, t_2, \mathsf{fma}\left(x, t_1, j \cdot \left(c \cdot a - i \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z y) (* t a))) (t_2 (- (* t i) (* z c))))
   (if (<= b -1.6e+96)
     (fma b t_2 (fma x t_1 (* j (fma y (- i) (* c a)))))
     (if (<= b 9800000000000.0)
       (fma
        z
        (- (* x y) (* b c))
        (- (fma c (* a j) (* i (- (* b t) (* y j)))) (* t (* x a))))
       (fma b t_2 (fma x t_1 (* j (- (* c a) (* i y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * y) - (t * a);
	double t_2 = (t * i) - (z * c);
	double tmp;
	if (b <= -1.6e+96) {
		tmp = fma(b, t_2, fma(x, t_1, (j * fma(y, -i, (c * a)))));
	} else if (b <= 9800000000000.0) {
		tmp = fma(z, ((x * y) - (b * c)), (fma(c, (a * j), (i * ((b * t) - (y * j)))) - (t * (x * a))));
	} else {
		tmp = fma(b, t_2, fma(x, t_1, (j * ((c * a) - (i * y)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * y) - Float64(t * a))
	t_2 = Float64(Float64(t * i) - Float64(z * c))
	tmp = 0.0
	if (b <= -1.6e+96)
		tmp = fma(b, t_2, fma(x, t_1, Float64(j * fma(y, Float64(-i), Float64(c * a)))));
	elseif (b <= 9800000000000.0)
		tmp = fma(z, Float64(Float64(x * y) - Float64(b * c)), Float64(fma(c, Float64(a * j), Float64(i * Float64(Float64(b * t) - Float64(y * j)))) - Float64(t * Float64(x * a))));
	else
		tmp = fma(b, t_2, fma(x, t_1, Float64(j * Float64(Float64(c * a) - Float64(i * y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+96], N[(b * t$95$2 + N[(x * t$95$1 + N[(j * N[(y * (-i) + N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9800000000000.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(a * j), $MachinePrecision] + N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * t$95$2 + N[(x * t$95$1 + N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.60000000000000003e96

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 74.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 74.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 74.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 74.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 82.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 82.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 82.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 82.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, a \cdot c\right)\right)\right)} \]

   if -1.60000000000000003e96 < b < 9.8e12

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 68.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 68.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 68.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 68.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 68.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 68.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 68.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 68.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 68.0%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in z around 0 79.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot x - c \cdot b\right) \cdot z + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right)\right) - -1 \cdot \left(i \cdot \left(t \cdot b\right)\right)} \]

   8. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y \cdot x - c \cdot b, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(t \cdot b - y \cdot j\right)\right) - t \cdot \left(a \cdot x\right)\right)} \]

   if 9.8e12 < b

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 79.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 79.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 79.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 79.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 79.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, z \cdot y - t \cdot a, j \cdot \mathsf{fma}\left(y, -i, c \cdot a\right)\right)\right)\\ \mathbf{elif}\;b \leq 9800000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot y - b \cdot c, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(b \cdot t - y \cdot j\right)\right) - t \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, z \cdot y - t \cdot a, j \cdot \left(c \cdot a - i \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 2: 80.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+90} \lor \neg \left(b \leq 11000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, z \cdot y - t \cdot a, j \cdot \left(c \cdot a - i \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot y - b \cdot c, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(b \cdot t - y \cdot j\right)\right) - t \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.25e+90) (not (<= b 11000000000000.0)))
   (fma
    b
    (- (* t i) (* z c))
    (fma x (- (* z y) (* t a)) (* j (- (* c a) (* i y)))))
   (fma
    z
    (- (* x y) (* b c))
    (- (fma c (* a j) (* i (- (* b t) (* y j)))) (* t (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.25e+90) || !(b <= 11000000000000.0)) {
		tmp = fma(b, ((t * i) - (z * c)), fma(x, ((z * y) - (t * a)), (j * ((c * a) - (i * y)))));
	} else {
		tmp = fma(z, ((x * y) - (b * c)), (fma(c, (a * j), (i * ((b * t) - (y * j)))) - (t * (x * a))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.25e+90) || !(b <= 11000000000000.0))
		tmp = fma(b, Float64(Float64(t * i) - Float64(z * c)), fma(x, Float64(Float64(z * y) - Float64(t * a)), Float64(j * Float64(Float64(c * a) - Float64(i * y)))));
	else
		tmp = fma(z, Float64(Float64(x * y) - Float64(b * c)), Float64(fma(c, Float64(a * j), Float64(i * Float64(Float64(b * t) - Float64(y * j)))) - Float64(t * Float64(x * a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.25e+90], N[Not[LessEqual[b, 11000000000000.0]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(a * j), $MachinePrecision] + N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2500000000000001e90 or 1.1e13 < b

   1. Initial program 73.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 73.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 73.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 73.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 73.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 73.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 81.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 81.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 81.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 81.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 81.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 81.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 81.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   if -1.2500000000000001e90 < b < 1.1e13

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 68.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 68.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 68.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 68.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 68.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 68.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 68.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 68.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 68.0%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in z around 0 79.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot x - c \cdot b\right) \cdot z + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right)\right) - -1 \cdot \left(i \cdot \left(t \cdot b\right)\right)} \]

   8. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y \cdot x - c \cdot b, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(t \cdot b - y \cdot j\right)\right) - t \cdot \left(a \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+90} \lor \neg \left(b \leq 11000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, z \cdot y - t \cdot a, j \cdot \left(c \cdot a - i \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot y - b \cdot c, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(b \cdot t - y \cdot j\right)\right) - t \cdot \left(x \cdot a\right)\right)\\ \end{array} \]

Alternative 3: 81.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - i \cdot y\right)\\ t_2 := \left(x \cdot \left(z \cdot y - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + t_1\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* i y))))
        (t_2 (+ (+ (* x (- (* z y) (* t a))) (* b (- (* t i) (* z c)))) t_1)))
   (if (<= t_2 INFINITY) t_2 t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (i * y));
	double t_2 = ((x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)))) + t_1;
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (i * y));
	double t_2 = ((x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)))) + t_1;
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (i * y))
	t_2 = ((x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)))) + t_1
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(i * y)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(z * y) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + t_1)
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (i * y));
	t_2 = ((x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)))) + t_1;
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 89.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 57.3%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(z \cdot y - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(c \cdot a - i \cdot y\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(z \cdot y - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \end{array} \]

Alternative 4: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - t \cdot x\right)\\ t_2 := i \cdot \left(b \cdot t - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+74}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) - c \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* t x))))
        (t_2 (+ (* i (- (* b t) (* y j))) (* z (- (* x y) (* b c))))))
   (if (<= a -8.2e+126)
     t_1
     (if (<= a -1.6e+74)
       (- (* i (* b t)) (* j (- (* i y) (* c a))))
       (if (<= a -2.25e+18)
         (* x (- (* z y) (* t a)))
         (if (<= a -1.05e-209)
           t_2
           (if (<= a -1.26e-216)
             (- (* j (- (* c a) (* i y))) (* c (* b z)))
             (if (<= a -3.3e-239)
               (* b (- (* t i) (* z c)))
               (if (<= a 4.6e+101) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (t * x));
	double t_2 = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (a <= -8.2e+126) {
		tmp = t_1;
	} else if (a <= -1.6e+74) {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	} else if (a <= -2.25e+18) {
		tmp = x * ((z * y) - (t * a));
	} else if (a <= -1.05e-209) {
		tmp = t_2;
	} else if (a <= -1.26e-216) {
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z));
	} else if (a <= -3.3e-239) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.6e+101) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (t * x))
    t_2 = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)))
    if (a <= (-8.2d+126)) then
        tmp = t_1
    else if (a <= (-1.6d+74)) then
        tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
    else if (a <= (-2.25d+18)) then
        tmp = x * ((z * y) - (t * a))
    else if (a <= (-1.05d-209)) then
        tmp = t_2
    else if (a <= (-1.26d-216)) then
        tmp = (j * ((c * a) - (i * y))) - (c * (b * z))
    else if (a <= (-3.3d-239)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 4.6d+101) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (t * x));
	double t_2 = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (a <= -8.2e+126) {
		tmp = t_1;
	} else if (a <= -1.6e+74) {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	} else if (a <= -2.25e+18) {
		tmp = x * ((z * y) - (t * a));
	} else if (a <= -1.05e-209) {
		tmp = t_2;
	} else if (a <= -1.26e-216) {
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z));
	} else if (a <= -3.3e-239) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.6e+101) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (t * x))
	t_2 = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)))
	tmp = 0
	if a <= -8.2e+126:
		tmp = t_1
	elif a <= -1.6e+74:
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
	elif a <= -2.25e+18:
		tmp = x * ((z * y) - (t * a))
	elif a <= -1.05e-209:
		tmp = t_2
	elif a <= -1.26e-216:
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z))
	elif a <= -3.3e-239:
		tmp = b * ((t * i) - (z * c))
	elif a <= 4.6e+101:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(t * x)))
	t_2 = Float64(Float64(i * Float64(Float64(b * t) - Float64(y * j))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (a <= -8.2e+126)
		tmp = t_1;
	elseif (a <= -1.6e+74)
		tmp = Float64(Float64(i * Float64(b * t)) - Float64(j * Float64(Float64(i * y) - Float64(c * a))));
	elseif (a <= -2.25e+18)
		tmp = Float64(x * Float64(Float64(z * y) - Float64(t * a)));
	elseif (a <= -1.05e-209)
		tmp = t_2;
	elseif (a <= -1.26e-216)
		tmp = Float64(Float64(j * Float64(Float64(c * a) - Float64(i * y))) - Float64(c * Float64(b * z)));
	elseif (a <= -3.3e-239)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 4.6e+101)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (t * x));
	t_2 = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (a <= -8.2e+126)
		tmp = t_1;
	elseif (a <= -1.6e+74)
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	elseif (a <= -2.25e+18)
		tmp = x * ((z * y) - (t * a));
	elseif (a <= -1.05e-209)
		tmp = t_2;
	elseif (a <= -1.26e-216)
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z));
	elseif (a <= -3.3e-239)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 4.6e+101)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+126], t$95$1, If[LessEqual[a, -1.6e+74], N[(N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(i * y), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.25e+18], N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.05e-209], t$95$2, If[LessEqual[a, -1.26e-216], N[(N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.3e-239], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+101], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8.2000000000000001e126 or 4.6000000000000003e101 < a

   1. Initial program 55.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 55.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 55.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 55.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 55.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 55.2%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 55.2%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 55.2%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in a around inf 75.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   7. Step-by-step derivation

      1. +-commutative 75.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 75.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 75.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   8. Simplified 75.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -8.2000000000000001e126 < a < -1.59999999999999997e74

   1. Initial program 85.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 92.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if -1.59999999999999997e74 < a < -2.25e18

   1. Initial program 61.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 61.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 61.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 61.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 61.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 54.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -2.25e18 < a < -1.04999999999999998e-209 or -3.29999999999999995e-239 < a < 4.6000000000000003e101

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 77.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 77.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 77.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 77.1%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 77.1%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 77.1%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in z around 0 83.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot x - c \cdot b\right) \cdot z + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right)\right) - -1 \cdot \left(i \cdot \left(t \cdot b\right)\right)} \]

   8. Simplified 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y \cdot x - c \cdot b, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(t \cdot b - y \cdot j\right)\right) - t \cdot \left(a \cdot x\right)\right)} \]

   9. Taylor expanded in a around 0 78.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -1.04999999999999998e-209 < a < -1.25999999999999999e-216

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 100.0%

         \[\leadsto \left(-1 \cdot c\right) \cdot \color{blue}{\left(z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*r* 100.0%

         \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. mul-1-neg 100.0%

         \[\leadsto \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if -1.25999999999999999e-216 < a < -3.29999999999999995e-239

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 76.9%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+74}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-209}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) - c \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \end{array} \]

Alternative 5: 56.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_2 := x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -3.7 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+42} \lor \neg \left(j \leq 5.9 \cdot 10^{+110}\right):\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* t a))))
        (t_2 (+ (* x (* z y)) (* b (- (* t i) (* z c))))))
   (if (<= j -3.7e-104)
     (* j (- (* c a) (* i y)))
     (if (<= j 5e-232)
       t_2
       (if (<= j 1.7e-198)
         t_1
         (if (<= j 8.5e-108)
           t_2
           (if (<= j 5.4e-82)
             t_1
             (if (<= j 1.4e-25)
               t_2
               (if (or (<= j 4.5e+42) (not (<= j 5.9e+110)))
                 (- (* i (* b t)) (* j (- (* i y) (* c a))))
                 (- (* c (* a j)) (* c (* b z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.7e-104) {
		tmp = j * ((c * a) - (i * y));
	} else if (j <= 5e-232) {
		tmp = t_2;
	} else if (j <= 1.7e-198) {
		tmp = t_1;
	} else if (j <= 8.5e-108) {
		tmp = t_2;
	} else if (j <= 5.4e-82) {
		tmp = t_1;
	} else if (j <= 1.4e-25) {
		tmp = t_2;
	} else if ((j <= 4.5e+42) || !(j <= 5.9e+110)) {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	} else {
		tmp = (c * (a * j)) - (c * (b * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((z * y) - (t * a))
    t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)))
    if (j <= (-3.7d-104)) then
        tmp = j * ((c * a) - (i * y))
    else if (j <= 5d-232) then
        tmp = t_2
    else if (j <= 1.7d-198) then
        tmp = t_1
    else if (j <= 8.5d-108) then
        tmp = t_2
    else if (j <= 5.4d-82) then
        tmp = t_1
    else if (j <= 1.4d-25) then
        tmp = t_2
    else if ((j <= 4.5d+42) .or. (.not. (j <= 5.9d+110))) then
        tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
    else
        tmp = (c * (a * j)) - (c * (b * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.7e-104) {
		tmp = j * ((c * a) - (i * y));
	} else if (j <= 5e-232) {
		tmp = t_2;
	} else if (j <= 1.7e-198) {
		tmp = t_1;
	} else if (j <= 8.5e-108) {
		tmp = t_2;
	} else if (j <= 5.4e-82) {
		tmp = t_1;
	} else if (j <= 1.4e-25) {
		tmp = t_2;
	} else if ((j <= 4.5e+42) || !(j <= 5.9e+110)) {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	} else {
		tmp = (c * (a * j)) - (c * (b * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * y) - (t * a))
	t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -3.7e-104:
		tmp = j * ((c * a) - (i * y))
	elif j <= 5e-232:
		tmp = t_2
	elif j <= 1.7e-198:
		tmp = t_1
	elif j <= 8.5e-108:
		tmp = t_2
	elif j <= 5.4e-82:
		tmp = t_1
	elif j <= 1.4e-25:
		tmp = t_2
	elif (j <= 4.5e+42) or not (j <= 5.9e+110):
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
	else:
		tmp = (c * (a * j)) - (c * (b * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	t_2 = Float64(Float64(x * Float64(z * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -3.7e-104)
		tmp = Float64(j * Float64(Float64(c * a) - Float64(i * y)));
	elseif (j <= 5e-232)
		tmp = t_2;
	elseif (j <= 1.7e-198)
		tmp = t_1;
	elseif (j <= 8.5e-108)
		tmp = t_2;
	elseif (j <= 5.4e-82)
		tmp = t_1;
	elseif (j <= 1.4e-25)
		tmp = t_2;
	elseif ((j <= 4.5e+42) || !(j <= 5.9e+110))
		tmp = Float64(Float64(i * Float64(b * t)) - Float64(j * Float64(Float64(i * y) - Float64(c * a))));
	else
		tmp = Float64(Float64(c * Float64(a * j)) - Float64(c * Float64(b * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((z * y) - (t * a));
	t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -3.7e-104)
		tmp = j * ((c * a) - (i * y));
	elseif (j <= 5e-232)
		tmp = t_2;
	elseif (j <= 1.7e-198)
		tmp = t_1;
	elseif (j <= 8.5e-108)
		tmp = t_2;
	elseif (j <= 5.4e-82)
		tmp = t_1;
	elseif (j <= 1.4e-25)
		tmp = t_2;
	elseif ((j <= 4.5e+42) || ~((j <= 5.9e+110)))
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	else
		tmp = (c * (a * j)) - (c * (b * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.7e-104], N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e-232], t$95$2, If[LessEqual[j, 1.7e-198], t$95$1, If[LessEqual[j, 8.5e-108], t$95$2, If[LessEqual[j, 5.4e-82], t$95$1, If[LessEqual[j, 1.4e-25], t$95$2, If[Or[LessEqual[j, 4.5e+42], N[Not[LessEqual[j, 5.9e+110]], $MachinePrecision]], N[(N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(i * y), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] - N[(c * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.6999999999999999e-104

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 64.6%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   if -3.6999999999999999e-104 < j < 4.9999999999999999e-232 or 1.6999999999999999e-198 < j < 8.49999999999999986e-108 or 5.4000000000000003e-82 < j < 1.39999999999999994e-25

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 79.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 79.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 79.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 79.8%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in j around 0 81.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 81.6%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      2. *-commutative 81.6%

         \[\leadsto \left(z \cdot y - \color{blue}{t \cdot a}\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   8. Simplified 81.6%

      \[\leadsto \color{blue}{\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   9. Taylor expanded in z around inf 74.1%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   if 4.9999999999999999e-232 < j < 1.6999999999999999e-198 or 8.49999999999999986e-108 < j < 5.4000000000000003e-82

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 81.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 1.39999999999999994e-25 < j < 4.50000000000000012e42 or 5.8999999999999997e110 < j

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 61.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 61.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 61.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 61.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 61.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 75.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if 4.50000000000000012e42 < j < 5.8999999999999997e110

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 71.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 71.0%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 71.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around 0 71.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + c \cdot \left(a \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.7 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-108}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+42} \lor \neg \left(j \leq 5.9 \cdot 10^{+110}\right):\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - c \cdot \left(b \cdot z\right)\\ \end{array} \]

Alternative 6: 53.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_2 := i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ t_3 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;i \leq -5 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.16 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 800000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+271}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* t a))))
        (t_2 (- (* i (* b t)) (* j (- (* i y) (* c a)))))
        (t_3 (* c (- (* a j) (* b z)))))
   (if (<= i -5e-42)
     t_2
     (if (<= i -2.45e-158)
       t_3
       (if (<= i -6.5e-194)
         t_1
         (if (<= i -2.16e-240)
           (* a (- (* c j) (* t x)))
           (if (<= i 3.8e-196)
             t_1
             (if (<= i 1.4e-22)
               t_3
               (if (<= i 800000000.0)
                 (* t (- (* b i) (* x a)))
                 (if (<= i 1.35e+271) t_2 (* b (- (* t i) (* z c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = (i * (b * t)) - (j * ((i * y) - (c * a)));
	double t_3 = c * ((a * j) - (b * z));
	double tmp;
	if (i <= -5e-42) {
		tmp = t_2;
	} else if (i <= -2.45e-158) {
		tmp = t_3;
	} else if (i <= -6.5e-194) {
		tmp = t_1;
	} else if (i <= -2.16e-240) {
		tmp = a * ((c * j) - (t * x));
	} else if (i <= 3.8e-196) {
		tmp = t_1;
	} else if (i <= 1.4e-22) {
		tmp = t_3;
	} else if (i <= 800000000.0) {
		tmp = t * ((b * i) - (x * a));
	} else if (i <= 1.35e+271) {
		tmp = t_2;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((z * y) - (t * a))
    t_2 = (i * (b * t)) - (j * ((i * y) - (c * a)))
    t_3 = c * ((a * j) - (b * z))
    if (i <= (-5d-42)) then
        tmp = t_2
    else if (i <= (-2.45d-158)) then
        tmp = t_3
    else if (i <= (-6.5d-194)) then
        tmp = t_1
    else if (i <= (-2.16d-240)) then
        tmp = a * ((c * j) - (t * x))
    else if (i <= 3.8d-196) then
        tmp = t_1
    else if (i <= 1.4d-22) then
        tmp = t_3
    else if (i <= 800000000.0d0) then
        tmp = t * ((b * i) - (x * a))
    else if (i <= 1.35d+271) then
        tmp = t_2
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = (i * (b * t)) - (j * ((i * y) - (c * a)));
	double t_3 = c * ((a * j) - (b * z));
	double tmp;
	if (i <= -5e-42) {
		tmp = t_2;
	} else if (i <= -2.45e-158) {
		tmp = t_3;
	} else if (i <= -6.5e-194) {
		tmp = t_1;
	} else if (i <= -2.16e-240) {
		tmp = a * ((c * j) - (t * x));
	} else if (i <= 3.8e-196) {
		tmp = t_1;
	} else if (i <= 1.4e-22) {
		tmp = t_3;
	} else if (i <= 800000000.0) {
		tmp = t * ((b * i) - (x * a));
	} else if (i <= 1.35e+271) {
		tmp = t_2;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * y) - (t * a))
	t_2 = (i * (b * t)) - (j * ((i * y) - (c * a)))
	t_3 = c * ((a * j) - (b * z))
	tmp = 0
	if i <= -5e-42:
		tmp = t_2
	elif i <= -2.45e-158:
		tmp = t_3
	elif i <= -6.5e-194:
		tmp = t_1
	elif i <= -2.16e-240:
		tmp = a * ((c * j) - (t * x))
	elif i <= 3.8e-196:
		tmp = t_1
	elif i <= 1.4e-22:
		tmp = t_3
	elif i <= 800000000.0:
		tmp = t * ((b * i) - (x * a))
	elif i <= 1.35e+271:
		tmp = t_2
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	t_2 = Float64(Float64(i * Float64(b * t)) - Float64(j * Float64(Float64(i * y) - Float64(c * a))))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (i <= -5e-42)
		tmp = t_2;
	elseif (i <= -2.45e-158)
		tmp = t_3;
	elseif (i <= -6.5e-194)
		tmp = t_1;
	elseif (i <= -2.16e-240)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(t * x)));
	elseif (i <= 3.8e-196)
		tmp = t_1;
	elseif (i <= 1.4e-22)
		tmp = t_3;
	elseif (i <= 800000000.0)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (i <= 1.35e+271)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((z * y) - (t * a));
	t_2 = (i * (b * t)) - (j * ((i * y) - (c * a)));
	t_3 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (i <= -5e-42)
		tmp = t_2;
	elseif (i <= -2.45e-158)
		tmp = t_3;
	elseif (i <= -6.5e-194)
		tmp = t_1;
	elseif (i <= -2.16e-240)
		tmp = a * ((c * j) - (t * x));
	elseif (i <= 3.8e-196)
		tmp = t_1;
	elseif (i <= 1.4e-22)
		tmp = t_3;
	elseif (i <= 800000000.0)
		tmp = t * ((b * i) - (x * a));
	elseif (i <= 1.35e+271)
		tmp = t_2;
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(i * y), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5e-42], t$95$2, If[LessEqual[i, -2.45e-158], t$95$3, If[LessEqual[i, -6.5e-194], t$95$1, If[LessEqual[i, -2.16e-240], N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.8e-196], t$95$1, If[LessEqual[i, 1.4e-22], t$95$3, If[LessEqual[i, 800000000.0], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e+271], t$95$2, N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.00000000000000003e-42 or 8e8 < i < 1.34999999999999995e271

   1. Initial program 65.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 65.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 65.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 65.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 65.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 65.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 65.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 67.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if -5.00000000000000003e-42 < i < -2.44999999999999997e-158 or 3.8000000000000001e-196 < i < 1.39999999999999997e-22

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 61.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 61.6%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 61.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -2.44999999999999997e-158 < i < -6.50000000000000019e-194 or -2.1599999999999999e-240 < i < 3.8000000000000001e-196

   1. Initial program 86.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 86.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 74.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -6.50000000000000019e-194 < i < -2.1599999999999999e-240

   1. Initial program 56.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 56.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 56.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 56.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 56.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 56.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 56.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 56.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 56.7%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 56.7%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 56.7%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in a around inf 89.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   7. Step-by-step derivation

      1. +-commutative 89.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 89.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 89.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   8. Simplified 89.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if 1.39999999999999997e-22 < i < 8e8

   1. Initial program 99.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 99.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 99.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 99.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 99.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 99.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 99.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 99.7%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 99.7%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 99.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 99.7%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 99.7%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 99.7%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 99.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 1.34999999999999995e271 < i

   1. Initial program 56.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 56.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 56.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 56.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 56.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 56.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 56.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 89.3%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-158}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;i \leq -2.16 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;i \leq 800000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+271}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 7: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(c \cdot a - i \cdot y\right)\\ t_3 := x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{if}\;j \leq -2.05 \cdot 10^{+191}:\\ \;\;\;\;t_2 - c \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-104}:\\ \;\;\;\;t_2 - a \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (* z y)) (* b (- (* t i) (* z c)))))
        (t_2 (* j (- (* c a) (* i y))))
        (t_3 (* x (- (* z y) (* t a)))))
   (if (<= j -2.05e+191)
     (- t_2 (* c (* b z)))
     (if (<= j -3.7e-104)
       (- t_2 (* a (* t x)))
       (if (<= j 1.8e-231)
         t_1
         (if (<= j 2.7e-199)
           t_3
           (if (<= j 6.6e-108)
             t_1
             (if (<= j 4.3e-82)
               t_3
               (if (<= j 2.7e-16)
                 t_1
                 (- (* i (* b t)) (* j (- (* i y) (* c a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	double t_2 = j * ((c * a) - (i * y));
	double t_3 = x * ((z * y) - (t * a));
	double tmp;
	if (j <= -2.05e+191) {
		tmp = t_2 - (c * (b * z));
	} else if (j <= -3.7e-104) {
		tmp = t_2 - (a * (t * x));
	} else if (j <= 1.8e-231) {
		tmp = t_1;
	} else if (j <= 2.7e-199) {
		tmp = t_3;
	} else if (j <= 6.6e-108) {
		tmp = t_1;
	} else if (j <= 4.3e-82) {
		tmp = t_3;
	} else if (j <= 2.7e-16) {
		tmp = t_1;
	} else {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * (z * y)) + (b * ((t * i) - (z * c)))
    t_2 = j * ((c * a) - (i * y))
    t_3 = x * ((z * y) - (t * a))
    if (j <= (-2.05d+191)) then
        tmp = t_2 - (c * (b * z))
    else if (j <= (-3.7d-104)) then
        tmp = t_2 - (a * (t * x))
    else if (j <= 1.8d-231) then
        tmp = t_1
    else if (j <= 2.7d-199) then
        tmp = t_3
    else if (j <= 6.6d-108) then
        tmp = t_1
    else if (j <= 4.3d-82) then
        tmp = t_3
    else if (j <= 2.7d-16) then
        tmp = t_1
    else
        tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	double t_2 = j * ((c * a) - (i * y));
	double t_3 = x * ((z * y) - (t * a));
	double tmp;
	if (j <= -2.05e+191) {
		tmp = t_2 - (c * (b * z));
	} else if (j <= -3.7e-104) {
		tmp = t_2 - (a * (t * x));
	} else if (j <= 1.8e-231) {
		tmp = t_1;
	} else if (j <= 2.7e-199) {
		tmp = t_3;
	} else if (j <= 6.6e-108) {
		tmp = t_1;
	} else if (j <= 4.3e-82) {
		tmp = t_3;
	} else if (j <= 2.7e-16) {
		tmp = t_1;
	} else {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * (z * y)) + (b * ((t * i) - (z * c)))
	t_2 = j * ((c * a) - (i * y))
	t_3 = x * ((z * y) - (t * a))
	tmp = 0
	if j <= -2.05e+191:
		tmp = t_2 - (c * (b * z))
	elif j <= -3.7e-104:
		tmp = t_2 - (a * (t * x))
	elif j <= 1.8e-231:
		tmp = t_1
	elif j <= 2.7e-199:
		tmp = t_3
	elif j <= 6.6e-108:
		tmp = t_1
	elif j <= 4.3e-82:
		tmp = t_3
	elif j <= 2.7e-16:
		tmp = t_1
	else:
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(z * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(j * Float64(Float64(c * a) - Float64(i * y)))
	t_3 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	tmp = 0.0
	if (j <= -2.05e+191)
		tmp = Float64(t_2 - Float64(c * Float64(b * z)));
	elseif (j <= -3.7e-104)
		tmp = Float64(t_2 - Float64(a * Float64(t * x)));
	elseif (j <= 1.8e-231)
		tmp = t_1;
	elseif (j <= 2.7e-199)
		tmp = t_3;
	elseif (j <= 6.6e-108)
		tmp = t_1;
	elseif (j <= 4.3e-82)
		tmp = t_3;
	elseif (j <= 2.7e-16)
		tmp = t_1;
	else
		tmp = Float64(Float64(i * Float64(b * t)) - Float64(j * Float64(Float64(i * y) - Float64(c * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	t_2 = j * ((c * a) - (i * y));
	t_3 = x * ((z * y) - (t * a));
	tmp = 0.0;
	if (j <= -2.05e+191)
		tmp = t_2 - (c * (b * z));
	elseif (j <= -3.7e-104)
		tmp = t_2 - (a * (t * x));
	elseif (j <= 1.8e-231)
		tmp = t_1;
	elseif (j <= 2.7e-199)
		tmp = t_3;
	elseif (j <= 6.6e-108)
		tmp = t_1;
	elseif (j <= 4.3e-82)
		tmp = t_3;
	elseif (j <= 2.7e-16)
		tmp = t_1;
	else
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.05e+191], N[(t$95$2 - N[(c * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-104], N[(t$95$2 - N[(a * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.8e-231], t$95$1, If[LessEqual[j, 2.7e-199], t$95$3, If[LessEqual[j, 6.6e-108], t$95$1, If[LessEqual[j, 4.3e-82], t$95$3, If[LessEqual[j, 2.7e-16], t$95$1, N[(N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(i * y), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.04999999999999995e191

   1. Initial program 58.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 83.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 83.5%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 83.5%

         \[\leadsto \left(-1 \cdot c\right) \cdot \color{blue}{\left(z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*r* 83.5%

         \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. mul-1-neg 83.5%

         \[\leadsto \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 83.5%

      \[\leadsto \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if -2.04999999999999995e191 < j < -3.6999999999999999e-104

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 66.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 66.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 66.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 66.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 66.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 70.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 70.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 70.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 70.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 70.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 70.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 70.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in z around 0 64.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   5. Taylor expanded in b around 0 70.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)} \]

   if -3.6999999999999999e-104 < j < 1.79999999999999987e-231 or 2.69999999999999989e-199 < j < 6.6000000000000004e-108 or 4.30000000000000019e-82 < j < 2.69999999999999999e-16

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 79.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 79.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 79.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 79.8%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in j around 0 81.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 81.6%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      2. *-commutative 81.6%

         \[\leadsto \left(z \cdot y - \color{blue}{t \cdot a}\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   8. Simplified 81.6%

      \[\leadsto \color{blue}{\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   9. Taylor expanded in z around inf 74.1%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   if 1.79999999999999987e-231 < j < 2.69999999999999989e-199 or 6.6000000000000004e-108 < j < 4.30000000000000019e-82

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 81.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 2.69999999999999999e-16 < j

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 68.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) - c \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) - a \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-108}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \end{array} \]

Alternative 8: 51.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-29}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-232}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 48:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* b z))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* y (- (* z x) (* i j)))))
   (if (<= y -5.2e+109)
     t_3
     (if (<= y -3.3e-29)
       (* i (- (* b t) (* y j)))
       (if (<= y -2.45e-216)
         t_1
         (if (<= y 3.55e-264)
           (* a (- (* c j) (* t x)))
           (if (<= y 2.4e-232)
             (* (* b c) (- z))
             (if (<= y 7e-148)
               t_2
               (if (<= y 48.0)
                 t_1
                 (if (<= y 2.5e+31) t_2 (if (<= y 4.5e+63) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = y * ((z * x) - (i * j));
	double tmp;
	if (y <= -5.2e+109) {
		tmp = t_3;
	} else if (y <= -3.3e-29) {
		tmp = i * ((b * t) - (y * j));
	} else if (y <= -2.45e-216) {
		tmp = t_1;
	} else if (y <= 3.55e-264) {
		tmp = a * ((c * j) - (t * x));
	} else if (y <= 2.4e-232) {
		tmp = (b * c) * -z;
	} else if (y <= 7e-148) {
		tmp = t_2;
	} else if (y <= 48.0) {
		tmp = t_1;
	} else if (y <= 2.5e+31) {
		tmp = t_2;
	} else if (y <= 4.5e+63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a * j) - (b * z))
    t_2 = t * ((b * i) - (x * a))
    t_3 = y * ((z * x) - (i * j))
    if (y <= (-5.2d+109)) then
        tmp = t_3
    else if (y <= (-3.3d-29)) then
        tmp = i * ((b * t) - (y * j))
    else if (y <= (-2.45d-216)) then
        tmp = t_1
    else if (y <= 3.55d-264) then
        tmp = a * ((c * j) - (t * x))
    else if (y <= 2.4d-232) then
        tmp = (b * c) * -z
    else if (y <= 7d-148) then
        tmp = t_2
    else if (y <= 48.0d0) then
        tmp = t_1
    else if (y <= 2.5d+31) then
        tmp = t_2
    else if (y <= 4.5d+63) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = y * ((z * x) - (i * j));
	double tmp;
	if (y <= -5.2e+109) {
		tmp = t_3;
	} else if (y <= -3.3e-29) {
		tmp = i * ((b * t) - (y * j));
	} else if (y <= -2.45e-216) {
		tmp = t_1;
	} else if (y <= 3.55e-264) {
		tmp = a * ((c * j) - (t * x));
	} else if (y <= 2.4e-232) {
		tmp = (b * c) * -z;
	} else if (y <= 7e-148) {
		tmp = t_2;
	} else if (y <= 48.0) {
		tmp = t_1;
	} else if (y <= 2.5e+31) {
		tmp = t_2;
	} else if (y <= 4.5e+63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (b * z))
	t_2 = t * ((b * i) - (x * a))
	t_3 = y * ((z * x) - (i * j))
	tmp = 0
	if y <= -5.2e+109:
		tmp = t_3
	elif y <= -3.3e-29:
		tmp = i * ((b * t) - (y * j))
	elif y <= -2.45e-216:
		tmp = t_1
	elif y <= 3.55e-264:
		tmp = a * ((c * j) - (t * x))
	elif y <= 2.4e-232:
		tmp = (b * c) * -z
	elif y <= 7e-148:
		tmp = t_2
	elif y <= 48.0:
		tmp = t_1
	elif y <= 2.5e+31:
		tmp = t_2
	elif y <= 4.5e+63:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(y * Float64(Float64(z * x) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5.2e+109)
		tmp = t_3;
	elseif (y <= -3.3e-29)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(y * j)));
	elseif (y <= -2.45e-216)
		tmp = t_1;
	elseif (y <= 3.55e-264)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(t * x)));
	elseif (y <= 2.4e-232)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (y <= 7e-148)
		tmp = t_2;
	elseif (y <= 48.0)
		tmp = t_1;
	elseif (y <= 2.5e+31)
		tmp = t_2;
	elseif (y <= 4.5e+63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (b * z));
	t_2 = t * ((b * i) - (x * a));
	t_3 = y * ((z * x) - (i * j));
	tmp = 0.0;
	if (y <= -5.2e+109)
		tmp = t_3;
	elseif (y <= -3.3e-29)
		tmp = i * ((b * t) - (y * j));
	elseif (y <= -2.45e-216)
		tmp = t_1;
	elseif (y <= 3.55e-264)
		tmp = a * ((c * j) - (t * x));
	elseif (y <= 2.4e-232)
		tmp = (b * c) * -z;
	elseif (y <= 7e-148)
		tmp = t_2;
	elseif (y <= 48.0)
		tmp = t_1;
	elseif (y <= 2.5e+31)
		tmp = t_2;
	elseif (y <= 4.5e+63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(z * x), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+109], t$95$3, If[LessEqual[y, -3.3e-29], N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.45e-216], t$95$1, If[LessEqual[y, 3.55e-264], N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-232], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 7e-148], t$95$2, If[LessEqual[y, 48.0], t$95$1, If[LessEqual[y, 2.5e+31], t$95$2, If[LessEqual[y, 4.5e+63], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.1999999999999997e109 or 4.50000000000000017e63 < y

   1. Initial program 61.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 61.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 61.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 73.1%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 73.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 73.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 73.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 73.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -5.1999999999999997e109 < y < -3.30000000000000028e-29

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 72.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 72.5%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 72.5%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 72.5%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in i around inf 58.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 58.3%

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(y \cdot j\right)\right)} \]

      2. neg-mul-1 58.3%

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{-y \cdot j}\right) \]

      3. fma-neg 58.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   8. Simplified 58.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -3.30000000000000028e-29 < y < -2.4500000000000001e-216 or 7.0000000000000001e-148 < y < 48 or 2.50000000000000013e31 < y < 4.50000000000000017e63

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 70.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 70.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -2.4500000000000001e-216 < y < 3.55000000000000013e-264

   1. Initial program 63.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 62.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 62.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 62.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 62.8%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in a around inf 67.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   7. Step-by-step derivation

      1. +-commutative 67.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 67.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 67.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if 3.55000000000000013e-264 < y < 2.39999999999999999e-232

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around 0 78.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg 78.6%

         \[\leadsto \color{blue}{\left(-c \cdot b\right)} \cdot z \]

      2. distribute-lft-neg-out 78.6%

         \[\leadsto \color{blue}{\left(\left(-c\right) \cdot b\right)} \cdot z \]

      3. *-commutative 78.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]

   7. Simplified 78.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]

   if 2.39999999999999999e-232 < y < 7.0000000000000001e-148 or 48 < y < 2.50000000000000013e31

   1. Initial program 93.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 93.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 93.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 93.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 93.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 93.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 63.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 63.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 63.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 63.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 63.4%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 63.4%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 63.4%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 63.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-29}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-232}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 48:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+63}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \end{array} \]

Alternative 9: 61.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_2 := x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2.45 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) - c \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* t a))))
        (t_2 (+ (* x (* z y)) (* b (- (* t i) (* z c))))))
   (if (<= j -2.45e-48)
     (- (* j (- (* c a) (* i y))) (* c (* b z)))
     (if (<= j 5e-232)
       t_2
       (if (<= j 1.15e-198)
         t_1
         (if (<= j 4.6e-110)
           t_2
           (if (<= j 1.5e-81)
             t_1
             (if (<= j 1.5e-27)
               t_2
               (- (* i (* b t)) (* j (- (* i y) (* c a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -2.45e-48) {
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z));
	} else if (j <= 5e-232) {
		tmp = t_2;
	} else if (j <= 1.15e-198) {
		tmp = t_1;
	} else if (j <= 4.6e-110) {
		tmp = t_2;
	} else if (j <= 1.5e-81) {
		tmp = t_1;
	} else if (j <= 1.5e-27) {
		tmp = t_2;
	} else {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((z * y) - (t * a))
    t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)))
    if (j <= (-2.45d-48)) then
        tmp = (j * ((c * a) - (i * y))) - (c * (b * z))
    else if (j <= 5d-232) then
        tmp = t_2
    else if (j <= 1.15d-198) then
        tmp = t_1
    else if (j <= 4.6d-110) then
        tmp = t_2
    else if (j <= 1.5d-81) then
        tmp = t_1
    else if (j <= 1.5d-27) then
        tmp = t_2
    else
        tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -2.45e-48) {
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z));
	} else if (j <= 5e-232) {
		tmp = t_2;
	} else if (j <= 1.15e-198) {
		tmp = t_1;
	} else if (j <= 4.6e-110) {
		tmp = t_2;
	} else if (j <= 1.5e-81) {
		tmp = t_1;
	} else if (j <= 1.5e-27) {
		tmp = t_2;
	} else {
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * y) - (t * a))
	t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -2.45e-48:
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z))
	elif j <= 5e-232:
		tmp = t_2
	elif j <= 1.15e-198:
		tmp = t_1
	elif j <= 4.6e-110:
		tmp = t_2
	elif j <= 1.5e-81:
		tmp = t_1
	elif j <= 1.5e-27:
		tmp = t_2
	else:
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	t_2 = Float64(Float64(x * Float64(z * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -2.45e-48)
		tmp = Float64(Float64(j * Float64(Float64(c * a) - Float64(i * y))) - Float64(c * Float64(b * z)));
	elseif (j <= 5e-232)
		tmp = t_2;
	elseif (j <= 1.15e-198)
		tmp = t_1;
	elseif (j <= 4.6e-110)
		tmp = t_2;
	elseif (j <= 1.5e-81)
		tmp = t_1;
	elseif (j <= 1.5e-27)
		tmp = t_2;
	else
		tmp = Float64(Float64(i * Float64(b * t)) - Float64(j * Float64(Float64(i * y) - Float64(c * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((z * y) - (t * a));
	t_2 = (x * (z * y)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -2.45e-48)
		tmp = (j * ((c * a) - (i * y))) - (c * (b * z));
	elseif (j <= 5e-232)
		tmp = t_2;
	elseif (j <= 1.15e-198)
		tmp = t_1;
	elseif (j <= 4.6e-110)
		tmp = t_2;
	elseif (j <= 1.5e-81)
		tmp = t_1;
	elseif (j <= 1.5e-27)
		tmp = t_2;
	else
		tmp = (i * (b * t)) - (j * ((i * y) - (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.45e-48], N[(N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e-232], t$95$2, If[LessEqual[j, 1.15e-198], t$95$1, If[LessEqual[j, 4.6e-110], t$95$2, If[LessEqual[j, 1.5e-81], t$95$1, If[LessEqual[j, 1.5e-27], t$95$2, N[(N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(i * y), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.4500000000000001e-48

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 73.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 73.0%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 73.0%

         \[\leadsto \left(-1 \cdot c\right) \cdot \color{blue}{\left(z \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*r* 73.0%

         \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. mul-1-neg 73.0%

         \[\leadsto \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 73.0%

      \[\leadsto \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if -2.4500000000000001e-48 < j < 4.9999999999999999e-232 or 1.15000000000000007e-198 < j < 4.6000000000000003e-110 or 1.4999999999999999e-81 < j < 1.5000000000000001e-27

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 78.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 78.2%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 78.2%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 78.2%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in j around 0 78.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 78.8%

         \[\leadsto \left(\color{blue}{z \cdot y} - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

      2. *-commutative 78.8%

         \[\leadsto \left(z \cdot y - \color{blue}{t \cdot a}\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   8. Simplified 78.8%

      \[\leadsto \color{blue}{\left(z \cdot y - t \cdot a\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   9. Taylor expanded in z around inf 70.2%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b \]

   if 4.9999999999999999e-232 < j < 1.15000000000000007e-198 or 4.6000000000000003e-110 < j < 1.4999999999999999e-81

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 81.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 1.5000000000000001e-27 < j

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 68.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.45 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) - c \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(z \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right) - j \cdot \left(i \cdot y - c \cdot a\right)\\ \end{array} \]

Alternative 10: 66.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-309}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+98}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* t x)))))
   (if (<= a -7.5e+105)
     t_1
     (if (<= a -9e-309)
       (+ (* x (- (* z y) (* t a))) (* b (- (* t i) (* z c))))
       (if (<= a 5.2e+98)
         (+ (* i (- (* b t) (* y j))) (* z (- (* x y) (* b c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (t * x));
	double tmp;
	if (a <= -7.5e+105) {
		tmp = t_1;
	} else if (a <= -9e-309) {
		tmp = (x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (a <= 5.2e+98) {
		tmp = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (t * x))
    if (a <= (-7.5d+105)) then
        tmp = t_1
    else if (a <= (-9d-309)) then
        tmp = (x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)))
    else if (a <= 5.2d+98) then
        tmp = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (t * x));
	double tmp;
	if (a <= -7.5e+105) {
		tmp = t_1;
	} else if (a <= -9e-309) {
		tmp = (x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (a <= 5.2e+98) {
		tmp = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (t * x))
	tmp = 0
	if a <= -7.5e+105:
		tmp = t_1
	elif a <= -9e-309:
		tmp = (x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)))
	elif a <= 5.2e+98:
		tmp = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(t * x)))
	tmp = 0.0
	if (a <= -7.5e+105)
		tmp = t_1;
	elseif (a <= -9e-309)
		tmp = Float64(Float64(x * Float64(Float64(z * y) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (a <= 5.2e+98)
		tmp = Float64(Float64(i * Float64(Float64(b * t) - Float64(y * j))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (t * x));
	tmp = 0.0;
	if (a <= -7.5e+105)
		tmp = t_1;
	elseif (a <= -9e-309)
		tmp = (x * ((z * y) - (t * a))) + (b * ((t * i) - (z * c)));
	elseif (a <= 5.2e+98)
		tmp = (i * ((b * t) - (y * j))) + (z * ((x * y) - (b * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+105], t$95$1, If[LessEqual[a, -9e-309], N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+98], N[(N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.5000000000000002e105 or 5.1999999999999999e98 < a

   1. Initial program 57.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 57.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 57.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 57.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 57.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 57.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 57.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 57.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 57.2%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 57.2%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 57.2%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in a around inf 75.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   7. Step-by-step derivation

      1. +-commutative 75.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 75.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 75.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   8. Simplified 75.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -7.5000000000000002e105 < a < -9.0000000000000021e-309

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 81.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 81.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 81.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 81.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 73.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   if -9.0000000000000021e-309 < a < 5.1999999999999999e98

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 72.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 72.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 72.8%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in z around 0 82.7%

      \[\leadsto \color{blue}{\left(\left(y \cdot x - c \cdot b\right) \cdot z + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right)\right) - -1 \cdot \left(i \cdot \left(t \cdot b\right)\right)} \]

   8. Simplified 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y \cdot x - c \cdot b, \mathsf{fma}\left(c, a \cdot j, i \cdot \left(t \cdot b - y \cdot j\right)\right) - t \cdot \left(a \cdot x\right)\right)} \]

   9. Taylor expanded in a around 0 76.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right) + \left(y \cdot x - c \cdot b\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-309}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+98}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \end{array} \]

Alternative 11: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-71}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* t a)))) (t_2 (* c (- (* a j) (* b z)))))
   (if (<= c -2e+24)
     t_2
     (if (<= c -1.45e-71)
       (* j (- (* c a) (* i y)))
       (if (<= c -3e-196)
         (* t (- (* b i) (* x a)))
         (if (<= c -6e-302)
           t_1
           (if (<= c 1.65e-286)
             (* i (- (* b t) (* y j)))
             (if (<= c 1.15e-203)
               t_1
               (if (<= c 6.5e-40) (* b (- (* t i) (* z c))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -2e+24) {
		tmp = t_2;
	} else if (c <= -1.45e-71) {
		tmp = j * ((c * a) - (i * y));
	} else if (c <= -3e-196) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= -6e-302) {
		tmp = t_1;
	} else if (c <= 1.65e-286) {
		tmp = i * ((b * t) - (y * j));
	} else if (c <= 1.15e-203) {
		tmp = t_1;
	} else if (c <= 6.5e-40) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((z * y) - (t * a))
    t_2 = c * ((a * j) - (b * z))
    if (c <= (-2d+24)) then
        tmp = t_2
    else if (c <= (-1.45d-71)) then
        tmp = j * ((c * a) - (i * y))
    else if (c <= (-3d-196)) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= (-6d-302)) then
        tmp = t_1
    else if (c <= 1.65d-286) then
        tmp = i * ((b * t) - (y * j))
    else if (c <= 1.15d-203) then
        tmp = t_1
    else if (c <= 6.5d-40) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -2e+24) {
		tmp = t_2;
	} else if (c <= -1.45e-71) {
		tmp = j * ((c * a) - (i * y));
	} else if (c <= -3e-196) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= -6e-302) {
		tmp = t_1;
	} else if (c <= 1.65e-286) {
		tmp = i * ((b * t) - (y * j));
	} else if (c <= 1.15e-203) {
		tmp = t_1;
	} else if (c <= 6.5e-40) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * y) - (t * a))
	t_2 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -2e+24:
		tmp = t_2
	elif c <= -1.45e-71:
		tmp = j * ((c * a) - (i * y))
	elif c <= -3e-196:
		tmp = t * ((b * i) - (x * a))
	elif c <= -6e-302:
		tmp = t_1
	elif c <= 1.65e-286:
		tmp = i * ((b * t) - (y * j))
	elif c <= 1.15e-203:
		tmp = t_1
	elif c <= 6.5e-40:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -2e+24)
		tmp = t_2;
	elseif (c <= -1.45e-71)
		tmp = Float64(j * Float64(Float64(c * a) - Float64(i * y)));
	elseif (c <= -3e-196)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= -6e-302)
		tmp = t_1;
	elseif (c <= 1.65e-286)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(y * j)));
	elseif (c <= 1.15e-203)
		tmp = t_1;
	elseif (c <= 6.5e-40)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((z * y) - (t * a));
	t_2 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -2e+24)
		tmp = t_2;
	elseif (c <= -1.45e-71)
		tmp = j * ((c * a) - (i * y));
	elseif (c <= -3e-196)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= -6e-302)
		tmp = t_1;
	elseif (c <= 1.65e-286)
		tmp = i * ((b * t) - (y * j));
	elseif (c <= 1.15e-203)
		tmp = t_1;
	elseif (c <= 6.5e-40)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+24], t$95$2, If[LessEqual[c, -1.45e-71], N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3e-196], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6e-302], t$95$1, If[LessEqual[c, 1.65e-286], N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-203], t$95$1, If[LessEqual[c, 6.5e-40], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -2e24 or 6.4999999999999999e-40 < c

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 65.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.3%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 65.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -2e24 < c < -1.4499999999999999e-71

   1. Initial program 47.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 47.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 47.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 60.3%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   if -1.4499999999999999e-71 < c < -3e-196

   1. Initial program 80.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 64.3%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 64.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 64.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 64.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 64.3%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 64.3%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 64.3%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -3e-196 < c < -5.99999999999999978e-302 or 1.6499999999999999e-286 < c < 1.14999999999999996e-203

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 89.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -5.99999999999999978e-302 < c < 1.6499999999999999e-286

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 99.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 99.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 99.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 99.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 99.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 99.5%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 99.5%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in i around inf 75.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 75.1%

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(y \cdot j\right)\right)} \]

      2. neg-mul-1 75.1%

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{-y \cdot j}\right) \]

      3. fma-neg 75.1%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   8. Simplified 75.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if 1.14999999999999996e-203 < c < 6.4999999999999999e-40

   1. Initial program 85.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 61.0%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+24}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-71}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]

Alternative 12: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot x - i \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -1.35 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* z x) (* i j)))) (t_2 (* c (- (* a j) (* b z)))))
   (if (<= c -1.35e+26)
     t_2
     (if (<= c -1.45e-67)
       (* j (- (* c a) (* i y)))
       (if (<= c 2.3e-291)
         (* t (- (* b i) (* x a)))
         (if (<= c 4.5e-216)
           t_1
           (if (<= c 8.5e-128)
             (* i (- (* b t) (* y j)))
             (if (<= c 7.6e-45) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((z * x) - (i * j));
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -1.35e+26) {
		tmp = t_2;
	} else if (c <= -1.45e-67) {
		tmp = j * ((c * a) - (i * y));
	} else if (c <= 2.3e-291) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 4.5e-216) {
		tmp = t_1;
	} else if (c <= 8.5e-128) {
		tmp = i * ((b * t) - (y * j));
	} else if (c <= 7.6e-45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z * x) - (i * j))
    t_2 = c * ((a * j) - (b * z))
    if (c <= (-1.35d+26)) then
        tmp = t_2
    else if (c <= (-1.45d-67)) then
        tmp = j * ((c * a) - (i * y))
    else if (c <= 2.3d-291) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 4.5d-216) then
        tmp = t_1
    else if (c <= 8.5d-128) then
        tmp = i * ((b * t) - (y * j))
    else if (c <= 7.6d-45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((z * x) - (i * j));
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -1.35e+26) {
		tmp = t_2;
	} else if (c <= -1.45e-67) {
		tmp = j * ((c * a) - (i * y));
	} else if (c <= 2.3e-291) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 4.5e-216) {
		tmp = t_1;
	} else if (c <= 8.5e-128) {
		tmp = i * ((b * t) - (y * j));
	} else if (c <= 7.6e-45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((z * x) - (i * j))
	t_2 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -1.35e+26:
		tmp = t_2
	elif c <= -1.45e-67:
		tmp = j * ((c * a) - (i * y))
	elif c <= 2.3e-291:
		tmp = t * ((b * i) - (x * a))
	elif c <= 4.5e-216:
		tmp = t_1
	elif c <= 8.5e-128:
		tmp = i * ((b * t) - (y * j))
	elif c <= 7.6e-45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(z * x) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -1.35e+26)
		tmp = t_2;
	elseif (c <= -1.45e-67)
		tmp = Float64(j * Float64(Float64(c * a) - Float64(i * y)));
	elseif (c <= 2.3e-291)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 4.5e-216)
		tmp = t_1;
	elseif (c <= 8.5e-128)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(y * j)));
	elseif (c <= 7.6e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((z * x) - (i * j));
	t_2 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -1.35e+26)
		tmp = t_2;
	elseif (c <= -1.45e-67)
		tmp = j * ((c * a) - (i * y));
	elseif (c <= 2.3e-291)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 4.5e-216)
		tmp = t_1;
	elseif (c <= 8.5e-128)
		tmp = i * ((b * t) - (y * j));
	elseif (c <= 7.6e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(z * x), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.35e+26], t$95$2, If[LessEqual[c, -1.45e-67], N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-291], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e-216], t$95$1, If[LessEqual[c, 8.5e-128], N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e-45], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.35e26 or 7.59999999999999994e-45 < c

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 65.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -1.35e26 < c < -1.45000000000000002e-67

   1. Initial program 47.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 47.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 47.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 60.3%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   if -1.45000000000000002e-67 < c < 2.3000000000000001e-291

   1. Initial program 85.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 59.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 59.6%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 59.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 59.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 59.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 59.6%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 59.6%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 59.6%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 2.3000000000000001e-291 < c < 4.4999999999999999e-216 or 8.4999999999999996e-128 < c < 7.59999999999999994e-45

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 70.3%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 70.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 70.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 70.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 4.4999999999999999e-216 < c < 8.4999999999999996e-128

   1. Initial program 95.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 95.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 95.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 95.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 95.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 95.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 94.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 94.4%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 94.4%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 94.4%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in i around inf 66.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 66.2%

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(y \cdot j\right)\right)} \]

      2. neg-mul-1 66.2%

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{-y \cdot j}\right) \]

      3. fma-neg 66.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   8. Simplified 66.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]

Alternative 13: 51.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;c \leq 3.05 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-159}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* b z)))))
   (if (<= c -2.9e+22)
     t_1
     (if (<= c -1.25e-66)
       (* j (- (* c a) (* i y)))
       (if (<= c 3.05e-291)
         (* t (- (* b i) (* x a)))
         (if (<= c 6e-216)
           (* y (- (* z x) (* i j)))
           (if (<= c 1.5e-159)
             (* i (- (* b t) (* y j)))
             (if (<= c 9.5e-40) (* b (- (* t i) (* z c))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -2.9e+22) {
		tmp = t_1;
	} else if (c <= -1.25e-66) {
		tmp = j * ((c * a) - (i * y));
	} else if (c <= 3.05e-291) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 6e-216) {
		tmp = y * ((z * x) - (i * j));
	} else if (c <= 1.5e-159) {
		tmp = i * ((b * t) - (y * j));
	} else if (c <= 9.5e-40) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (b * z))
    if (c <= (-2.9d+22)) then
        tmp = t_1
    else if (c <= (-1.25d-66)) then
        tmp = j * ((c * a) - (i * y))
    else if (c <= 3.05d-291) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 6d-216) then
        tmp = y * ((z * x) - (i * j))
    else if (c <= 1.5d-159) then
        tmp = i * ((b * t) - (y * j))
    else if (c <= 9.5d-40) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -2.9e+22) {
		tmp = t_1;
	} else if (c <= -1.25e-66) {
		tmp = j * ((c * a) - (i * y));
	} else if (c <= 3.05e-291) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 6e-216) {
		tmp = y * ((z * x) - (i * j));
	} else if (c <= 1.5e-159) {
		tmp = i * ((b * t) - (y * j));
	} else if (c <= 9.5e-40) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -2.9e+22:
		tmp = t_1
	elif c <= -1.25e-66:
		tmp = j * ((c * a) - (i * y))
	elif c <= 3.05e-291:
		tmp = t * ((b * i) - (x * a))
	elif c <= 6e-216:
		tmp = y * ((z * x) - (i * j))
	elif c <= 1.5e-159:
		tmp = i * ((b * t) - (y * j))
	elif c <= 9.5e-40:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -2.9e+22)
		tmp = t_1;
	elseif (c <= -1.25e-66)
		tmp = Float64(j * Float64(Float64(c * a) - Float64(i * y)));
	elseif (c <= 3.05e-291)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 6e-216)
		tmp = Float64(y * Float64(Float64(z * x) - Float64(i * j)));
	elseif (c <= 1.5e-159)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(y * j)));
	elseif (c <= 9.5e-40)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -2.9e+22)
		tmp = t_1;
	elseif (c <= -1.25e-66)
		tmp = j * ((c * a) - (i * y));
	elseif (c <= 3.05e-291)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 6e-216)
		tmp = y * ((z * x) - (i * j));
	elseif (c <= 1.5e-159)
		tmp = i * ((b * t) - (y * j));
	elseif (c <= 9.5e-40)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.9e+22], t$95$1, If[LessEqual[c, -1.25e-66], N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.05e-291], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e-216], N[(y * N[(N[(z * x), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e-159], N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-40], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -2.9e22 or 9.5000000000000006e-40 < c

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 65.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.3%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 65.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -2.9e22 < c < -1.2499999999999999e-66

   1. Initial program 47.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 47.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 47.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 47.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 60.3%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   if -1.2499999999999999e-66 < c < 3.05e-291

   1. Initial program 85.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 85.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 85.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 85.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 85.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 59.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 59.6%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 59.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 59.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 59.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 59.6%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 59.6%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 59.6%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if 3.05e-291 < c < 6.00000000000000025e-216

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 90.0%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 90.0%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 90.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 90.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 6.00000000000000025e-216 < c < 1.50000000000000005e-159

   1. Initial program 93.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 93.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 93.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 93.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 93.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 93.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 93.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 93.1%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 93.1%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 93.1%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in i around inf 73.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 73.7%

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(y \cdot j\right)\right)} \]

      2. neg-mul-1 73.7%

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{-y \cdot j}\right) \]

      3. fma-neg 73.7%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   8. Simplified 73.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if 1.50000000000000005e-159 < c < 9.5000000000000006e-40

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 81.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 81.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 81.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 81.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 60.2%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;c \leq 3.05 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-159}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]

Alternative 14: 29.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-220}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-227}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-193}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-113}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= y -5.2e+60)
     (* (- i) (* y j))
     (if (<= y -9.2e-220)
       (* c (* b (- z)))
       (if (<= y 1.65e-280)
         t_1
         (if (<= y 3.9e-227)
           (* (* b c) (- z))
           (if (<= y 1.65e-193)
             (* (* x a) (- t))
             (if (<= y 2.7e-113)
               (* i (* b t))
               (if (<= y 1.72e+72) t_1 (* y (* z x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (y <= -5.2e+60) {
		tmp = -i * (y * j);
	} else if (y <= -9.2e-220) {
		tmp = c * (b * -z);
	} else if (y <= 1.65e-280) {
		tmp = t_1;
	} else if (y <= 3.9e-227) {
		tmp = (b * c) * -z;
	} else if (y <= 1.65e-193) {
		tmp = (x * a) * -t;
	} else if (y <= 2.7e-113) {
		tmp = i * (b * t);
	} else if (y <= 1.72e+72) {
		tmp = t_1;
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (a * j)
    if (y <= (-5.2d+60)) then
        tmp = -i * (y * j)
    else if (y <= (-9.2d-220)) then
        tmp = c * (b * -z)
    else if (y <= 1.65d-280) then
        tmp = t_1
    else if (y <= 3.9d-227) then
        tmp = (b * c) * -z
    else if (y <= 1.65d-193) then
        tmp = (x * a) * -t
    else if (y <= 2.7d-113) then
        tmp = i * (b * t)
    else if (y <= 1.72d+72) then
        tmp = t_1
    else
        tmp = y * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (y <= -5.2e+60) {
		tmp = -i * (y * j);
	} else if (y <= -9.2e-220) {
		tmp = c * (b * -z);
	} else if (y <= 1.65e-280) {
		tmp = t_1;
	} else if (y <= 3.9e-227) {
		tmp = (b * c) * -z;
	} else if (y <= 1.65e-193) {
		tmp = (x * a) * -t;
	} else if (y <= 2.7e-113) {
		tmp = i * (b * t);
	} else if (y <= 1.72e+72) {
		tmp = t_1;
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if y <= -5.2e+60:
		tmp = -i * (y * j)
	elif y <= -9.2e-220:
		tmp = c * (b * -z)
	elif y <= 1.65e-280:
		tmp = t_1
	elif y <= 3.9e-227:
		tmp = (b * c) * -z
	elif y <= 1.65e-193:
		tmp = (x * a) * -t
	elif y <= 2.7e-113:
		tmp = i * (b * t)
	elif y <= 1.72e+72:
		tmp = t_1
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (y <= -5.2e+60)
		tmp = Float64(Float64(-i) * Float64(y * j));
	elseif (y <= -9.2e-220)
		tmp = Float64(c * Float64(b * Float64(-z)));
	elseif (y <= 1.65e-280)
		tmp = t_1;
	elseif (y <= 3.9e-227)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (y <= 1.65e-193)
		tmp = Float64(Float64(x * a) * Float64(-t));
	elseif (y <= 2.7e-113)
		tmp = Float64(i * Float64(b * t));
	elseif (y <= 1.72e+72)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	tmp = 0.0;
	if (y <= -5.2e+60)
		tmp = -i * (y * j);
	elseif (y <= -9.2e-220)
		tmp = c * (b * -z);
	elseif (y <= 1.65e-280)
		tmp = t_1;
	elseif (y <= 3.9e-227)
		tmp = (b * c) * -z;
	elseif (y <= 1.65e-193)
		tmp = (x * a) * -t;
	elseif (y <= 2.7e-113)
		tmp = i * (b * t);
	elseif (y <= 1.72e+72)
		tmp = t_1;
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+60], N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.2e-220], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-280], t$95$1, If[LessEqual[y, 3.9e-227], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 1.65e-193], N[(N[(x * a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y, 2.7e-113], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.72e+72], t$95$1, N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -5.20000000000000016e60

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 63.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 63.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 63.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 63.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 63.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 65.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 65.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 65.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 65.5%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 65.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 65.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 65.5%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 69.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around inf 49.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

   5. Taylor expanded in t around 0 46.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto \color{blue}{-i \cdot \left(y \cdot j\right)} \]

      2. distribute-rgt-neg-out 46.1%

         \[\leadsto \color{blue}{i \cdot \left(-y \cdot j\right)} \]

      3. distribute-rgt-neg-in 46.1%

         \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-j\right)\right)} \]

   7. Simplified 46.1%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-j\right)\right)} \]

   if -5.20000000000000016e60 < y < -9.19999999999999922e-220

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 53.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 53.6%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 53.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around 0 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. distribute-rgt-neg-in 39.0%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} \]

      3. distribute-rgt-neg-in 39.0%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   9. Simplified 39.0%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]

   if -9.19999999999999922e-220 < y < 1.64999999999999995e-280 or 2.69999999999999996e-113 < y < 1.71999999999999993e72

   1. Initial program 64.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 53.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 53.9%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 53.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around inf 39.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 1.64999999999999995e-280 < y < 3.8999999999999999e-227

   1. Initial program 80.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 67.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around 0 67.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg 67.3%

         \[\leadsto \color{blue}{\left(-c \cdot b\right)} \cdot z \]

      2. distribute-lft-neg-out 67.3%

         \[\leadsto \color{blue}{\left(\left(-c\right) \cdot b\right)} \cdot z \]

      3. *-commutative 67.3%

         \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]

   7. Simplified 67.3%

      \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]

   if 3.8999999999999999e-227 < y < 1.6499999999999999e-193

   1. Initial program 87.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 76.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 76.1%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 76.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 76.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 76.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 76.1%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 76.1%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 76.1%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 76.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   7. Taylor expanded in i around 0 76.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 76.0%

         \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. distribute-lft-neg-out 76.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot x\right)} \]

      3. *-commutative 76.0%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   9. Simplified 76.0%

      \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   if 1.6499999999999999e-193 < y < 2.69999999999999996e-113

   1. Initial program 87.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 87.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 87.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 87.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 87.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 87.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 63.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 45.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 1.71999999999999993e72 < y

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 46.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-220}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-280}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-227}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-193}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-113}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 15: 42.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+170}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-121}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* t x)))))
   (if (<= z -6.5e+170)
     (* y (* z x))
     (if (<= z -4.8e+84)
       (* c (* b (- z)))
       (if (<= z 2.7e-166)
         t_1
         (if (<= z 3.5e-121)
           (* i (* b t))
           (if (<= z 7e+187) t_1 (* (* b c) (- z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (t * x));
	double tmp;
	if (z <= -6.5e+170) {
		tmp = y * (z * x);
	} else if (z <= -4.8e+84) {
		tmp = c * (b * -z);
	} else if (z <= 2.7e-166) {
		tmp = t_1;
	} else if (z <= 3.5e-121) {
		tmp = i * (b * t);
	} else if (z <= 7e+187) {
		tmp = t_1;
	} else {
		tmp = (b * c) * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (t * x))
    if (z <= (-6.5d+170)) then
        tmp = y * (z * x)
    else if (z <= (-4.8d+84)) then
        tmp = c * (b * -z)
    else if (z <= 2.7d-166) then
        tmp = t_1
    else if (z <= 3.5d-121) then
        tmp = i * (b * t)
    else if (z <= 7d+187) then
        tmp = t_1
    else
        tmp = (b * c) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (t * x));
	double tmp;
	if (z <= -6.5e+170) {
		tmp = y * (z * x);
	} else if (z <= -4.8e+84) {
		tmp = c * (b * -z);
	} else if (z <= 2.7e-166) {
		tmp = t_1;
	} else if (z <= 3.5e-121) {
		tmp = i * (b * t);
	} else if (z <= 7e+187) {
		tmp = t_1;
	} else {
		tmp = (b * c) * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (t * x))
	tmp = 0
	if z <= -6.5e+170:
		tmp = y * (z * x)
	elif z <= -4.8e+84:
		tmp = c * (b * -z)
	elif z <= 2.7e-166:
		tmp = t_1
	elif z <= 3.5e-121:
		tmp = i * (b * t)
	elif z <= 7e+187:
		tmp = t_1
	else:
		tmp = (b * c) * -z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(t * x)))
	tmp = 0.0
	if (z <= -6.5e+170)
		tmp = Float64(y * Float64(z * x));
	elseif (z <= -4.8e+84)
		tmp = Float64(c * Float64(b * Float64(-z)));
	elseif (z <= 2.7e-166)
		tmp = t_1;
	elseif (z <= 3.5e-121)
		tmp = Float64(i * Float64(b * t));
	elseif (z <= 7e+187)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (t * x));
	tmp = 0.0;
	if (z <= -6.5e+170)
		tmp = y * (z * x);
	elseif (z <= -4.8e+84)
		tmp = c * (b * -z);
	elseif (z <= 2.7e-166)
		tmp = t_1;
	elseif (z <= 3.5e-121)
		tmp = i * (b * t);
	elseif (z <= 7e+187)
		tmp = t_1;
	else
		tmp = (b * c) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+170], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e+84], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-166], t$95$1, If[LessEqual[z, 3.5e-121], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+187], t$95$1, N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.5e170

   1. Initial program 54.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 54.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 54.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 54.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 54.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 54.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 54.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 72.9%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 50.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -6.5e170 < z < -4.7999999999999999e84

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 64.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around 0 59.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 59.4%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. distribute-rgt-neg-in 59.4%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} \]

      3. distribute-rgt-neg-in 59.4%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   9. Simplified 59.4%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]

   if -4.7999999999999999e84 < z < 2.70000000000000006e-166 or 3.49999999999999993e-121 < z < 6.9999999999999995e187

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 73.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 73.4%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 73.4%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 73.4%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in a around inf 46.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   7. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   8. Simplified 46.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if 2.70000000000000006e-166 < z < 3.49999999999999993e-121

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 78.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 62.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 55.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 6.9999999999999995e187 < z

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 83.2%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around 0 69.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg 69.3%

         \[\leadsto \color{blue}{\left(-c \cdot b\right)} \cdot z \]

      2. distribute-lft-neg-out 69.3%

         \[\leadsto \color{blue}{\left(\left(-c\right) \cdot b\right)} \cdot z \]

      3. *-commutative 69.3%

         \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{\left(b \cdot \left(-c\right)\right)} \cdot z \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+170}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-166}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-121}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \end{array} \]

Alternative 16: 43.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot a\right) \cdot \left(-t\right)\\ t_2 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x a) (- t))) (t_2 (* c (- (* a j) (* b z)))))
   (if (<= c -2.2e-64)
     t_2
     (if (<= c -7.8e-299)
       t_1
       (if (<= c 4.8e-216)
         (* y (* z x))
         (if (<= c 1.3e-205) t_1 (if (<= c 1.15e-112) (* i (* b t)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * a) * -t;
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -2.2e-64) {
		tmp = t_2;
	} else if (c <= -7.8e-299) {
		tmp = t_1;
	} else if (c <= 4.8e-216) {
		tmp = y * (z * x);
	} else if (c <= 1.3e-205) {
		tmp = t_1;
	} else if (c <= 1.15e-112) {
		tmp = i * (b * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * a) * -t
    t_2 = c * ((a * j) - (b * z))
    if (c <= (-2.2d-64)) then
        tmp = t_2
    else if (c <= (-7.8d-299)) then
        tmp = t_1
    else if (c <= 4.8d-216) then
        tmp = y * (z * x)
    else if (c <= 1.3d-205) then
        tmp = t_1
    else if (c <= 1.15d-112) then
        tmp = i * (b * t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * a) * -t;
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -2.2e-64) {
		tmp = t_2;
	} else if (c <= -7.8e-299) {
		tmp = t_1;
	} else if (c <= 4.8e-216) {
		tmp = y * (z * x);
	} else if (c <= 1.3e-205) {
		tmp = t_1;
	} else if (c <= 1.15e-112) {
		tmp = i * (b * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * a) * -t
	t_2 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -2.2e-64:
		tmp = t_2
	elif c <= -7.8e-299:
		tmp = t_1
	elif c <= 4.8e-216:
		tmp = y * (z * x)
	elif c <= 1.3e-205:
		tmp = t_1
	elif c <= 1.15e-112:
		tmp = i * (b * t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * a) * Float64(-t))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -2.2e-64)
		tmp = t_2;
	elseif (c <= -7.8e-299)
		tmp = t_1;
	elseif (c <= 4.8e-216)
		tmp = Float64(y * Float64(z * x));
	elseif (c <= 1.3e-205)
		tmp = t_1;
	elseif (c <= 1.15e-112)
		tmp = Float64(i * Float64(b * t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * a) * -t;
	t_2 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -2.2e-64)
		tmp = t_2;
	elseif (c <= -7.8e-299)
		tmp = t_1;
	elseif (c <= 4.8e-216)
		tmp = y * (z * x);
	elseif (c <= 1.3e-205)
		tmp = t_1;
	elseif (c <= 1.15e-112)
		tmp = i * (b * t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e-64], t$95$2, If[LessEqual[c, -7.8e-299], t$95$1, If[LessEqual[c, 4.8e-216], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-205], t$95$1, If[LessEqual[c, 1.15e-112], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.2e-64 or 1.14999999999999995e-112 < c

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 57.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 57.9%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 57.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -2.2e-64 < c < -7.7999999999999997e-299 or 4.80000000000000007e-216 < c < 1.2999999999999999e-205

   1. Initial program 83.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 63.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 63.1%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 63.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 63.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 63.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 63.1%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 63.1%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 63.1%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 63.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   7. Taylor expanded in i around 0 50.6%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 50.6%

         \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. distribute-lft-neg-out 50.6%

         \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot x\right)} \]

      3. *-commutative 50.6%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   9. Simplified 50.6%

      \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   if -7.7999999999999997e-299 < c < 4.80000000000000007e-216

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 40.4%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 45.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 1.2999999999999999e-205 < c < 1.14999999999999995e-112

   1. Initial program 95.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 95.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 95.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 95.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 95.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 95.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 65.9%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 56.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-299}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-205}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]

Alternative 17: 30.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot x\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-245}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 0.78:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* z x))) (t_2 (* c (* a j))))
   (if (<= j -3.8e-104)
     t_2
     (if (<= j -7.5e-228)
       t_1
       (if (<= j 1.45e-245)
         (* i (* b t))
         (if (<= j 8e-198)
           (* a (* t (- x)))
           (if (<= j 9e-115) (* t (* b i)) (if (<= j 0.78) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (z * x);
	double t_2 = c * (a * j);
	double tmp;
	if (j <= -3.8e-104) {
		tmp = t_2;
	} else if (j <= -7.5e-228) {
		tmp = t_1;
	} else if (j <= 1.45e-245) {
		tmp = i * (b * t);
	} else if (j <= 8e-198) {
		tmp = a * (t * -x);
	} else if (j <= 9e-115) {
		tmp = t * (b * i);
	} else if (j <= 0.78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z * x)
    t_2 = c * (a * j)
    if (j <= (-3.8d-104)) then
        tmp = t_2
    else if (j <= (-7.5d-228)) then
        tmp = t_1
    else if (j <= 1.45d-245) then
        tmp = i * (b * t)
    else if (j <= 8d-198) then
        tmp = a * (t * -x)
    else if (j <= 9d-115) then
        tmp = t * (b * i)
    else if (j <= 0.78d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (z * x);
	double t_2 = c * (a * j);
	double tmp;
	if (j <= -3.8e-104) {
		tmp = t_2;
	} else if (j <= -7.5e-228) {
		tmp = t_1;
	} else if (j <= 1.45e-245) {
		tmp = i * (b * t);
	} else if (j <= 8e-198) {
		tmp = a * (t * -x);
	} else if (j <= 9e-115) {
		tmp = t * (b * i);
	} else if (j <= 0.78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (z * x)
	t_2 = c * (a * j)
	tmp = 0
	if j <= -3.8e-104:
		tmp = t_2
	elif j <= -7.5e-228:
		tmp = t_1
	elif j <= 1.45e-245:
		tmp = i * (b * t)
	elif j <= 8e-198:
		tmp = a * (t * -x)
	elif j <= 9e-115:
		tmp = t * (b * i)
	elif j <= 0.78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(z * x))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (j <= -3.8e-104)
		tmp = t_2;
	elseif (j <= -7.5e-228)
		tmp = t_1;
	elseif (j <= 1.45e-245)
		tmp = Float64(i * Float64(b * t));
	elseif (j <= 8e-198)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (j <= 9e-115)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 0.78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (z * x);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (j <= -3.8e-104)
		tmp = t_2;
	elseif (j <= -7.5e-228)
		tmp = t_1;
	elseif (j <= 1.45e-245)
		tmp = i * (b * t);
	elseif (j <= 8e-198)
		tmp = a * (t * -x);
	elseif (j <= 9e-115)
		tmp = t * (b * i);
	elseif (j <= 0.78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e-104], t$95$2, If[LessEqual[j, -7.5e-228], t$95$1, If[LessEqual[j, 1.45e-245], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e-198], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e-115], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.78], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.8000000000000001e-104 or 0.78000000000000003 < j

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -3.8000000000000001e-104 < j < -7.4999999999999999e-228 or 9.00000000000000046e-115 < j < 0.78000000000000003

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 54.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 40.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -7.4999999999999999e-228 < j < 1.45e-245

   1. Initial program 89.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 89.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 89.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 89.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 89.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 89.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 63.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 37.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 1.45e-245 < j < 7.9999999999999993e-198

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 77.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 77.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 77.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 77.0%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in a around inf 40.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   7. Step-by-step derivation

      1. +-commutative 40.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 40.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 40.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   9. Taylor expanded in c around 0 40.0%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 40.0%

          \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

       2. distribute-lft-neg-in 40.0%

          \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

       3. *-commutative 40.0%

          \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   11. Simplified 40.0%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 7.9999999999999993e-198 < j < 9.00000000000000046e-115

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 56.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 56.8%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 56.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 56.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 56.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 56.8%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 56.8%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 56.8%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 56.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   7. Taylor expanded in i around inf 39.8%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-245}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 0.78:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 18: 50.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(b \cdot t - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.96 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-298}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* b t) (* y j)))) (t_2 (* c (- (* a j) (* b z)))))
   (if (<= c -7.5e+22)
     t_2
     (if (<= c -1.96e-163)
       t_1
       (if (<= c -4e-298)
         (* (* x a) (- t))
         (if (<= c 1000000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((b * t) - (y * j));
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -7.5e+22) {
		tmp = t_2;
	} else if (c <= -1.96e-163) {
		tmp = t_1;
	} else if (c <= -4e-298) {
		tmp = (x * a) * -t;
	} else if (c <= 1000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((b * t) - (y * j))
    t_2 = c * ((a * j) - (b * z))
    if (c <= (-7.5d+22)) then
        tmp = t_2
    else if (c <= (-1.96d-163)) then
        tmp = t_1
    else if (c <= (-4d-298)) then
        tmp = (x * a) * -t
    else if (c <= 1000000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((b * t) - (y * j));
	double t_2 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -7.5e+22) {
		tmp = t_2;
	} else if (c <= -1.96e-163) {
		tmp = t_1;
	} else if (c <= -4e-298) {
		tmp = (x * a) * -t;
	} else if (c <= 1000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((b * t) - (y * j))
	t_2 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -7.5e+22:
		tmp = t_2
	elif c <= -1.96e-163:
		tmp = t_1
	elif c <= -4e-298:
		tmp = (x * a) * -t
	elif c <= 1000000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(b * t) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -7.5e+22)
		tmp = t_2;
	elseif (c <= -1.96e-163)
		tmp = t_1;
	elseif (c <= -4e-298)
		tmp = Float64(Float64(x * a) * Float64(-t));
	elseif (c <= 1000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((b * t) - (y * j));
	t_2 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -7.5e+22)
		tmp = t_2;
	elseif (c <= -1.96e-163)
		tmp = t_1;
	elseif (c <= -4e-298)
		tmp = (x * a) * -t;
	elseif (c <= 1000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e+22], t$95$2, If[LessEqual[c, -1.96e-163], t$95$1, If[LessEqual[c, -4e-298], N[(N[(x * a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[c, 1000000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.5000000000000002e22 or 1e12 < c

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 67.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 67.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -7.5000000000000002e22 < c < -1.9599999999999999e-163 or -3.99999999999999965e-298 < c < 1e12

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 73.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 73.7%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 73.7%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 73.7%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in i around inf 51.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 52.8%

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(y \cdot j\right)\right)} \]

      2. neg-mul-1 52.8%

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{-y \cdot j}\right) \]

      3. fma-neg 51.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   8. Simplified 51.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -1.9599999999999999e-163 < c < -3.99999999999999965e-298

   1. Initial program 90.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 90.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 90.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 90.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 90.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 90.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 62.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 62.6%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 62.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 62.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 62.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 62.6%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 62.6%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 62.6%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 62.6%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   7. Taylor expanded in i around 0 57.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 57.9%

         \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. distribute-lft-neg-out 57.9%

         \[\leadsto t \cdot \color{blue}{\left(\left(-a\right) \cdot x\right)} \]

      3. *-commutative 57.9%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   9. Simplified 57.9%

      \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -1.96 \cdot 10^{-163}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-298}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;c \leq 1000000000000:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]

Alternative 19: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-268}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.5e+105)
   (* c (* b (- z)))
   (if (<= b -4.4e-147)
     (* a (* c j))
     (if (<= b -2.1e-268)
       (* z (* x y))
       (if (<= b 1.15e-278)
         (* c (* a j))
         (if (<= b 3.8e-27) (* y (* z x)) (* i (* b t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.5e+105) {
		tmp = c * (b * -z);
	} else if (b <= -4.4e-147) {
		tmp = a * (c * j);
	} else if (b <= -2.1e-268) {
		tmp = z * (x * y);
	} else if (b <= 1.15e-278) {
		tmp = c * (a * j);
	} else if (b <= 3.8e-27) {
		tmp = y * (z * x);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-4.5d+105)) then
        tmp = c * (b * -z)
    else if (b <= (-4.4d-147)) then
        tmp = a * (c * j)
    else if (b <= (-2.1d-268)) then
        tmp = z * (x * y)
    else if (b <= 1.15d-278) then
        tmp = c * (a * j)
    else if (b <= 3.8d-27) then
        tmp = y * (z * x)
    else
        tmp = i * (b * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.5e+105) {
		tmp = c * (b * -z);
	} else if (b <= -4.4e-147) {
		tmp = a * (c * j);
	} else if (b <= -2.1e-268) {
		tmp = z * (x * y);
	} else if (b <= 1.15e-278) {
		tmp = c * (a * j);
	} else if (b <= 3.8e-27) {
		tmp = y * (z * x);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.5e+105:
		tmp = c * (b * -z)
	elif b <= -4.4e-147:
		tmp = a * (c * j)
	elif b <= -2.1e-268:
		tmp = z * (x * y)
	elif b <= 1.15e-278:
		tmp = c * (a * j)
	elif b <= 3.8e-27:
		tmp = y * (z * x)
	else:
		tmp = i * (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.5e+105)
		tmp = Float64(c * Float64(b * Float64(-z)));
	elseif (b <= -4.4e-147)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= -2.1e-268)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.15e-278)
		tmp = Float64(c * Float64(a * j));
	elseif (b <= 3.8e-27)
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(i * Float64(b * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.5e+105)
		tmp = c * (b * -z);
	elseif (b <= -4.4e-147)
		tmp = a * (c * j);
	elseif (b <= -2.1e-268)
		tmp = z * (x * y);
	elseif (b <= 1.15e-278)
		tmp = c * (a * j);
	elseif (b <= 3.8e-27)
		tmp = y * (z * x);
	else
		tmp = i * (b * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.5e+105], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.4e-147], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-268], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-278], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-27], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.5000000000000001e105

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 56.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.5%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 56.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around 0 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 48.6%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. distribute-rgt-neg-in 48.6%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} \]

      3. distribute-rgt-neg-in 48.6%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   9. Simplified 48.6%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]

   if -4.5000000000000001e105 < b < -4.4000000000000002e-147

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 74.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 74.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 74.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 74.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 74.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 74.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 74.0%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 74.0%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in a around inf 51.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   7. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   9. Taylor expanded in c around inf 37.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   10. Step-by-step derivation

       1. *-commutative 37.4%

          \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   11. Simplified 37.4%

       \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -4.4000000000000002e-147 < b < -2.09999999999999998e-268

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 75.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 40.7%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 40.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -2.09999999999999998e-268 < b < 1.15000000000000001e-278

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 66.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 53.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 53.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around inf 50.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 1.15000000000000001e-278 < b < 3.8e-27

   1. Initial program 65.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 65.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 65.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 65.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 47.1%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 31.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 3.8e-27 < b

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 39.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-268}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]

Alternative 20: 52.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 340000000000:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* b z)))))
   (if (<= c -9.5e-64)
     t_1
     (if (<= c -6.8e-298)
       (* t (- (* b i) (* x a)))
       (if (<= c 340000000000.0) (* i (- (* b t) (* y j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -9.5e-64) {
		tmp = t_1;
	} else if (c <= -6.8e-298) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 340000000000.0) {
		tmp = i * ((b * t) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (b * z))
    if (c <= (-9.5d-64)) then
        tmp = t_1
    else if (c <= (-6.8d-298)) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 340000000000.0d0) then
        tmp = i * ((b * t) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -9.5e-64) {
		tmp = t_1;
	} else if (c <= -6.8e-298) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 340000000000.0) {
		tmp = i * ((b * t) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -9.5e-64:
		tmp = t_1
	elif c <= -6.8e-298:
		tmp = t * ((b * i) - (x * a))
	elif c <= 340000000000.0:
		tmp = i * ((b * t) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -9.5e-64)
		tmp = t_1;
	elseif (c <= -6.8e-298)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 340000000000.0)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -9.5e-64)
		tmp = t_1;
	elseif (c <= -6.8e-298)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 340000000000.0)
		tmp = i * ((b * t) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e-64], t$95$1, If[LessEqual[c, -6.8e-298], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 340000000000.0], N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.50000000000000043e-64 or 3.4e11 < c

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 62.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 63.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 63.0%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 63.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   if -9.50000000000000043e-64 < c < -6.8e-298

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 83.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 61.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 61.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 61.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 61.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 61.4%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 61.4%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 61.4%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   if -6.8e-298 < c < 3.4e11

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 80.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 80.1%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. *-commutative 80.1%

         \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 80.1%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Taylor expanded in i around inf 53.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 53.3%

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(y \cdot j\right)\right)} \]

      2. neg-mul-1 53.3%

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{-y \cdot j}\right) \]

      3. fma-neg 53.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   8. Simplified 53.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 340000000000:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]

Alternative 21: 30.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot x\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 70000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* z x))) (t_2 (* c (* a j))))
   (if (<= j -3.8e-104)
     t_2
     (if (<= j -3.9e-230)
       t_1
       (if (<= j 9e-115) (* t (* b i)) (if (<= j 70000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (z * x);
	double t_2 = c * (a * j);
	double tmp;
	if (j <= -3.8e-104) {
		tmp = t_2;
	} else if (j <= -3.9e-230) {
		tmp = t_1;
	} else if (j <= 9e-115) {
		tmp = t * (b * i);
	} else if (j <= 70000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z * x)
    t_2 = c * (a * j)
    if (j <= (-3.8d-104)) then
        tmp = t_2
    else if (j <= (-3.9d-230)) then
        tmp = t_1
    else if (j <= 9d-115) then
        tmp = t * (b * i)
    else if (j <= 70000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (z * x);
	double t_2 = c * (a * j);
	double tmp;
	if (j <= -3.8e-104) {
		tmp = t_2;
	} else if (j <= -3.9e-230) {
		tmp = t_1;
	} else if (j <= 9e-115) {
		tmp = t * (b * i);
	} else if (j <= 70000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (z * x)
	t_2 = c * (a * j)
	tmp = 0
	if j <= -3.8e-104:
		tmp = t_2
	elif j <= -3.9e-230:
		tmp = t_1
	elif j <= 9e-115:
		tmp = t * (b * i)
	elif j <= 70000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(z * x))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (j <= -3.8e-104)
		tmp = t_2;
	elseif (j <= -3.9e-230)
		tmp = t_1;
	elseif (j <= 9e-115)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 70000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (z * x);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (j <= -3.8e-104)
		tmp = t_2;
	elseif (j <= -3.9e-230)
		tmp = t_1;
	elseif (j <= 9e-115)
		tmp = t * (b * i);
	elseif (j <= 70000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e-104], t$95$2, If[LessEqual[j, -3.9e-230], t$95$1, If[LessEqual[j, 9e-115], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 70000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.8000000000000001e-104 or 7e4 < j

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -3.8000000000000001e-104 < j < -3.9000000000000002e-230 or 9.00000000000000046e-115 < j < 7e4

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 54.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 40.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.9000000000000002e-230 < j < 9.00000000000000046e-115

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 48.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      2. associate-*r* 48.7%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      3. neg-mul-1 48.7%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      4. cancel-sign-sub 48.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + i \cdot b\right)} \]

      5. +-commutative 48.7%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

      6. mul-1-neg 48.7%

         \[\leadsto t \cdot \left(i \cdot b + \color{blue}{\left(-a \cdot x\right)}\right) \]

      7. unsub-neg 48.7%

         \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   6. Simplified 48.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   7. Taylor expanded in i around inf 30.0%

      \[\leadsto t \cdot \color{blue}{\left(i \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 70000:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 22: 29.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-119} \lor \neg \left(j \leq 0.62\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.9e-119) (not (<= j 0.62))) (* c (* a j)) (* i (* b t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.9e-119) || !(j <= 0.62)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.9d-119)) .or. (.not. (j <= 0.62d0))) then
        tmp = c * (a * j)
    else
        tmp = i * (b * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.9e-119) || !(j <= 0.62)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.9e-119) or not (j <= 0.62):
		tmp = c * (a * j)
	else:
		tmp = i * (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.9e-119) || !(j <= 0.62))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(b * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.9e-119) || ~((j <= 0.62)))
		tmp = c * (a * j);
	else
		tmp = i * (b * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.9e-119], N[Not[LessEqual[j, 0.62]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.89999999999999987e-119 or 0.619999999999999996 < j

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 64.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 64.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 64.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 64.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 50.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 50.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around inf 37.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -1.89999999999999987e-119 < j < 0.619999999999999996

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 49.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 25.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-119} \lor \neg \left(j \leq 0.62\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]

Alternative 23: 23.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 70.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   2. cancel-sign-sub-inv 70.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   3. *-commutative 70.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

   4. remove-double-neg 70.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

   5. *-commutative 70.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

3. Simplified 70.6%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]
4. Step-by-step derivation

   1. add-cube-cbrt 70.1%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   2. *-commutative 70.1%

      \[\leadsto \left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   3. *-commutative 70.1%

      \[\leadsto \left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

5. Applied egg-rr 70.1%

   \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}\right) \cdot \sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)}} + j \cdot \left(a \cdot c - y \cdot i\right) \]

6. Taylor expanded in a around inf 39.8%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
7. Step-by-step derivation

   1. +-commutative 39.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 39.8%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 39.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

8. Simplified 39.8%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

9. Taylor expanded in c around inf 24.7%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
10. Step-by-step derivation

    1. *-commutative 24.7%

       \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

11. Simplified 24.7%

    \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

12. Final simplification 24.7%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Alternative 24: 23.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(a \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* c (* a j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = c * (a * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return c * (a * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(c * Float64(a * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = c * (a * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 70.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   2. cancel-sign-sub-inv 70.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   3. *-commutative 70.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

   4. remove-double-neg 70.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

   5. *-commutative 70.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

3. Simplified 70.6%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

4. Taylor expanded in c around inf 43.5%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
5. Step-by-step derivation

   1. *-commutative 43.5%

      \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

6. Simplified 43.5%

   \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

7. Taylor expanded in j around inf 25.2%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

8. Final simplification 25.2%

   \[\leadsto c \cdot \left(a \cdot j\right) \]

Developer target: 59.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))