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

Percentage Accurate: 73.5% → 82.1%

Time: 29.8s

Alternatives: 27

Speedup: 0.5×

• 58.5% 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: 73.5% 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: 82.1% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t i) (* z c))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= (+ t_2 (- (* b t_1) (* x (- (* t a) (* y z))))) INFINITY)
     (fma b t_1 (fma x (- (* y z) (* t a)) t_2))
     (* t (- (* b i) (* x 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 = (t * i) - (z * c);
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if ((t_2 + ((b * t_1) - (x * ((t * a) - (y * z))))) <= ((double) INFINITY)) {
		tmp = fma(b, t_1, fma(x, ((y * z) - (t * a)), t_2));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Julia

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

Wolfram

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

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 89.9%

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

      1. sub-neg 89.9%

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

      2. +-commutative 89.9%

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

      3. associate-+l+ 89.9%

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

      4. distribute-rgt-neg-in 89.9%

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

      5. +-commutative 89.9%

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

      6. fma-def 89.9%

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

      7. sub-neg 89.9%

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

      8. +-commutative 89.9%

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

      9. distribute-neg-in 89.9%

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

      10. unsub-neg 89.9%

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

      11. remove-double-neg 89.9%

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

      12. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   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. Step-by-step derivation

      1. add-cube-cbrt 0.0%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in t around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-*r* 56.3%

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

      5. neg-mul-1 56.3%

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

      6. cancel-sign-sub 56.3%

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

      7. *-commutative 56.3%

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

      8. +-commutative 56.3%

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

      9. unsub-neg 56.3%

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

      10. *-commutative 56.3%

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

      11. *-commutative 56.3%

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

   8. Simplified 56.3%

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

4. Final simplification 82.8%

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

Alternative 2: 82.1% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z)))))
        (t_2 (- (* a c) (* y i))))
   (if (<= (+ (* j t_2) t_1) INFINITY)
     (fma j t_2 t_1)
     (* t (- (* b i) (* x 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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if (((j * t_2) + t_1) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Julia

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

Wolfram

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

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 89.9%

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

      1. +-commutative 89.9%

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

      2. fma-def 89.9%

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

      3. *-commutative 89.9%

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

      4. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   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. Step-by-step derivation

      1. add-cube-cbrt 0.0%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in t around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-*r* 56.3%

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

      5. neg-mul-1 56.3%

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

      6. cancel-sign-sub 56.3%

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

      7. *-commutative 56.3%

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

      8. +-commutative 56.3%

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

      9. unsub-neg 56.3%

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

      10. *-commutative 56.3%

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

      11. *-commutative 56.3%

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

   8. Simplified 56.3%

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

4. Final simplification 82.8%

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

Alternative 3: 82.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* j (- (* a c) (* y i)))
          (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z)))))))
   (if (<= t_1 INFINITY) t_1 (* t (- (* b i) (* x 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 = (j * ((a * c) - (y * i))) + ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	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 * ((a * c) - (y * i))) + ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 89.9%

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

   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. Step-by-step derivation

      1. add-cube-cbrt 0.0%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in t around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-*r* 56.3%

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

      5. neg-mul-1 56.3%

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

      6. cancel-sign-sub 56.3%

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

      7. *-commutative 56.3%

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

      8. +-commutative 56.3%

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

      9. unsub-neg 56.3%

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

      10. *-commutative 56.3%

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

      11. *-commutative 56.3%

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

   8. Simplified 56.3%

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

4. Final simplification 82.8%

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

Alternative 4: 68.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - t_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -0.046:\\ \;\;\;\;t_3 - \left(z \cdot \left(b \cdot c\right) + t_1\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-101}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* t a) (* y z))))
        (t_2 (- (* b (- (* t i) (* z c))) t_1))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -0.046)
     (- t_3 (+ (* z (* b c)) t_1))
     (if (<= j -1.25e-176)
       t_2
       (if (<= j 5.6e-101)
         (+ (- (* z (- (* x y) (* b c))) (* a (* x t))) (* i (* t b)))
         (if (<= j 2.45e+17)
           t_2
           (if (<= j 1.06e+144)
             (- (* t (* b i)) (* j (- (* y i) (* a c))))
             (if (<= j 8.5e+171) t_2 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 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -0.046) {
		tmp = t_3 - ((z * (b * c)) + t_1);
	} else if (j <= -1.25e-176) {
		tmp = t_2;
	} else if (j <= 5.6e-101) {
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (i * (t * b));
	} else if (j <= 2.45e+17) {
		tmp = t_2;
	} else if (j <= 1.06e+144) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 8.5e+171) {
		tmp = t_2;
	} 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 = x * ((t * a) - (y * z))
    t_2 = (b * ((t * i) - (z * c))) - t_1
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-0.046d0)) then
        tmp = t_3 - ((z * (b * c)) + t_1)
    else if (j <= (-1.25d-176)) then
        tmp = t_2
    else if (j <= 5.6d-101) then
        tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (i * (t * b))
    else if (j <= 2.45d+17) then
        tmp = t_2
    else if (j <= 1.06d+144) then
        tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
    else if (j <= 8.5d+171) then
        tmp = t_2
    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 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -0.046) {
		tmp = t_3 - ((z * (b * c)) + t_1);
	} else if (j <= -1.25e-176) {
		tmp = t_2;
	} else if (j <= 5.6e-101) {
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (i * (t * b));
	} else if (j <= 2.45e+17) {
		tmp = t_2;
	} else if (j <= 1.06e+144) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 8.5e+171) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((t * a) - (y * z))
	t_2 = (b * ((t * i) - (z * c))) - t_1
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -0.046:
		tmp = t_3 - ((z * (b * c)) + t_1)
	elif j <= -1.25e-176:
		tmp = t_2
	elif j <= 5.6e-101:
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (i * (t * b))
	elif j <= 2.45e+17:
		tmp = t_2
	elif j <= 1.06e+144:
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
	elif j <= 8.5e+171:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_2 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -0.046)
		tmp = Float64(t_3 - Float64(Float64(z * Float64(b * c)) + t_1));
	elseif (j <= -1.25e-176)
		tmp = t_2;
	elseif (j <= 5.6e-101)
		tmp = Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(x * t))) + Float64(i * Float64(t * b)));
	elseif (j <= 2.45e+17)
		tmp = t_2;
	elseif (j <= 1.06e+144)
		tmp = Float64(Float64(t * Float64(b * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (j <= 8.5e+171)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((t * a) - (y * z));
	t_2 = (b * ((t * i) - (z * c))) - t_1;
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -0.046)
		tmp = t_3 - ((z * (b * c)) + t_1);
	elseif (j <= -1.25e-176)
		tmp = t_2;
	elseif (j <= 5.6e-101)
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (i * (t * b));
	elseif (j <= 2.45e+17)
		tmp = t_2;
	elseif (j <= 1.06e+144)
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	elseif (j <= 8.5e+171)
		tmp = t_2;
	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[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -0.046], N[(t$95$3 - N[(N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.25e-176], t$95$2, If[LessEqual[j, 5.6e-101], N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.45e+17], t$95$2, If[LessEqual[j, 1.06e+144], N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+171], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -0.045999999999999999

   1. Initial program 71.2%

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

      1. cancel-sign-sub 71.2%

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

      2. cancel-sign-sub-inv 71.2%

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

      3. *-commutative 71.2%

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

      4. remove-double-neg 71.2%

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

      5. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in z around inf 70.2%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*l* 68.3%

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

   6. Simplified 68.3%

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

   if -0.045999999999999999 < j < -1.25e-176 or 5.59999999999999978e-101 < j < 2.45e17 or 1.06e144 < j < 8.4999999999999995e171

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

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

      2. fma-def 77.3%

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

      3. *-commutative 77.3%

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

      4. *-commutative 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in j around 0 75.8%

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

   if -1.25e-176 < j < 5.59999999999999978e-101

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. fma-def 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in j around 0 78.0%

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

   5. Taylor expanded in z around 0 85.3%

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

   if 2.45e17 < j < 1.06e144

   1. Initial program 50.7%

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

      1. cancel-sign-sub 50.7%

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

      2. cancel-sign-sub-inv 50.7%

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

      3. *-commutative 50.7%

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

      4. remove-double-neg 50.7%

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

      5. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in i around inf 62.5%

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

      1. associate-*r* 57.4%

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

      2. *-commutative 57.4%

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

      3. associate-*r* 66.6%

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

   6. Simplified 66.6%

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

   if 8.4999999999999995e171 < j

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. fma-def 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in j around inf 79.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.046:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-101}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+171}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 68.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;j \leq -9.2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (* b i)) (* j (- (* y i) (* a c)))))
        (t_2 (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z))))))
   (if (<= j -9.2e+68)
     t_1
     (if (<= j 2.6e+18)
       t_2
       (if (<= j 3.2e+143)
         t_1
         (if (<= j 8.6e+170) t_2 (* j (- (* a c) (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (b * i)) - (j * ((y * i) - (a * c)));
	double t_2 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -9.2e+68) {
		tmp = t_1;
	} else if (j <= 2.6e+18) {
		tmp = t_2;
	} else if (j <= 3.2e+143) {
		tmp = t_1;
	} else if (j <= 8.6e+170) {
		tmp = t_2;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	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 = (t * (b * i)) - (j * ((y * i) - (a * c)))
    t_2 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
    if (j <= (-9.2d+68)) then
        tmp = t_1
    else if (j <= 2.6d+18) then
        tmp = t_2
    else if (j <= 3.2d+143) then
        tmp = t_1
    else if (j <= 8.6d+170) then
        tmp = t_2
    else
        tmp = j * ((a * c) - (y * i))
    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 = (t * (b * i)) - (j * ((y * i) - (a * c)));
	double t_2 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -9.2e+68) {
		tmp = t_1;
	} else if (j <= 2.6e+18) {
		tmp = t_2;
	} else if (j <= 3.2e+143) {
		tmp = t_1;
	} else if (j <= 8.6e+170) {
		tmp = t_2;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (b * i)) - (j * ((y * i) - (a * c)))
	t_2 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
	tmp = 0
	if j <= -9.2e+68:
		tmp = t_1
	elif j <= 2.6e+18:
		tmp = t_2
	elif j <= 3.2e+143:
		tmp = t_1
	elif j <= 8.6e+170:
		tmp = t_2
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(b * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	t_2 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (j <= -9.2e+68)
		tmp = t_1;
	elseif (j <= 2.6e+18)
		tmp = t_2;
	elseif (j <= 3.2e+143)
		tmp = t_1;
	elseif (j <= 8.6e+170)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * (b * i)) - (j * ((y * i) - (a * c)));
	t_2 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (j <= -9.2e+68)
		tmp = t_1;
	elseif (j <= 2.6e+18)
		tmp = t_2;
	elseif (j <= 3.2e+143)
		tmp = t_1;
	elseif (j <= 8.6e+170)
		tmp = t_2;
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.2e+68], t$95$1, If[LessEqual[j, 2.6e+18], t$95$2, If[LessEqual[j, 3.2e+143], t$95$1, If[LessEqual[j, 8.6e+170], t$95$2, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -9.1999999999999999e68 or 2.6e18 < j < 3.20000000000000016e143

   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 64.7%

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

      1. associate-*r* 63.0%

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

      2. *-commutative 63.0%

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

      3. associate-*r* 64.4%

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

   6. Simplified 64.4%

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

   if -9.1999999999999999e68 < j < 2.6e18 or 3.20000000000000016e143 < j < 8.5999999999999997e170

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-def 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in j around 0 75.5%

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

   if 8.5999999999999997e170 < j

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. fma-def 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in j around inf 79.7%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{+170}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 6: 68.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.6 \cdot 10^{+67}:\\ \;\;\;\;\left(t_2 + y \cdot \left(x \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z)))))
        (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.6e+67)
     (- (+ t_2 (* y (* x z))) (* c (* z b)))
     (if (<= j 6.2e+17)
       t_1
       (if (<= j 4.3e+142)
         (- (* t (* b i)) (* j (- (* y i) (* a c))))
         (if (<= j 4.6e+174) 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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.6e+67) {
		tmp = (t_2 + (y * (x * z))) - (c * (z * b));
	} else if (j <= 6.2e+17) {
		tmp = t_1;
	} else if (j <= 4.3e+142) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 4.6e+174) {
		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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-1.6d+67)) then
        tmp = (t_2 + (y * (x * z))) - (c * (z * b))
    else if (j <= 6.2d+17) then
        tmp = t_1
    else if (j <= 4.3d+142) then
        tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
    else if (j <= 4.6d+174) 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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.6e+67) {
		tmp = (t_2 + (y * (x * z))) - (c * (z * b));
	} else if (j <= 6.2e+17) {
		tmp = t_1;
	} else if (j <= 4.3e+142) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 4.6e+174) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.6e+67:
		tmp = (t_2 + (y * (x * z))) - (c * (z * b))
	elif j <= 6.2e+17:
		tmp = t_1
	elif j <= 4.3e+142:
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
	elif j <= 4.6e+174:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.6e+67)
		tmp = Float64(Float64(t_2 + Float64(y * Float64(x * z))) - Float64(c * Float64(z * b)));
	elseif (j <= 6.2e+17)
		tmp = t_1;
	elseif (j <= 4.3e+142)
		tmp = Float64(Float64(t * Float64(b * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (j <= 4.6e+174)
		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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.6e+67)
		tmp = (t_2 + (y * (x * z))) - (c * (z * b));
	elseif (j <= 6.2e+17)
		tmp = t_1;
	elseif (j <= 4.3e+142)
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	elseif (j <= 4.6e+174)
		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[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.6e+67], N[(N[(t$95$2 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e+17], t$95$1, If[LessEqual[j, 4.3e+142], N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.6e+174], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.59999999999999991e67

   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. +-commutative 72.7%

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

      2. fma-def 75.3%

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

      3. *-commutative 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in t around 0 68.7%

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

   if -1.59999999999999991e67 < j < 6.2e17 or 4.30000000000000012e142 < j < 4.5999999999999996e174

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-def 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in j around 0 75.5%

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

   if 6.2e17 < j < 4.30000000000000012e142

   1. Initial program 50.7%

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

      1. cancel-sign-sub 50.7%

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

      2. cancel-sign-sub-inv 50.7%

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

      3. *-commutative 50.7%

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

      4. remove-double-neg 50.7%

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

      5. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in i around inf 62.5%

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

      1. associate-*r* 57.4%

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

      2. *-commutative 57.4%

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

      3. associate-*r* 66.6%

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

   6. Simplified 66.6%

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

   if 4.5999999999999996e174 < j

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. fma-def 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in j around inf 79.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+67}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 7: 69.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - t_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -0.056:\\ \;\;\;\;t_3 - \left(z \cdot \left(b \cdot c\right) + t_1\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* t a) (* y z))))
        (t_2 (- (* b (- (* t i) (* z c))) t_1))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -0.056)
     (- t_3 (+ (* z (* b c)) t_1))
     (if (<= j 3e+18)
       t_2
       (if (<= j 4e+142)
         (- (* t (* b i)) (* j (- (* y i) (* a c))))
         (if (<= j 3e+170) t_2 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 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -0.056) {
		tmp = t_3 - ((z * (b * c)) + t_1);
	} else if (j <= 3e+18) {
		tmp = t_2;
	} else if (j <= 4e+142) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 3e+170) {
		tmp = t_2;
	} 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 = x * ((t * a) - (y * z))
    t_2 = (b * ((t * i) - (z * c))) - t_1
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-0.056d0)) then
        tmp = t_3 - ((z * (b * c)) + t_1)
    else if (j <= 3d+18) then
        tmp = t_2
    else if (j <= 4d+142) then
        tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
    else if (j <= 3d+170) then
        tmp = t_2
    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 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -0.056) {
		tmp = t_3 - ((z * (b * c)) + t_1);
	} else if (j <= 3e+18) {
		tmp = t_2;
	} else if (j <= 4e+142) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 3e+170) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((t * a) - (y * z))
	t_2 = (b * ((t * i) - (z * c))) - t_1
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -0.056:
		tmp = t_3 - ((z * (b * c)) + t_1)
	elif j <= 3e+18:
		tmp = t_2
	elif j <= 4e+142:
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
	elif j <= 3e+170:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_2 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -0.056)
		tmp = Float64(t_3 - Float64(Float64(z * Float64(b * c)) + t_1));
	elseif (j <= 3e+18)
		tmp = t_2;
	elseif (j <= 4e+142)
		tmp = Float64(Float64(t * Float64(b * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (j <= 3e+170)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((t * a) - (y * z));
	t_2 = (b * ((t * i) - (z * c))) - t_1;
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -0.056)
		tmp = t_3 - ((z * (b * c)) + t_1);
	elseif (j <= 3e+18)
		tmp = t_2;
	elseif (j <= 4e+142)
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	elseif (j <= 3e+170)
		tmp = t_2;
	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[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -0.056], N[(t$95$3 - N[(N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e+18], t$95$2, If[LessEqual[j, 4e+142], N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e+170], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -0.0560000000000000012

   1. Initial program 71.2%

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

      1. cancel-sign-sub 71.2%

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

      2. cancel-sign-sub-inv 71.2%

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

      3. *-commutative 71.2%

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

      4. remove-double-neg 71.2%

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

      5. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in z around inf 70.2%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*l* 68.3%

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

   6. Simplified 68.3%

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

   if -0.0560000000000000012 < j < 3e18 or 4.0000000000000002e142 < j < 2.99999999999999997e170

   1. Initial program 73.5%

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

      1. +-commutative 73.5%

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

      2. fma-def 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in j around 0 77.0%

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

   if 3e18 < j < 4.0000000000000002e142

   1. Initial program 50.7%

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

      1. cancel-sign-sub 50.7%

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

      2. cancel-sign-sub-inv 50.7%

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

      3. *-commutative 50.7%

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

      4. remove-double-neg 50.7%

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

      5. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in i around inf 62.5%

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

      1. associate-*r* 57.4%

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

      2. *-commutative 57.4%

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

      3. associate-*r* 66.6%

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

   6. Simplified 66.6%

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

   if 2.99999999999999997e170 < j

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. fma-def 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in j around inf 79.7%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.056:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+170}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 8: 40.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.3 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-278}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -6.3e+25)
     t_2
     (if (<= a -2e-17)
       t_1
       (if (<= a -1.05e-37)
         t_2
         (if (<= a -1.25e-192)
           (* x (* y z))
           (if (<= a -4.2e-271)
             (* i (* y (- j)))
             (if (<= a 8.2e-278)
               (* t (* b i))
               (if (<= a 5.5e-100)
                 (* z (* x y))
                 (if (<= a 1.85e+117) 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 = b * (t * i);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.3e+25) {
		tmp = t_2;
	} else if (a <= -2e-17) {
		tmp = t_1;
	} else if (a <= -1.05e-37) {
		tmp = t_2;
	} else if (a <= -1.25e-192) {
		tmp = x * (y * z);
	} else if (a <= -4.2e-271) {
		tmp = i * (y * -j);
	} else if (a <= 8.2e-278) {
		tmp = t * (b * i);
	} else if (a <= 5.5e-100) {
		tmp = z * (x * y);
	} else if (a <= 1.85e+117) {
		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 = b * (t * i)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-6.3d+25)) then
        tmp = t_2
    else if (a <= (-2d-17)) then
        tmp = t_1
    else if (a <= (-1.05d-37)) then
        tmp = t_2
    else if (a <= (-1.25d-192)) then
        tmp = x * (y * z)
    else if (a <= (-4.2d-271)) then
        tmp = i * (y * -j)
    else if (a <= 8.2d-278) then
        tmp = t * (b * i)
    else if (a <= 5.5d-100) then
        tmp = z * (x * y)
    else if (a <= 1.85d+117) 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 = b * (t * i);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.3e+25) {
		tmp = t_2;
	} else if (a <= -2e-17) {
		tmp = t_1;
	} else if (a <= -1.05e-37) {
		tmp = t_2;
	} else if (a <= -1.25e-192) {
		tmp = x * (y * z);
	} else if (a <= -4.2e-271) {
		tmp = i * (y * -j);
	} else if (a <= 8.2e-278) {
		tmp = t * (b * i);
	} else if (a <= 5.5e-100) {
		tmp = z * (x * y);
	} else if (a <= 1.85e+117) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -6.3e+25:
		tmp = t_2
	elif a <= -2e-17:
		tmp = t_1
	elif a <= -1.05e-37:
		tmp = t_2
	elif a <= -1.25e-192:
		tmp = x * (y * z)
	elif a <= -4.2e-271:
		tmp = i * (y * -j)
	elif a <= 8.2e-278:
		tmp = t * (b * i)
	elif a <= 5.5e-100:
		tmp = z * (x * y)
	elif a <= 1.85e+117:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.3e+25)
		tmp = t_2;
	elseif (a <= -2e-17)
		tmp = t_1;
	elseif (a <= -1.05e-37)
		tmp = t_2;
	elseif (a <= -1.25e-192)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -4.2e-271)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 8.2e-278)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 5.5e-100)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.85e+117)
		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 = b * (t * i);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -6.3e+25)
		tmp = t_2;
	elseif (a <= -2e-17)
		tmp = t_1;
	elseif (a <= -1.05e-37)
		tmp = t_2;
	elseif (a <= -1.25e-192)
		tmp = x * (y * z);
	elseif (a <= -4.2e-271)
		tmp = i * (y * -j);
	elseif (a <= 8.2e-278)
		tmp = t * (b * i);
	elseif (a <= 5.5e-100)
		tmp = z * (x * y);
	elseif (a <= 1.85e+117)
		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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.3e+25], t$95$2, If[LessEqual[a, -2e-17], t$95$1, If[LessEqual[a, -1.05e-37], t$95$2, If[LessEqual[a, -1.25e-192], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-271], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-278], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-100], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+117], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.29999999999999973e25 or -2.00000000000000014e-17 < a < -1.05e-37 or 1.8499999999999999e117 < a

   1. Initial program 60.2%

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

      1. +-commutative 60.2%

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

      2. fma-def 63.3%

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

      3. *-commutative 63.3%

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

      4. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in a around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. unsub-neg 65.7%

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

   6. Simplified 65.7%

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

   if -6.29999999999999973e25 < a < -2.00000000000000014e-17 or 5.50000000000000011e-100 < a < 1.8499999999999999e117

   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. +-commutative 75.7%

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

      2. fma-def 79.1%

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

      3. *-commutative 79.1%

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

      4. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in j around 0 65.8%

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

   5. Taylor expanded in i around inf 35.9%

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

      1. *-commutative 35.9%

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

      2. *-commutative 35.9%

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

      3. associate-*l* 39.8%

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

   7. Simplified 39.8%

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

   if -1.05e-37 < a < -1.25e-192

   1. Initial program 68.9%

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

      1. sub-neg 68.9%

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

      2. +-commutative 68.9%

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

      3. associate-+l+ 68.9%

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

      4. distribute-rgt-neg-in 68.9%

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

      5. +-commutative 68.9%

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

      6. fma-def 69.1%

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

      7. sub-neg 69.1%

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

      8. +-commutative 69.1%

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

      9. distribute-neg-in 69.1%

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

      10. unsub-neg 69.1%

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

      11. remove-double-neg 69.1%

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

      12. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in i around 0 75.6%

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

   5. Taylor expanded in y around inf 37.4%

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

      1. associate-*r* 44.5%

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

   7. Simplified 44.5%

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

   if -1.25e-192 < a < -4.2000000000000001e-271

   1. Initial program 83.6%

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

      1. +-commutative 83.6%

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

      2. fma-def 83.6%

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

      3. *-commutative 83.6%

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

      4. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in j around inf 54.8%

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

   5. Taylor expanded in c around 0 49.9%

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

      1. neg-mul-1 49.9%

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

      2. associate-*r* 46.2%

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

      3. *-commutative 46.2%

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

      4. associate-*r* 50.3%

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

      5. distribute-rgt-neg-in 50.3%

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

      6. *-commutative 50.3%

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

      7. distribute-rgt-neg-in 50.3%

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

   7. Simplified 50.3%

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

   if -4.2000000000000001e-271 < a < 8.20000000000000002e-278

   1. Initial program 69.7%

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

      1. sub-neg 69.7%

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

      2. +-commutative 69.7%

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

      3. associate-+l+ 69.7%

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

      4. distribute-rgt-neg-in 69.7%

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

      5. +-commutative 69.7%

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

      6. fma-def 69.7%

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

      7. sub-neg 69.7%

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

      8. +-commutative 69.7%

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

      9. distribute-neg-in 69.7%

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

      10. unsub-neg 69.7%

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

      11. remove-double-neg 69.7%

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

      12. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in t around inf 62.6%

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

   5. Taylor expanded in i around inf 62.5%

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

   if 8.20000000000000002e-278 < a < 5.50000000000000011e-100

   1. Initial program 86.1%

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

      1. sub-neg 86.1%

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

      2. +-commutative 86.1%

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

      3. associate-+l+ 86.1%

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

      4. distribute-rgt-neg-in 86.1%

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

      5. +-commutative 86.1%

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

      6. fma-def 86.1%

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

      7. sub-neg 86.1%

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

      8. +-commutative 86.1%

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

      9. distribute-neg-in 86.1%

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

      10. unsub-neg 86.1%

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

      11. remove-double-neg 86.1%

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

      12. *-commutative 86.1%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in i around 0 75.5%

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

   5. Taylor expanded in y around inf 40.6%

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

      1. *-commutative 40.6%

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

      2. associate-*l* 43.1%

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

      3. *-commutative 43.1%

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

   7. Simplified 43.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-278}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 9: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* i (* y j))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -5.2e+70)
     t_2
     (if (<= x -6.6e-174)
       t_1
       (if (<= x -5.8e-296)
         (* i (- (* t b) (* y j)))
         (if (<= x 4.1e+15) 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 = (b * ((t * i) - (z * c))) - (i * (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.2e+70) {
		tmp = t_2;
	} else if (x <= -6.6e-174) {
		tmp = t_1;
	} else if (x <= -5.8e-296) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 4.1e+15) {
		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 = (b * ((t * i) - (z * c))) - (i * (y * j))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-5.2d+70)) then
        tmp = t_2
    else if (x <= (-6.6d-174)) then
        tmp = t_1
    else if (x <= (-5.8d-296)) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= 4.1d+15) 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 = (b * ((t * i) - (z * c))) - (i * (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.2e+70) {
		tmp = t_2;
	} else if (x <= -6.6e-174) {
		tmp = t_1;
	} else if (x <= -5.8e-296) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 4.1e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) - (i * (y * j))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5.2e+70:
		tmp = t_2
	elif x <= -6.6e-174:
		tmp = t_1
	elif x <= -5.8e-296:
		tmp = i * ((t * b) - (y * j))
	elif x <= 4.1e+15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(i * Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5.2e+70)
		tmp = t_2;
	elseif (x <= -6.6e-174)
		tmp = t_1;
	elseif (x <= -5.8e-296)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= 4.1e+15)
		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 = (b * ((t * i) - (z * c))) - (i * (y * j));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5.2e+70)
		tmp = t_2;
	elseif (x <= -6.6e-174)
		tmp = t_1;
	elseif (x <= -5.8e-296)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= 4.1e+15)
		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[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+70], t$95$2, If[LessEqual[x, -6.6e-174], t$95$1, If[LessEqual[x, -5.8e-296], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2000000000000001e70 or 4.1e15 < x

   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. +-commutative 73.8%

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

      2. fma-def 74.6%

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

      3. *-commutative 74.6%

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

      4. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in x around inf 67.2%

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

   if -5.2000000000000001e70 < x < -6.6000000000000002e-174 or -5.79999999999999965e-296 < x < 4.1e15

   1. Initial program 71.7%

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

      1. +-commutative 71.7%

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

      2. fma-def 75.6%

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

      3. *-commutative 75.6%

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

      4. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in a around 0 72.4%

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

   5. Taylor expanded in x around 0 65.8%

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

      1. sub-neg 65.8%

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

      2. +-commutative 65.8%

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

      3. mul-1-neg 65.8%

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

      4. associate-*r* 64.5%

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

      5. *-commutative 64.5%

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

      6. associate-*r* 66.7%

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

      7. unsub-neg 66.7%

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

   7. Simplified 65.8%

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

   if -6.6000000000000002e-174 < x < -5.79999999999999965e-296

   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. +-commutative 57.3%

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

      2. fma-def 60.4%

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

      3. *-commutative 60.4%

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

      4. *-commutative 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in i around inf 75.7%

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

      1. sub-neg 75.7%

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

      2. mul-1-neg 75.7%

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

      3. remove-double-neg 75.7%

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

      4. +-commutative 75.7%

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

      5. mul-1-neg 75.7%

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

      6. unsub-neg 75.7%

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

   6. Simplified 75.7%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 10: 64.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+107} \lor \neg \left(t \leq 3.2 \cdot 10^{+101}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -2.4e+107) (not (<= t 3.2e+101)))
   (* t (- (* b i) (* x a)))
   (+ (* b (- (* t i) (* z c))) (* y (- (* x z) (* i j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -2.4e+107) || !(t <= 3.2e+101)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	}
	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 ((t <= (-2.4d+107)) .or. (.not. (t <= 3.2d+101))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)))
    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 ((t <= -2.4e+107) || !(t <= 3.2e+101)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -2.4e+107) or not (t <= 3.2e+101):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -2.4e+107) || !(t <= 3.2e+101))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -2.4e+107) || ~((t <= 3.2e+101)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -2.4e+107], N[Not[LessEqual[t, 3.2e+101]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4000000000000001e107 or 3.20000000000000005e101 < t

   1. Initial program 57.2%

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

      1. cancel-sign-sub 57.2%

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

      2. cancel-sign-sub-inv 57.2%

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

      3. *-commutative 57.2%

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

      4. remove-double-neg 57.2%

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

      5. *-commutative 57.2%

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

   3. Simplified 57.2%

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

      1. add-cube-cbrt 57.1%

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

   5. Applied egg-rr 57.1%

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

   6. Taylor expanded in t around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-*r* 71.9%

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

      5. neg-mul-1 71.9%

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

      6. cancel-sign-sub 71.9%

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

      7. *-commutative 71.9%

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

      8. +-commutative 71.9%

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

      9. unsub-neg 71.9%

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

      10. *-commutative 71.9%

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

      11. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   if -2.4000000000000001e107 < t < 3.20000000000000005e101

   1. Initial program 79.3%

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

      1. +-commutative 79.3%

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

      2. fma-def 79.9%

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

      3. *-commutative 79.9%

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

      4. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in a around 0 64.9%

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

   5. Taylor expanded in y around -inf 66.1%

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

      1. fma-udef 66.1%

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

      2. mul-1-neg 66.1%

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

      3. fma-neg 66.1%

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

      4. mul-1-neg 66.1%

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

      5. *-commutative 66.1%

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

      6. *-commutative 66.1%

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

      7. *-commutative 66.1%

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

      8. distribute-rgt-neg-in 66.1%

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

      9. neg-sub0 66.1%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} - y \cdot \left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right) \]

      10. *-commutative 66.1%

          \[\leadsto b \cdot \left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) - y \cdot \left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right) \]

      11. *-commutative 66.1%

          \[\leadsto b \cdot \left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) - y \cdot \left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right) \]

      12. associate--r- 66.1%

          \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} - y \cdot \left(i \cdot j + -1 \cdot \left(z \cdot x\right)\right) \]

      13. neg-sub0 66.1%

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

      14. +-commutative 66.1%

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

      15. sub-neg 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+107} \lor \neg \left(t \leq 3.2 \cdot 10^{+101}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 11: 44.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.25 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -8.4 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-121}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -2.25e+82)
     t_2
     (if (<= c -5.2e-141)
       (* a (- (* c j) (* x t)))
       (if (<= c -8.4e-293)
         (* i (* t b))
         (if (<= c 1.05e-182)
           t_1
           (if (<= c 2.9e-121) (* b (* t i)) (if (<= c 7e-73) 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 = z * (x * y);
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.25e+82) {
		tmp = t_2;
	} else if (c <= -5.2e-141) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= -8.4e-293) {
		tmp = i * (t * b);
	} else if (c <= 1.05e-182) {
		tmp = t_1;
	} else if (c <= 2.9e-121) {
		tmp = b * (t * i);
	} else if (c <= 7e-73) {
		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 = z * (x * y)
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-2.25d+82)) then
        tmp = t_2
    else if (c <= (-5.2d-141)) then
        tmp = a * ((c * j) - (x * t))
    else if (c <= (-8.4d-293)) then
        tmp = i * (t * b)
    else if (c <= 1.05d-182) then
        tmp = t_1
    else if (c <= 2.9d-121) then
        tmp = b * (t * i)
    else if (c <= 7d-73) 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 = z * (x * y);
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.25e+82) {
		tmp = t_2;
	} else if (c <= -5.2e-141) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= -8.4e-293) {
		tmp = i * (t * b);
	} else if (c <= 1.05e-182) {
		tmp = t_1;
	} else if (c <= 2.9e-121) {
		tmp = b * (t * i);
	} else if (c <= 7e-73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.25e+82:
		tmp = t_2
	elif c <= -5.2e-141:
		tmp = a * ((c * j) - (x * t))
	elif c <= -8.4e-293:
		tmp = i * (t * b)
	elif c <= 1.05e-182:
		tmp = t_1
	elif c <= 2.9e-121:
		tmp = b * (t * i)
	elif c <= 7e-73:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.25e+82)
		tmp = t_2;
	elseif (c <= -5.2e-141)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (c <= -8.4e-293)
		tmp = Float64(i * Float64(t * b));
	elseif (c <= 1.05e-182)
		tmp = t_1;
	elseif (c <= 2.9e-121)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 7e-73)
		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 = z * (x * y);
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.25e+82)
		tmp = t_2;
	elseif (c <= -5.2e-141)
		tmp = a * ((c * j) - (x * t));
	elseif (c <= -8.4e-293)
		tmp = i * (t * b);
	elseif (c <= 1.05e-182)
		tmp = t_1;
	elseif (c <= 2.9e-121)
		tmp = b * (t * i);
	elseif (c <= 7e-73)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.25e+82], t$95$2, If[LessEqual[c, -5.2e-141], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.4e-293], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e-182], t$95$1, If[LessEqual[c, 2.9e-121], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e-73], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.2499999999999998e82 or 6.9999999999999995e-73 < c

   1. Initial program 58.4%

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

      1. +-commutative 58.4%

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

      2. fma-def 61.1%

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

      3. *-commutative 61.1%

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

      4. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in c around inf 56.9%

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

      1. *-commutative 56.9%

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

   6. Simplified 56.9%

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

   if -2.2499999999999998e82 < c < -5.20000000000000022e-141

   1. Initial program 87.2%

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

      1. +-commutative 87.2%

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

      2. fma-def 89.1%

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

      3. *-commutative 89.1%

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

      4. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 46.0%

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

      1. mul-1-neg 46.0%

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

      2. unsub-neg 46.0%

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

   6. Simplified 46.0%

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

   if -5.20000000000000022e-141 < c < -8.40000000000000021e-293

   1. Initial program 82.3%

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

      1. sub-neg 82.3%

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

      2. +-commutative 82.3%

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

      3. associate-+l+ 82.3%

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

      4. distribute-rgt-neg-in 82.3%

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

      5. +-commutative 82.3%

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

      6. fma-def 85.6%

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

      7. sub-neg 85.6%

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

      8. +-commutative 85.6%

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

      9. distribute-neg-in 85.6%

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

      10. unsub-neg 85.6%

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

      11. remove-double-neg 85.6%

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

      12. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in t around inf 61.0%

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

   5. Taylor expanded in i around inf 54.3%

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

   if -8.40000000000000021e-293 < c < 1.05e-182 or 2.9e-121 < c < 6.9999999999999995e-73

   1. Initial program 71.6%

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

      1. sub-neg 71.6%

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

      2. +-commutative 71.6%

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

      3. associate-+l+ 71.6%

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

      4. distribute-rgt-neg-in 71.6%

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

      5. +-commutative 71.6%

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

      6. fma-def 71.6%

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

      7. sub-neg 71.6%

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

      8. +-commutative 71.6%

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

      9. distribute-neg-in 71.6%

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

      10. unsub-neg 71.6%

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

      11. remove-double-neg 71.6%

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

      12. *-commutative 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in i around 0 52.7%

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

   5. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-*l* 50.9%

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

      3. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if 1.05e-182 < c < 2.9e-121

   1. Initial program 80.7%

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

      1. +-commutative 80.7%

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

      2. fma-def 87.4%

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

      3. *-commutative 87.4%

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

      4. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in j around 0 91.7%

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

   5. Taylor expanded in i around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. *-commutative 52.1%

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

      3. associate-*l* 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+82}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -8.4 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-182}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-121}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 12: 51.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -3.8e+42)
     t_3
     (if (<= c -5.2e-117)
       t_2
       (if (<= c -1.08e-128)
         t_1
         (if (<= c -5.5e-293)
           t_2
           (if (<= c 2.05e-296) t_1 (if (<= c 9.2e+30) t_2 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 = z * (x * y);
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.8e+42) {
		tmp = t_3;
	} else if (c <= -5.2e-117) {
		tmp = t_2;
	} else if (c <= -1.08e-128) {
		tmp = t_1;
	} else if (c <= -5.5e-293) {
		tmp = t_2;
	} else if (c <= 2.05e-296) {
		tmp = t_1;
	} else if (c <= 9.2e+30) {
		tmp = t_2;
	} 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 = z * (x * y)
    t_2 = i * ((t * b) - (y * j))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-3.8d+42)) then
        tmp = t_3
    else if (c <= (-5.2d-117)) then
        tmp = t_2
    else if (c <= (-1.08d-128)) then
        tmp = t_1
    else if (c <= (-5.5d-293)) then
        tmp = t_2
    else if (c <= 2.05d-296) then
        tmp = t_1
    else if (c <= 9.2d+30) then
        tmp = t_2
    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 = z * (x * y);
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.8e+42) {
		tmp = t_3;
	} else if (c <= -5.2e-117) {
		tmp = t_2;
	} else if (c <= -1.08e-128) {
		tmp = t_1;
	} else if (c <= -5.5e-293) {
		tmp = t_2;
	} else if (c <= 2.05e-296) {
		tmp = t_1;
	} else if (c <= 9.2e+30) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = i * ((t * b) - (y * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -3.8e+42:
		tmp = t_3
	elif c <= -5.2e-117:
		tmp = t_2
	elif c <= -1.08e-128:
		tmp = t_1
	elif c <= -5.5e-293:
		tmp = t_2
	elif c <= 2.05e-296:
		tmp = t_1
	elif c <= 9.2e+30:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.8e+42)
		tmp = t_3;
	elseif (c <= -5.2e-117)
		tmp = t_2;
	elseif (c <= -1.08e-128)
		tmp = t_1;
	elseif (c <= -5.5e-293)
		tmp = t_2;
	elseif (c <= 2.05e-296)
		tmp = t_1;
	elseif (c <= 9.2e+30)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = i * ((t * b) - (y * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.8e+42)
		tmp = t_3;
	elseif (c <= -5.2e-117)
		tmp = t_2;
	elseif (c <= -1.08e-128)
		tmp = t_1;
	elseif (c <= -5.5e-293)
		tmp = t_2;
	elseif (c <= 2.05e-296)
		tmp = t_1;
	elseif (c <= 9.2e+30)
		tmp = t_2;
	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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e+42], t$95$3, If[LessEqual[c, -5.2e-117], t$95$2, If[LessEqual[c, -1.08e-128], t$95$1, If[LessEqual[c, -5.5e-293], t$95$2, If[LessEqual[c, 2.05e-296], t$95$1, If[LessEqual[c, 9.2e+30], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.7999999999999998e42 or 9.2e30 < c

   1. Initial program 61.7%

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

      1. +-commutative 61.7%

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

      2. fma-def 64.6%

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

      3. *-commutative 64.6%

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

      4. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in c around inf 60.4%

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

      1. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if -3.7999999999999998e42 < c < -5.19999999999999966e-117 or -1.08e-128 < c < -5.50000000000000028e-293 or 2.04999999999999997e-296 < c < 9.2e30

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. fma-def 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in i around inf 56.9%

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

      1. sub-neg 56.9%

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

      2. mul-1-neg 56.9%

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

      3. remove-double-neg 56.9%

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

      4. +-commutative 56.9%

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

      5. mul-1-neg 56.9%

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

      6. unsub-neg 56.9%

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

   6. Simplified 56.9%

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

   if -5.19999999999999966e-117 < c < -1.08e-128 or -5.50000000000000028e-293 < c < 2.04999999999999997e-296

   1. Initial program 93.6%

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

      1. sub-neg 93.6%

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

      2. +-commutative 93.6%

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

      3. associate-+l+ 93.6%

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

      4. distribute-rgt-neg-in 93.6%

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

      5. +-commutative 93.6%

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

      6. fma-def 93.6%

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

      7. sub-neg 93.6%

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

      8. +-commutative 93.6%

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

      9. distribute-neg-in 93.6%

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

      10. unsub-neg 93.6%

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

      11. remove-double-neg 93.6%

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

      12. *-commutative 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in i around 0 75.5%

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

   5. Taylor expanded in y around inf 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-*l* 78.0%

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

      3. *-commutative 78.0%

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

   7. Simplified 78.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-117}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-296}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+30}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 13: 52.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.7 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4.2e+95)
     t_3
     (if (<= b -5.3e-108)
       t_2
       (if (<= b 7.7e-177)
         t_1
         (if (<= b 3.4e-104)
           t_2
           (if (<= b 7.8e-16)
             t_1
             (if (<= b 3.8e+136) (* t (- (* b i) (* x a))) 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 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.2e+95) {
		tmp = t_3;
	} else if (b <= -5.3e-108) {
		tmp = t_2;
	} else if (b <= 7.7e-177) {
		tmp = t_1;
	} else if (b <= 3.4e-104) {
		tmp = t_2;
	} else if (b <= 7.8e-16) {
		tmp = t_1;
	} else if (b <= 3.8e+136) {
		tmp = t * ((b * i) - (x * a));
	} 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 = y * ((x * z) - (i * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4.2d+95)) then
        tmp = t_3
    else if (b <= (-5.3d-108)) then
        tmp = t_2
    else if (b <= 7.7d-177) then
        tmp = t_1
    else if (b <= 3.4d-104) then
        tmp = t_2
    else if (b <= 7.8d-16) then
        tmp = t_1
    else if (b <= 3.8d+136) then
        tmp = t * ((b * i) - (x * a))
    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 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.2e+95) {
		tmp = t_3;
	} else if (b <= -5.3e-108) {
		tmp = t_2;
	} else if (b <= 7.7e-177) {
		tmp = t_1;
	} else if (b <= 3.4e-104) {
		tmp = t_2;
	} else if (b <= 7.8e-16) {
		tmp = t_1;
	} else if (b <= 3.8e+136) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.2e+95:
		tmp = t_3
	elif b <= -5.3e-108:
		tmp = t_2
	elif b <= 7.7e-177:
		tmp = t_1
	elif b <= 3.4e-104:
		tmp = t_2
	elif b <= 7.8e-16:
		tmp = t_1
	elif b <= 3.8e+136:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.2e+95)
		tmp = t_3;
	elseif (b <= -5.3e-108)
		tmp = t_2;
	elseif (b <= 7.7e-177)
		tmp = t_1;
	elseif (b <= 3.4e-104)
		tmp = t_2;
	elseif (b <= 7.8e-16)
		tmp = t_1;
	elseif (b <= 3.8e+136)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.2e+95)
		tmp = t_3;
	elseif (b <= -5.3e-108)
		tmp = t_2;
	elseif (b <= 7.7e-177)
		tmp = t_1;
	elseif (b <= 3.4e-104)
		tmp = t_2;
	elseif (b <= 7.8e-16)
		tmp = t_1;
	elseif (b <= 3.8e+136)
		tmp = t * ((b * i) - (x * a));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+95], t$95$3, If[LessEqual[b, -5.3e-108], t$95$2, If[LessEqual[b, 7.7e-177], t$95$1, If[LessEqual[b, 3.4e-104], t$95$2, If[LessEqual[b, 7.8e-16], t$95$1, If[LessEqual[b, 3.8e+136], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.2e95 or 3.80000000000000015e136 < b

   1. Initial program 72.1%

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

      1. +-commutative 72.1%

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

      2. fma-def 76.1%

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

      3. *-commutative 76.1%

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

      4. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in b around inf 63.8%

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

   if -4.2e95 < b < -5.29999999999999989e-108 or 7.7000000000000002e-177 < b < 3.40000000000000015e-104

   1. Initial program 76.2%

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

      1. +-commutative 76.2%

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

      2. fma-def 78.6%

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

      3. *-commutative 78.6%

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

      4. *-commutative 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in a around inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. unsub-neg 60.5%

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

   6. Simplified 60.5%

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

   if -5.29999999999999989e-108 < b < 7.7000000000000002e-177 or 3.40000000000000015e-104 < b < 7.79999999999999954e-16

   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. +-commutative 66.4%

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

      2. fma-def 67.7%

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

      3. *-commutative 67.7%

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

      4. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in y around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

   6. Simplified 63.7%

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

   if 7.79999999999999954e-16 < b < 3.80000000000000015e136

   1. Initial program 70.9%

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

      1. cancel-sign-sub 70.9%

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

      2. cancel-sign-sub-inv 70.9%

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

      3. *-commutative 70.9%

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

      4. remove-double-neg 70.9%

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

      5. *-commutative 70.9%

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

   3. Simplified 70.9%

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

      1. add-cube-cbrt 70.4%

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

   5. Applied egg-rr 70.4%

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

   6. Taylor expanded in t around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. *-commutative 59.1%

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

      4. associate-*r* 59.1%

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

      5. neg-mul-1 59.1%

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

      6. cancel-sign-sub 59.1%

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

      7. *-commutative 59.1%

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

      8. +-commutative 59.1%

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

      9. unsub-neg 59.1%

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

      10. *-commutative 59.1%

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

      11. *-commutative 59.1%

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

   8. Simplified 59.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-108}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.7 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 14: 50.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -2.9e+65)
     t_2
     (if (<= i -5e-105)
       t_1
       (if (<= i 1.8e-163)
         (* c (- (* a j) (* z b)))
         (if (<= i 1.2e+113)
           t_1
           (if (<= i 1.4e+128) (* a (- (* c j) (* x 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 = t * ((b * i) - (x * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.9e+65) {
		tmp = t_2;
	} else if (i <= -5e-105) {
		tmp = t_1;
	} else if (i <= 1.8e-163) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.2e+113) {
		tmp = t_1;
	} else if (i <= 1.4e+128) {
		tmp = a * ((c * j) - (x * 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 = t * ((b * i) - (x * a))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-2.9d+65)) then
        tmp = t_2
    else if (i <= (-5d-105)) then
        tmp = t_1
    else if (i <= 1.8d-163) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1.2d+113) then
        tmp = t_1
    else if (i <= 1.4d+128) then
        tmp = a * ((c * j) - (x * 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 = t * ((b * i) - (x * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.9e+65) {
		tmp = t_2;
	} else if (i <= -5e-105) {
		tmp = t_1;
	} else if (i <= 1.8e-163) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.2e+113) {
		tmp = t_1;
	} else if (i <= 1.4e+128) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.9e+65:
		tmp = t_2
	elif i <= -5e-105:
		tmp = t_1
	elif i <= 1.8e-163:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1.2e+113:
		tmp = t_1
	elif i <= 1.4e+128:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.9e+65)
		tmp = t_2;
	elseif (i <= -5e-105)
		tmp = t_1;
	elseif (i <= 1.8e-163)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1.2e+113)
		tmp = t_1;
	elseif (i <= 1.4e+128)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * 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 = t * ((b * i) - (x * a));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.9e+65)
		tmp = t_2;
	elseif (i <= -5e-105)
		tmp = t_1;
	elseif (i <= 1.8e-163)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1.2e+113)
		tmp = t_1;
	elseif (i <= 1.4e+128)
		tmp = a * ((c * j) - (x * 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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.9e+65], t$95$2, If[LessEqual[i, -5e-105], t$95$1, If[LessEqual[i, 1.8e-163], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e+113], t$95$1, If[LessEqual[i, 1.4e+128], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.9e65 or 1.39999999999999991e128 < i

   1. Initial program 56.5%

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

      1. +-commutative 56.5%

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

      2. fma-def 60.7%

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

      3. *-commutative 60.7%

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

      4. *-commutative 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in i around inf 71.1%

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

      1. sub-neg 71.1%

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

      2. mul-1-neg 71.1%

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

      3. remove-double-neg 71.1%

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

      4. +-commutative 71.1%

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

      5. mul-1-neg 71.1%

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

      6. unsub-neg 71.1%

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

   6. Simplified 71.1%

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

   if -2.9e65 < i < -4.99999999999999963e-105 or 1.7999999999999999e-163 < i < 1.19999999999999992e113

   1. Initial program 76.1%

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

      1. cancel-sign-sub 76.1%

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

      2. cancel-sign-sub-inv 76.1%

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

      3. *-commutative 76.1%

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

      4. remove-double-neg 76.1%

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

      5. *-commutative 76.1%

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

   3. Simplified 76.1%

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

      1. add-cube-cbrt 75.6%

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

   5. Applied egg-rr 75.6%

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

   6. Taylor expanded in t around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. *-commutative 50.1%

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

      4. associate-*r* 50.1%

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

      5. neg-mul-1 50.1%

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

      6. cancel-sign-sub 50.1%

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

      7. *-commutative 50.1%

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

      8. +-commutative 50.1%

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

      9. unsub-neg 50.1%

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

      10. *-commutative 50.1%

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

      11. *-commutative 50.1%

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

   8. Simplified 50.1%

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

   if -4.99999999999999963e-105 < i < 1.7999999999999999e-163

   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. +-commutative 85.4%

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

      2. fma-def 85.4%

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

      3. *-commutative 85.4%

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

      4. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in c around inf 53.2%

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

      1. *-commutative 53.2%

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

   6. Simplified 53.2%

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

   if 1.19999999999999992e113 < i < 1.39999999999999991e128

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. fma-def 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in a around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 15: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -42000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -42000000.0)
     t_2
     (if (<= z 6.5e-220)
       t_1
       (if (<= z 1.6e-185)
         (* a (- (* c j) (* x t)))
         (if (<= z 1.65e-130)
           t_1
           (if (<= z 2.4e+34) (* t (- (* b i) (* x a))) 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 * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -42000000.0) {
		tmp = t_2;
	} else if (z <= 6.5e-220) {
		tmp = t_1;
	} else if (z <= 1.6e-185) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 1.65e-130) {
		tmp = t_1;
	} else if (z <= 2.4e+34) {
		tmp = t * ((b * i) - (x * a));
	} 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 * ((t * b) - (y * j))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-42000000.0d0)) then
        tmp = t_2
    else if (z <= 6.5d-220) then
        tmp = t_1
    else if (z <= 1.6d-185) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= 1.65d-130) then
        tmp = t_1
    else if (z <= 2.4d+34) then
        tmp = t * ((b * i) - (x * a))
    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 * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -42000000.0) {
		tmp = t_2;
	} else if (z <= 6.5e-220) {
		tmp = t_1;
	} else if (z <= 1.6e-185) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 1.65e-130) {
		tmp = t_1;
	} else if (z <= 2.4e+34) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -42000000.0:
		tmp = t_2
	elif z <= 6.5e-220:
		tmp = t_1
	elif z <= 1.6e-185:
		tmp = a * ((c * j) - (x * t))
	elif z <= 1.65e-130:
		tmp = t_1
	elif z <= 2.4e+34:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -42000000.0)
		tmp = t_2;
	elseif (z <= 6.5e-220)
		tmp = t_1;
	elseif (z <= 1.6e-185)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= 1.65e-130)
		tmp = t_1;
	elseif (z <= 2.4e+34)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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 * ((t * b) - (y * j));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -42000000.0)
		tmp = t_2;
	elseif (z <= 6.5e-220)
		tmp = t_1;
	elseif (z <= 1.6e-185)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= 1.65e-130)
		tmp = t_1;
	elseif (z <= 2.4e+34)
		tmp = t * ((b * i) - (x * a));
	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[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -42000000.0], t$95$2, If[LessEqual[z, 6.5e-220], t$95$1, If[LessEqual[z, 1.6e-185], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-130], t$95$1, If[LessEqual[z, 2.4e+34], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2e7 or 2.39999999999999987e34 < z

   1. Initial program 62.4%

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

      1. +-commutative 62.4%

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

      2. fma-def 62.4%

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

      3. *-commutative 62.4%

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

      4. *-commutative 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in z around inf 67.7%

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

   if -4.2e7 < z < 6.50000000000000005e-220 or 1.5999999999999999e-185 < z < 1.6499999999999999e-130

   1. Initial program 82.6%

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

      1. +-commutative 82.6%

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

      2. fma-def 86.2%

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

      3. *-commutative 86.2%

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

      4. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in i around inf 61.7%

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

      1. sub-neg 61.7%

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

      2. mul-1-neg 61.7%

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

      3. remove-double-neg 61.7%

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

      4. +-commutative 61.7%

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

      5. mul-1-neg 61.7%

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

      6. unsub-neg 61.7%

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

   6. Simplified 61.7%

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

   if 6.50000000000000005e-220 < z < 1.5999999999999999e-185

   1. Initial program 67.8%

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

      1. +-commutative 67.8%

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

      2. fma-def 67.8%

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

      3. *-commutative 67.8%

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

      4. *-commutative 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   if 1.6499999999999999e-130 < z < 2.39999999999999987e34

   1. Initial program 72.0%

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

      1. cancel-sign-sub 72.0%

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

      2. cancel-sign-sub-inv 72.0%

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

      3. *-commutative 72.0%

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

      4. remove-double-neg 72.0%

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

      5. *-commutative 72.0%

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

   3. Simplified 72.0%

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

      1. add-cube-cbrt 71.5%

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

   5. Applied egg-rr 71.5%

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

   6. Taylor expanded in t around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. *-commutative 61.7%

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

      4. associate-*r* 61.7%

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

      5. neg-mul-1 61.7%

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

      6. cancel-sign-sub 61.7%

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

      7. *-commutative 61.7%

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

      8. +-commutative 61.7%

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

      9. unsub-neg 61.7%

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

      10. *-commutative 61.7%

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

      11. *-commutative 61.7%

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

   8. Simplified 61.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -42000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-220}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 16: 52.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -5e+70)
     t_3
     (if (<= x -2.3e-127)
       t_2
       (if (<= x 5.2e-272)
         t_1
         (if (<= x 4.6e-219) t_2 (if (<= x 5.6e+16) 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 = i * ((t * b) - (y * j));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5e+70) {
		tmp = t_3;
	} else if (x <= -2.3e-127) {
		tmp = t_2;
	} else if (x <= 5.2e-272) {
		tmp = t_1;
	} else if (x <= 4.6e-219) {
		tmp = t_2;
	} else if (x <= 5.6e+16) {
		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 = i * ((t * b) - (y * j))
    t_2 = b * ((t * i) - (z * c))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-5d+70)) then
        tmp = t_3
    else if (x <= (-2.3d-127)) then
        tmp = t_2
    else if (x <= 5.2d-272) then
        tmp = t_1
    else if (x <= 4.6d-219) then
        tmp = t_2
    else if (x <= 5.6d+16) 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 = i * ((t * b) - (y * j));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5e+70) {
		tmp = t_3;
	} else if (x <= -2.3e-127) {
		tmp = t_2;
	} else if (x <= 5.2e-272) {
		tmp = t_1;
	} else if (x <= 4.6e-219) {
		tmp = t_2;
	} else if (x <= 5.6e+16) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = b * ((t * i) - (z * c))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5e+70:
		tmp = t_3
	elif x <= -2.3e-127:
		tmp = t_2
	elif x <= 5.2e-272:
		tmp = t_1
	elif x <= 4.6e-219:
		tmp = t_2
	elif x <= 5.6e+16:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5e+70)
		tmp = t_3;
	elseif (x <= -2.3e-127)
		tmp = t_2;
	elseif (x <= 5.2e-272)
		tmp = t_1;
	elseif (x <= 4.6e-219)
		tmp = t_2;
	elseif (x <= 5.6e+16)
		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 = i * ((t * b) - (y * j));
	t_2 = b * ((t * i) - (z * c));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5e+70)
		tmp = t_3;
	elseif (x <= -2.3e-127)
		tmp = t_2;
	elseif (x <= 5.2e-272)
		tmp = t_1;
	elseif (x <= 4.6e-219)
		tmp = t_2;
	elseif (x <= 5.6e+16)
		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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+70], t$95$3, If[LessEqual[x, -2.3e-127], t$95$2, If[LessEqual[x, 5.2e-272], t$95$1, If[LessEqual[x, 4.6e-219], t$95$2, If[LessEqual[x, 5.6e+16], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.0000000000000002e70 or 5.6e16 < x

   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. +-commutative 73.8%

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

      2. fma-def 74.6%

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

      3. *-commutative 74.6%

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

      4. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in x around inf 67.2%

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

   if -5.0000000000000002e70 < x < -2.30000000000000019e-127 or 5.19999999999999983e-272 < x < 4.59999999999999977e-219

   1. Initial program 77.6%

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

      1. +-commutative 77.6%

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

      2. fma-def 82.6%

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

      3. *-commutative 82.6%

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

      4. *-commutative 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in b around inf 71.0%

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

   if -2.30000000000000019e-127 < x < 5.19999999999999983e-272 or 4.59999999999999977e-219 < x < 5.6e16

   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. +-commutative 64.3%

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

      2. fma-def 67.5%

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

      3. *-commutative 67.5%

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

      4. *-commutative 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in i around inf 63.5%

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

      1. sub-neg 63.5%

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

      2. mul-1-neg 63.5%

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

      3. remove-double-neg 63.5%

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

      4. +-commutative 63.5%

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

      5. mul-1-neg 63.5%

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

      6. unsub-neg 63.5%

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

   6. Simplified 63.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-272}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+16}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 17: 61.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+24} \lor \neg \left(x \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -2.9e+24) (not (<= x 3.6e+15)))
   (- (* x (- (* y z) (* t a))) (* b (* z c)))
   (- (* b (- (* t i) (* z c))) (* i (* y j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -2.9e+24) || !(x <= 3.6e+15)) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	}
	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 ((x <= (-2.9d+24)) .or. (.not. (x <= 3.6d+15))) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else
        tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
    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 ((x <= -2.9e+24) || !(x <= 3.6e+15)) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -2.9e+24) or not (x <= 3.6e+15):
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	else:
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -2.9e+24) || !(x <= 3.6e+15))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(i * Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -2.9e+24) || ~((x <= 3.6e+15)))
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	else
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -2.9e+24], N[Not[LessEqual[x, 3.6e+15]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.89999999999999979e24 or 3.6e15 < x

   1. Initial program 74.0%

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

      1. +-commutative 74.0%

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

      2. fma-def 75.5%

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

      3. *-commutative 75.5%

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

      4. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in j around 0 70.1%

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

   5. Taylor expanded in c around inf 69.5%

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

   if -2.89999999999999979e24 < x < 3.6e15

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-def 70.8%

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

      3. *-commutative 70.8%

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

      4. *-commutative 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in a around 0 69.0%

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

   5. Taylor expanded in x around 0 64.3%

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

      1. sub-neg 64.3%

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

      2. +-commutative 64.3%

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

      3. mul-1-neg 64.3%

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

      4. associate-*r* 62.4%

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

      5. *-commutative 62.4%

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

      6. associate-*r* 65.8%

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

      7. unsub-neg 65.8%

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

   7. Simplified 64.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+24} \lor \neg \left(x \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]

Alternative 18: 58.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -7000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -7000000.0)
     t_1
     (if (<= z 2.1e-108)
       (- (* t (* b i)) (* j (- (* y i) (* a c))))
       (if (<= z 5.4e+33) (* t (- (* b i) (* x a))) 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -7000000.0) {
		tmp = t_1;
	} else if (z <= 2.1e-108) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (z <= 5.4e+33) {
		tmp = t * ((b * i) - (x * a));
	} 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 = z * ((x * y) - (b * c))
    if (z <= (-7000000.0d0)) then
        tmp = t_1
    else if (z <= 2.1d-108) then
        tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
    else if (z <= 5.4d+33) then
        tmp = t * ((b * i) - (x * a))
    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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -7000000.0) {
		tmp = t_1;
	} else if (z <= 2.1e-108) {
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	} else if (z <= 5.4e+33) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -7000000.0:
		tmp = t_1
	elif z <= 2.1e-108:
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)))
	elif z <= 5.4e+33:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -7000000.0)
		tmp = t_1;
	elseif (z <= 2.1e-108)
		tmp = Float64(Float64(t * Float64(b * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (z <= 5.4e+33)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -7000000.0)
		tmp = t_1;
	elseif (z <= 2.1e-108)
		tmp = (t * (b * i)) - (j * ((y * i) - (a * c)));
	elseif (z <= 5.4e+33)
		tmp = t * ((b * i) - (x * a));
	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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7000000.0], t$95$1, If[LessEqual[z, 2.1e-108], N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+33], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7e6 or 5.39999999999999982e33 < z

   1. Initial program 62.4%

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

      1. +-commutative 62.4%

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

      2. fma-def 62.4%

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

      3. *-commutative 62.4%

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

      4. *-commutative 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in z around inf 67.7%

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

   if -7e6 < z < 2.0999999999999999e-108

   1. Initial program 81.4%

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

      1. cancel-sign-sub 81.4%

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

      2. cancel-sign-sub-inv 81.4%

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

      3. *-commutative 81.4%

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

      4. remove-double-neg 81.4%

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

      5. *-commutative 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in i around inf 65.6%

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

      1. associate-*r* 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*r* 60.4%

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

   6. Simplified 60.4%

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

   if 2.0999999999999999e-108 < z < 5.39999999999999982e33

   1. Initial program 71.8%

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

      1. cancel-sign-sub 71.8%

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

      2. cancel-sign-sub-inv 71.8%

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

      3. *-commutative 71.8%

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

      4. remove-double-neg 71.8%

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

      5. *-commutative 71.8%

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

   3. Simplified 71.8%

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

      1. add-cube-cbrt 71.3%

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

   5. Applied egg-rr 71.3%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*r* 62.8%

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

      5. neg-mul-1 62.8%

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

      6. cancel-sign-sub 62.8%

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

      7. *-commutative 62.8%

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

      8. +-commutative 62.8%

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

      9. unsub-neg 62.8%

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

      10. *-commutative 62.8%

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

      11. *-commutative 62.8%

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

   8. Simplified 62.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 19: 30.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+203}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-282}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 75000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -5.8e+203)
   (* y (* x z))
   (if (<= x -4.2e+99)
     (* a (* x (- t)))
     (if (<= x -5e-17)
       (* b (* z (- c)))
       (if (<= x -2.3e-214)
         (* a (* c j))
         (if (<= x -2.8e-282)
           (* i (* t b))
           (if (<= x 75000000000.0) (* b (* t i)) (* z (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -5.8e+203) {
		tmp = y * (x * z);
	} else if (x <= -4.2e+99) {
		tmp = a * (x * -t);
	} else if (x <= -5e-17) {
		tmp = b * (z * -c);
	} else if (x <= -2.3e-214) {
		tmp = a * (c * j);
	} else if (x <= -2.8e-282) {
		tmp = i * (t * b);
	} else if (x <= 75000000000.0) {
		tmp = b * (t * i);
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-5.8d+203)) then
        tmp = y * (x * z)
    else if (x <= (-4.2d+99)) then
        tmp = a * (x * -t)
    else if (x <= (-5d-17)) then
        tmp = b * (z * -c)
    else if (x <= (-2.3d-214)) then
        tmp = a * (c * j)
    else if (x <= (-2.8d-282)) then
        tmp = i * (t * b)
    else if (x <= 75000000000.0d0) then
        tmp = b * (t * i)
    else
        tmp = z * (x * y)
    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 (x <= -5.8e+203) {
		tmp = y * (x * z);
	} else if (x <= -4.2e+99) {
		tmp = a * (x * -t);
	} else if (x <= -5e-17) {
		tmp = b * (z * -c);
	} else if (x <= -2.3e-214) {
		tmp = a * (c * j);
	} else if (x <= -2.8e-282) {
		tmp = i * (t * b);
	} else if (x <= 75000000000.0) {
		tmp = b * (t * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -5.8e+203:
		tmp = y * (x * z)
	elif x <= -4.2e+99:
		tmp = a * (x * -t)
	elif x <= -5e-17:
		tmp = b * (z * -c)
	elif x <= -2.3e-214:
		tmp = a * (c * j)
	elif x <= -2.8e-282:
		tmp = i * (t * b)
	elif x <= 75000000000.0:
		tmp = b * (t * i)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -5.8e+203)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= -4.2e+99)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= -5e-17)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -2.3e-214)
		tmp = Float64(a * Float64(c * j));
	elseif (x <= -2.8e-282)
		tmp = Float64(i * Float64(t * b));
	elseif (x <= 75000000000.0)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -5.8e+203)
		tmp = y * (x * z);
	elseif (x <= -4.2e+99)
		tmp = a * (x * -t);
	elseif (x <= -5e-17)
		tmp = b * (z * -c);
	elseif (x <= -2.3e-214)
		tmp = a * (c * j);
	elseif (x <= -2.8e-282)
		tmp = i * (t * b);
	elseif (x <= 75000000000.0)
		tmp = b * (t * i);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -5.8e+203], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e+99], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e-17], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-214], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e-282], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 75000000000.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -5.80000000000000021e203

   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. sub-neg 73.4%

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

      2. +-commutative 73.4%

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

      3. associate-+l+ 73.4%

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

      4. distribute-rgt-neg-in 73.4%

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

      5. +-commutative 73.4%

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

      6. fma-def 73.6%

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

      7. sub-neg 73.6%

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

      8. +-commutative 73.6%

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

      9. distribute-neg-in 73.6%

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

      10. unsub-neg 73.6%

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

      11. remove-double-neg 73.6%

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

      12. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in i around 0 77.1%

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

   5. Taylor expanded in y around inf 57.4%

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

   if -5.80000000000000021e203 < x < -4.2000000000000002e99

   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. +-commutative 73.9%

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

      2. fma-def 73.9%

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

      3. *-commutative 73.9%

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

      4. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in a around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. unsub-neg 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in c around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-lft-neg-out 56.3%

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

      3. *-commutative 56.3%

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

   9. Simplified 56.3%

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

   if -4.2000000000000002e99 < x < -4.9999999999999999e-17

   1. Initial program 78.6%

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

      1. +-commutative 78.6%

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

      2. fma-def 82.1%

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

      3. *-commutative 82.1%

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

      4. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in a around 0 78.4%

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

   5. Taylor expanded in c around inf 37.4%

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

      1. mul-1-neg 37.4%

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

      2. *-commutative 37.4%

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

      3. associate-*r* 47.2%

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

      4. distribute-rgt-neg-in 47.2%

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

   7. Simplified 47.2%

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

   if -4.9999999999999999e-17 < x < -2.30000000000000011e-214

   1. Initial program 72.3%

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

      1. +-commutative 72.3%

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

      2. fma-def 72.3%

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

      3. *-commutative 72.3%

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

      4. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in a around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   6. Simplified 58.5%

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

   7. Taylor expanded in c around inf 40.0%

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

   if -2.30000000000000011e-214 < x < -2.7999999999999999e-282

   1. Initial program 67.3%

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

      1. sub-neg 67.3%

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

      2. +-commutative 67.3%

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

      3. associate-+l+ 67.3%

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

      4. distribute-rgt-neg-in 67.3%

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

      5. +-commutative 67.3%

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

      6. fma-def 67.3%

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

      7. sub-neg 67.3%

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

      8. +-commutative 67.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 67.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 67.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 67.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 67.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 59.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 59.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -2.7999999999999999e-282 < x < 7.5e10

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 62.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 68.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 68.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 68.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 48.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf 38.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. *-commutative 38.1%

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot i \]

      3. associate-*l* 40.2%

         \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   7. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 7.5e10 < x

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 74.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 74.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 74.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 74.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 74.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 74.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 74.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 74.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 74.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around 0 64.7%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)}\right) \]

   5. Taylor expanded in y around inf 37.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.2%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 42.2%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 42.2%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   7. Simplified 42.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+203}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-282}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 75000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 20: 45.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+249}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+44} \lor \neg \left(x \leq 68000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.05e+249)
   (* z (* x y))
   (if (<= x -5.2e+120)
     (* a (- (* c j) (* x t)))
     (if (or (<= x -1.12e+44) (not (<= x 68000000000.0)))
       (* y (- (* x z) (* i j)))
       (* i (- (* t b) (* y j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.05e+249) {
		tmp = z * (x * y);
	} else if (x <= -5.2e+120) {
		tmp = a * ((c * j) - (x * t));
	} else if ((x <= -1.12e+44) || !(x <= 68000000000.0)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	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 (x <= (-1.05d+249)) then
        tmp = z * (x * y)
    else if (x <= (-5.2d+120)) then
        tmp = a * ((c * j) - (x * t))
    else if ((x <= (-1.12d+44)) .or. (.not. (x <= 68000000000.0d0))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = i * ((t * b) - (y * j))
    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 (x <= -1.05e+249) {
		tmp = z * (x * y);
	} else if (x <= -5.2e+120) {
		tmp = a * ((c * j) - (x * t));
	} else if ((x <= -1.12e+44) || !(x <= 68000000000.0)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.05e+249:
		tmp = z * (x * y)
	elif x <= -5.2e+120:
		tmp = a * ((c * j) - (x * t))
	elif (x <= -1.12e+44) or not (x <= 68000000000.0):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.05e+249)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= -5.2e+120)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif ((x <= -1.12e+44) || !(x <= 68000000000.0))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.05e+249)
		tmp = z * (x * y);
	elseif (x <= -5.2e+120)
		tmp = a * ((c * j) - (x * t));
	elseif ((x <= -1.12e+44) || ~((x <= 68000000000.0)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.05e+249], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e+120], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.12e+44], N[Not[LessEqual[x, 68000000000.0]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.0499999999999999e249

   1. Initial program 64.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 64.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 64.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 64.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 64.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 64.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 65.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 65.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 65.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 65.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 65.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 65.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 65.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 65.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around 0 65.5%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)}\right) \]

   5. Taylor expanded in y around inf 59.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative 59.7%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 61.6%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 61.6%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   7. Simplified 61.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -1.0499999999999999e249 < x < -5.1999999999999998e120

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 82.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 65.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 65.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 65.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -5.1999999999999998e120 < x < -1.12000000000000008e44 or 6.8e10 < x

   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. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 74.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around inf 54.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 54.8%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 54.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 54.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.12000000000000008e44 < x < 6.8e10

   1. Initial program 67.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 71.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 57.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 57.7%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(t \cdot b\right)\right)\right)} \]

      2. mul-1-neg 57.7%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-t \cdot b\right)}\right)\right) \]

      3. remove-double-neg 57.7%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{t \cdot b}\right) \]

      4. +-commutative 57.7%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 57.7%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 57.7%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 57.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+249}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+44} \lor \neg \left(x \leq 68000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 21: 30.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq -21500:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 27500000000:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -5.2e+70)
     t_1
     (if (<= x -3.6e+16)
       (* (* z b) (- c))
       (if (<= x -21500.0)
         (* b (* t i))
         (if (<= x -1.2e-211)
           (* a (* c j))
           (if (<= x 27500000000.0) (* i (* t b)) 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 = z * (x * y);
	double tmp;
	if (x <= -5.2e+70) {
		tmp = t_1;
	} else if (x <= -3.6e+16) {
		tmp = (z * b) * -c;
	} else if (x <= -21500.0) {
		tmp = b * (t * i);
	} else if (x <= -1.2e-211) {
		tmp = a * (c * j);
	} else if (x <= 27500000000.0) {
		tmp = i * (t * b);
	} 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 = z * (x * y)
    if (x <= (-5.2d+70)) then
        tmp = t_1
    else if (x <= (-3.6d+16)) then
        tmp = (z * b) * -c
    else if (x <= (-21500.0d0)) then
        tmp = b * (t * i)
    else if (x <= (-1.2d-211)) then
        tmp = a * (c * j)
    else if (x <= 27500000000.0d0) then
        tmp = i * (t * b)
    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 = z * (x * y);
	double tmp;
	if (x <= -5.2e+70) {
		tmp = t_1;
	} else if (x <= -3.6e+16) {
		tmp = (z * b) * -c;
	} else if (x <= -21500.0) {
		tmp = b * (t * i);
	} else if (x <= -1.2e-211) {
		tmp = a * (c * j);
	} else if (x <= 27500000000.0) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -5.2e+70:
		tmp = t_1
	elif x <= -3.6e+16:
		tmp = (z * b) * -c
	elif x <= -21500.0:
		tmp = b * (t * i)
	elif x <= -1.2e-211:
		tmp = a * (c * j)
	elif x <= 27500000000.0:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -5.2e+70)
		tmp = t_1;
	elseif (x <= -3.6e+16)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (x <= -21500.0)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= -1.2e-211)
		tmp = Float64(a * Float64(c * j));
	elseif (x <= 27500000000.0)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -5.2e+70)
		tmp = t_1;
	elseif (x <= -3.6e+16)
		tmp = (z * b) * -c;
	elseif (x <= -21500.0)
		tmp = b * (t * i);
	elseif (x <= -1.2e-211)
		tmp = a * (c * j);
	elseif (x <= 27500000000.0)
		tmp = i * (t * b);
	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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+70], t$95$1, If[LessEqual[x, -3.6e+16], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[x, -21500.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e-211], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 27500000000.0], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.2000000000000001e70 or 2.75e10 < x

   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. sub-neg 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 74.2%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 74.2%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 74.2%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 74.2%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 75.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 75.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 75.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 75.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 75.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 75.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 75.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around 0 71.3%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)}\right) \]

   5. Taylor expanded in y around inf 40.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 43.5%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 43.5%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   7. Simplified 43.5%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -5.2000000000000001e70 < x < -3.6e16

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 87.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 87.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 87.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 86.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in c around inf 55.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.1%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      2. *-commutative 55.1%

         \[\leadsto -c \cdot \color{blue}{\left(z \cdot b\right)} \]

   7. Simplified 55.1%

      \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

   if -3.6e16 < x < -21500

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 66.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 66.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 66.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 66.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf 66.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 66.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. *-commutative 66.9%

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot i \]

      3. associate-*l* 66.9%

         \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   7. Simplified 66.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -21500 < x < -1.2000000000000001e-211

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 74.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 57.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 57.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 57.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 41.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -1.2000000000000001e-211 < x < 2.75e10

   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. sub-neg 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 64.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 64.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 64.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 64.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 65.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 65.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 65.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 65.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 65.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 65.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 65.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 65.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 47.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 43.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq -21500:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 27500000000:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 22: 30.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 100000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= x -1.55e+203)
     t_1
     (if (<= x -4.4e+98)
       (* a (* x (- t)))
       (if (<= x -3e+39)
         t_1
         (if (<= x 100000000000.0) (* b (* t i)) (* z (* x 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 = y * (x * z);
	double tmp;
	if (x <= -1.55e+203) {
		tmp = t_1;
	} else if (x <= -4.4e+98) {
		tmp = a * (x * -t);
	} else if (x <= -3e+39) {
		tmp = t_1;
	} else if (x <= 100000000000.0) {
		tmp = b * (t * i);
	} else {
		tmp = z * (x * y);
	}
	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 = y * (x * z)
    if (x <= (-1.55d+203)) then
        tmp = t_1
    else if (x <= (-4.4d+98)) then
        tmp = a * (x * -t)
    else if (x <= (-3d+39)) then
        tmp = t_1
    else if (x <= 100000000000.0d0) then
        tmp = b * (t * i)
    else
        tmp = z * (x * y)
    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 * (x * z);
	double tmp;
	if (x <= -1.55e+203) {
		tmp = t_1;
	} else if (x <= -4.4e+98) {
		tmp = a * (x * -t);
	} else if (x <= -3e+39) {
		tmp = t_1;
	} else if (x <= 100000000000.0) {
		tmp = b * (t * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if x <= -1.55e+203:
		tmp = t_1
	elif x <= -4.4e+98:
		tmp = a * (x * -t)
	elif x <= -3e+39:
		tmp = t_1
	elif x <= 100000000000.0:
		tmp = b * (t * i)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (x <= -1.55e+203)
		tmp = t_1;
	elseif (x <= -4.4e+98)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= -3e+39)
		tmp = t_1;
	elseif (x <= 100000000000.0)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (x <= -1.55e+203)
		tmp = t_1;
	elseif (x <= -4.4e+98)
		tmp = a * (x * -t);
	elseif (x <= -3e+39)
		tmp = t_1;
	elseif (x <= 100000000000.0)
		tmp = b * (t * i);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+203], t$95$1, If[LessEqual[x, -4.4e+98], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e+39], t$95$1, If[LessEqual[x, 100000000000.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.55e203 or -4.40000000000000017e98 < x < -3e39

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 74.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 74.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 74.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 74.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 74.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 74.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 74.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 74.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 74.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 74.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around 0 75.4%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)}\right) \]

   5. Taylor expanded in y around inf 56.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.55e203 < x < -4.40000000000000017e98

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 75.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 63.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 63.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 63.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 55.9%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 55.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 55.9%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 55.9%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -3e39 < x < 1e11

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 70.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 52.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf 38.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. *-commutative 38.9%

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot i \]

      3. associate-*l* 40.1%

         \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1e11 < x

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 74.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 74.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 74.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 74.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 74.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 74.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 74.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 74.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 74.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around 0 64.7%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)}\right) \]

   5. Taylor expanded in y around inf 37.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.2%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 42.2%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 42.2%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   7. Simplified 42.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+203}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 100000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 23: 29.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+41} \lor \neg \left(c \leq 6.8 \cdot 10^{+25}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -8e+41) (not (<= c 6.8e+25))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8e+41) || !(c <= 6.8e+25)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	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 ((c <= (-8d+41)) .or. (.not. (c <= 6.8d+25))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    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 ((c <= -8e+41) || !(c <= 6.8e+25)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -8e+41) or not (c <= 6.8e+25):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -8e+41) || !(c <= 6.8e+25))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -8e+41) || ~((c <= 6.8e+25)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -8e+41], N[Not[LessEqual[c, 6.8e+25]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.00000000000000005e41 or 6.79999999999999967e25 < 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. +-commutative 62.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 64.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 64.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 47.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 47.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 47.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 37.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -8.00000000000000005e41 < c < 6.79999999999999967e25

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 79.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 66.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf 34.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot i \]

      3. associate-*l* 35.2%

         \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   7. Simplified 35.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+41} \lor \neg \left(c \leq 6.8 \cdot 10^{+25}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 24: 30.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+39} \lor \neg \left(x \leq 7200000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -2.2e+39) (not (<= x 7200000000.0)))
   (* y (* x z))
   (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -2.2e+39) || !(x <= 7200000000.0)) {
		tmp = y * (x * z);
	} else {
		tmp = b * (t * i);
	}
	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 ((x <= (-2.2d+39)) .or. (.not. (x <= 7200000000.0d0))) then
        tmp = y * (x * z)
    else
        tmp = b * (t * i)
    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 ((x <= -2.2e+39) || !(x <= 7200000000.0)) {
		tmp = y * (x * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -2.2e+39) or not (x <= 7200000000.0):
		tmp = y * (x * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -2.2e+39) || !(x <= 7200000000.0))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -2.2e+39) || ~((x <= 7200000000.0)))
		tmp = y * (x * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -2.2e+39], N[Not[LessEqual[x, 7200000000.0]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000001e39 or 7.2e9 < x

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 74.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 74.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 74.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 74.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 76.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 76.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 76.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 76.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 76.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 76.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 76.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around 0 71.7%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)}\right) \]

   5. Taylor expanded in y around inf 40.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -2.2000000000000001e39 < x < 7.2e9

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 70.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 52.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf 38.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. *-commutative 38.9%

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot i \]

      3. associate-*l* 40.1%

         \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+39} \lor \neg \left(x \leq 7200000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 25: 30.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+39} \lor \neg \left(x \leq 42000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -2.7e+39) (not (<= x 42000000000.0)))
   (* z (* x y))
   (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -2.7e+39) || !(x <= 42000000000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	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 ((x <= (-2.7d+39)) .or. (.not. (x <= 42000000000.0d0))) then
        tmp = z * (x * y)
    else
        tmp = b * (t * i)
    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 ((x <= -2.7e+39) || !(x <= 42000000000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -2.7e+39) or not (x <= 42000000000.0):
		tmp = z * (x * y)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -2.7e+39) || !(x <= 42000000000.0))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -2.7e+39) || ~((x <= 42000000000.0)))
		tmp = z * (x * y);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -2.7e+39], N[Not[LessEqual[x, 42000000000.0]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.70000000000000003e39 or 4.2e10 < x

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 74.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 74.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 74.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 74.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 76.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 76.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 76.2%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 76.2%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 76.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 76.2%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 76.2%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around 0 71.7%

      \[\leadsto \mathsf{fma}\left(b, t \cdot i - z \cdot c, \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)}\right) \]

   5. Taylor expanded in y around inf 40.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 43.2%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

      3. *-commutative 43.2%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   7. Simplified 43.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -2.70000000000000003e39 < x < 4.2e10

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 70.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 52.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf 38.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. *-commutative 38.9%

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot i \]

      3. associate-*l* 40.1%

         \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+39} \lor \neg \left(x \leq 42000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 26: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.28e-77)
   (* b (* t i))
   (if (<= t 7e+56) (* c (* a j)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.28e-77) {
		tmp = b * (t * i);
	} else if (t <= 7e+56) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	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 (t <= (-1.28d-77)) then
        tmp = b * (t * i)
    else if (t <= 7d+56) then
        tmp = c * (a * j)
    else
        tmp = i * (t * b)
    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 (t <= -1.28e-77) {
		tmp = b * (t * i);
	} else if (t <= 7e+56) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.28e-77:
		tmp = b * (t * i)
	elif t <= 7e+56:
		tmp = c * (a * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.28e-77)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 7e+56)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.28e-77)
		tmp = b * (t * i);
	elseif (t <= 7e+56)
		tmp = c * (a * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.28e-77], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+56], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.28e-77

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 63.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 68.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 68.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 68.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 68.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 65.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   5. Taylor expanded in i around inf 35.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot i} \]

      2. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot i \]

      3. associate-*l* 36.9%

         \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   7. Simplified 36.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -1.28e-77 < t < 6.99999999999999999e56

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 82.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 82.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 34.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 34.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 34.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 28.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 6.99999999999999999e56 < t

   1. Initial program 58.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 58.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 58.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 58.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 58.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 58.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 62.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 62.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 62.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 62.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 62.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 62.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 62.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 71.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 45.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 27: 22.0% 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 70.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. +-commutative 70.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   2. fma-def 73.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   3. *-commutative 73.3%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

   4. *-commutative 73.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

3. Simplified 73.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 36.8%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 36.8%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   2. unsub-neg 36.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 36.8%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 20.7%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

8. Final simplification 20.7%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.9% 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 2023230 
(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)))))