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

Percentage Accurate: 73.6% → 83.0%

Time: 34.2s

Alternatives: 26

Speedup: 0.5×

• 56.7% 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: 73.6% 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: 83.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t\_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_1 + \left(y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2 + j \cdot \mathsf{fma}\left(a, c, y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \sqrt[3]{{\left(t \cdot b - y \cdot j\right)}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ t_1 (* x (- (* y z) (* t a)))))
        (t_3 (+ t_2 (* j (- (* a c) (* y i))))))
   (if (<= t_3 (- INFINITY))
     (+ t_1 (+ (* y (- (* x z) (* i j))) (* a (- (* c j) (* x t)))))
     (if (<= t_3 INFINITY)
       (+ t_2 (* j (fma a c (* y (- i)))))
       (* i (cbrt (pow (- (* t b) (* y j)) 3.0)))))))

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));
	double t_2 = t_1 + (x * ((y * z) - (t * a)));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1 + ((y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2 + (j * fma(a, c, (y * -i)));
	} else {
		tmp = i * cbrt(pow(((t * b) - (y * j)), 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_3 = Float64(t_2 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_1 + Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(c * j) - Float64(x * t)))));
	elseif (t_3 <= Inf)
		tmp = Float64(t_2 + Float64(j * fma(a, c, Float64(y * Float64(-i)))));
	else
		tmp = Float64(i * cbrt((Float64(Float64(t * b) - Float64(y * j)) ^ 3.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$1 + N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$2 + N[(j * N[(a * c + N[(y * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[Power[N[Power[N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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 81.6%

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

   3. Taylor expanded in a around -inf 83.8%

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

   5. Simplified 89.2%

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

   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)))) < +inf.0

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. *-commutative 91.3%

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

      4. sub-neg 91.3%

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

      5. *-commutative 91.3%

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

      6. fma-def 91.3%

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

   3. Simplified 91.3%

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

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 15.1%

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

   5. Simplified 20.1%

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

   6. Taylor expanded in i around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

   8. Simplified 47.9%

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

      1. add-cbrt-cube 52.7%

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

      2. pow3 52.7%

         \[\leadsto i \cdot \sqrt[3]{\color{blue}{{\left(t \cdot b - j \cdot y\right)}^{3}}} \]

      3. *-commutative 52.7%

         \[\leadsto i \cdot \sqrt[3]{{\left(t \cdot b - \color{blue}{y \cdot j}\right)}^{3}} \]

   10. Applied egg-rr 52.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\right)\\ \mathbf{elif}\;\left(b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \mathsf{fma}\left(a, c, y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \sqrt[3]{{\left(t \cdot b - y \cdot j\right)}^{3}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t\_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_1 + \left(y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2 + j \cdot \mathsf{fma}\left(a, c, y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ t_1 (* x (- (* y z) (* t a)))))
        (t_3 (+ t_2 (* j (- (* a c) (* y i))))))
   (if (<= t_3 (- INFINITY))
     (+ t_1 (+ (* y (- (* x z) (* i j))) (* a (- (* c j) (* x t)))))
     (if (<= t_3 INFINITY)
       (+ t_2 (* j (fma a c (* y (- i)))))
       (* 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 t_1 = b * ((t * i) - (z * c));
	double t_2 = t_1 + (x * ((y * z) - (t * a)));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1 + ((y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2 + (j * fma(a, c, (y * -i)));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_3 = Float64(t_2 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_1 + Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(c * j) - Float64(x * t)))));
	elseif (t_3 <= Inf)
		tmp = Float64(t_2 + Float64(j * fma(a, c, Float64(y * Float64(-i)))));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$1 + N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$2 + N[(j * N[(a * c + N[(y * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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 81.6%

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

   3. Taylor expanded in a around -inf 83.8%

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

   5. Simplified 89.2%

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

   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)))) < +inf.0

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. *-commutative 91.3%

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

      4. sub-neg 91.3%

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

      5. *-commutative 91.3%

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

      6. fma-def 91.3%

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

   3. Simplified 91.3%

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

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 15.1%

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

   5. Simplified 20.1%

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

   6. Taylor expanded in i around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

   8. Simplified 47.9%

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

4. Final simplification 83.9%

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

Alternative 3: 81.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := \left(t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1 + \left(y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 + Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(c * j) - Float64(x * t)))));
	elseif (t_2 <= Inf)
		tmp = t_2;
	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)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (t_1 + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1 + ((y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t))));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 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 81.6%

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

   3. Taylor expanded in a around -inf 83.8%

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

   5. Simplified 89.2%

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

   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)))) < +inf.0

   1. Initial program 91.3%

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

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 15.1%

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

   5. Simplified 20.1%

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

   6. Taylor expanded in i around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

   8. Simplified 47.9%

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

4. Final simplification 83.9%

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

Alternative 4: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(Float64(y * z) - Float64(t * a)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	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)
	t_1 = ((b * ((t * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $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 88.1%

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

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 15.1%

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

   5. Simplified 20.1%

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

   6. Taylor expanded in i around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

   8. Simplified 47.9%

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

4. Final simplification 81.8%

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

Alternative 5: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+40}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-62}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-18} \lor \neg \left(b \leq 1.8 \cdot 10^{+14}\right) \land b \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -7e+40)
     t_3
     (if (<= b -1.35e-120)
       t_1
       (if (<= b -5e-162)
         (* y (* x z))
         (if (<= b -5.9e-167)
           t_1
           (if (<= b 5e-141)
             t_2
             (if (<= b 4.8e-62)
               (* i (* y (- j)))
               (if (or (<= b 1.2e-18)
                       (and (not (<= b 1.8e+14)) (<= b 1.35e+66)))
                 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 = y * (i * -j);
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7e+40) {
		tmp = t_3;
	} else if (b <= -1.35e-120) {
		tmp = t_1;
	} else if (b <= -5e-162) {
		tmp = y * (x * z);
	} else if (b <= -5.9e-167) {
		tmp = t_1;
	} else if (b <= 5e-141) {
		tmp = t_2;
	} else if (b <= 4.8e-62) {
		tmp = i * (y * -j);
	} else if ((b <= 1.2e-18) || (!(b <= 1.8e+14) && (b <= 1.35e+66))) {
		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 = y * (i * -j)
    t_2 = a * ((c * j) - (x * t))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-7d+40)) then
        tmp = t_3
    else if (b <= (-1.35d-120)) then
        tmp = t_1
    else if (b <= (-5d-162)) then
        tmp = y * (x * z)
    else if (b <= (-5.9d-167)) then
        tmp = t_1
    else if (b <= 5d-141) then
        tmp = t_2
    else if (b <= 4.8d-62) then
        tmp = i * (y * -j)
    else if ((b <= 1.2d-18) .or. (.not. (b <= 1.8d+14)) .and. (b <= 1.35d+66)) 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 = y * (i * -j);
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7e+40) {
		tmp = t_3;
	} else if (b <= -1.35e-120) {
		tmp = t_1;
	} else if (b <= -5e-162) {
		tmp = y * (x * z);
	} else if (b <= -5.9e-167) {
		tmp = t_1;
	} else if (b <= 5e-141) {
		tmp = t_2;
	} else if (b <= 4.8e-62) {
		tmp = i * (y * -j);
	} else if ((b <= 1.2e-18) || (!(b <= 1.8e+14) && (b <= 1.35e+66))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = a * ((c * j) - (x * t))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7e+40:
		tmp = t_3
	elif b <= -1.35e-120:
		tmp = t_1
	elif b <= -5e-162:
		tmp = y * (x * z)
	elif b <= -5.9e-167:
		tmp = t_1
	elif b <= 5e-141:
		tmp = t_2
	elif b <= 4.8e-62:
		tmp = i * (y * -j)
	elif (b <= 1.2e-18) or (not (b <= 1.8e+14) and (b <= 1.35e+66)):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-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 <= -7e+40)
		tmp = t_3;
	elseif (b <= -1.35e-120)
		tmp = t_1;
	elseif (b <= -5e-162)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= -5.9e-167)
		tmp = t_1;
	elseif (b <= 5e-141)
		tmp = t_2;
	elseif (b <= 4.8e-62)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif ((b <= 1.2e-18) || (!(b <= 1.8e+14) && (b <= 1.35e+66)))
		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 = y * (i * -j);
	t_2 = a * ((c * j) - (x * t));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7e+40)
		tmp = t_3;
	elseif (b <= -1.35e-120)
		tmp = t_1;
	elseif (b <= -5e-162)
		tmp = y * (x * z);
	elseif (b <= -5.9e-167)
		tmp = t_1;
	elseif (b <= 5e-141)
		tmp = t_2;
	elseif (b <= 4.8e-62)
		tmp = i * (y * -j);
	elseif ((b <= 1.2e-18) || (~((b <= 1.8e+14)) && (b <= 1.35e+66)))
		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[(y * N[(i * (-j)), $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, -7e+40], t$95$3, If[LessEqual[b, -1.35e-120], t$95$1, If[LessEqual[b, -5e-162], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.9e-167], t$95$1, If[LessEqual[b, 5e-141], t$95$2, If[LessEqual[b, 4.8e-62], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.2e-18], And[N[Not[LessEqual[b, 1.8e+14]], $MachinePrecision], LessEqual[b, 1.35e+66]]], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.9999999999999998e40 or 1.19999999999999997e-18 < b < 1.8e14 or 1.35e66 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 68.5%

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

   if -6.9999999999999998e40 < b < -1.3499999999999999e-120 or -5.00000000000000014e-162 < b < -5.90000000000000022e-167

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. *-commutative 48.4%

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

      3. distribute-rgt-neg-in 48.4%

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

   8. Simplified 48.4%

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

   if -1.3499999999999999e-120 < b < -5.00000000000000014e-162

   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. Add Preprocessing

   3. Taylor expanded in y around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. mul-1-neg 87.3%

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

      3. unsub-neg 87.3%

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

      4. *-commutative 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in x around inf 75.0%

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

   if -5.90000000000000022e-167 < b < 4.9999999999999999e-141 or 4.79999999999999967e-62 < b < 1.19999999999999997e-18 or 1.8e14 < b < 1.35e66

   1. Initial program 69.4%

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

   3. Taylor expanded in a around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

      4. *-commutative 57.2%

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

      5. *-commutative 57.2%

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

   5. Simplified 57.2%

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

   if 4.9999999999999999e-141 < b < 4.79999999999999967e-62

   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. Add Preprocessing

   3. Taylor expanded in y around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in x around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. *-commutative 54.7%

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

      3. distribute-rgt-neg-in 54.7%

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

   8. Simplified 54.7%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-62}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-18} \lor \neg \left(b \leq 1.8 \cdot 10^{+14}\right) \land b \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -5.2e+38)
     t_3
     (if (<= b -1.9e-117)
       t_1
       (if (<= b -7.2e-166)
         (* y (* x z))
         (if (<= b -5.8e-167)
           t_1
           (if (<= b 4.3e-141)
             t_2
             (if (<= b 6.5e-60)
               (* i (* y (- j)))
               (if (<= b 3.1e-19)
                 t_2
                 (if (<= b 3.1e+20)
                   (* c (- (* a j) (* z b)))
                   (if (<= b 2.55e+66) 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 = y * (i * -j);
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e+38) {
		tmp = t_3;
	} else if (b <= -1.9e-117) {
		tmp = t_1;
	} else if (b <= -7.2e-166) {
		tmp = y * (x * z);
	} else if (b <= -5.8e-167) {
		tmp = t_1;
	} else if (b <= 4.3e-141) {
		tmp = t_2;
	} else if (b <= 6.5e-60) {
		tmp = i * (y * -j);
	} else if (b <= 3.1e-19) {
		tmp = t_2;
	} else if (b <= 3.1e+20) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 2.55e+66) {
		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 = y * (i * -j)
    t_2 = a * ((c * j) - (x * t))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-5.2d+38)) then
        tmp = t_3
    else if (b <= (-1.9d-117)) then
        tmp = t_1
    else if (b <= (-7.2d-166)) then
        tmp = y * (x * z)
    else if (b <= (-5.8d-167)) then
        tmp = t_1
    else if (b <= 4.3d-141) then
        tmp = t_2
    else if (b <= 6.5d-60) then
        tmp = i * (y * -j)
    else if (b <= 3.1d-19) then
        tmp = t_2
    else if (b <= 3.1d+20) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 2.55d+66) 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 = y * (i * -j);
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e+38) {
		tmp = t_3;
	} else if (b <= -1.9e-117) {
		tmp = t_1;
	} else if (b <= -7.2e-166) {
		tmp = y * (x * z);
	} else if (b <= -5.8e-167) {
		tmp = t_1;
	} else if (b <= 4.3e-141) {
		tmp = t_2;
	} else if (b <= 6.5e-60) {
		tmp = i * (y * -j);
	} else if (b <= 3.1e-19) {
		tmp = t_2;
	} else if (b <= 3.1e+20) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 2.55e+66) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = a * ((c * j) - (x * t))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.2e+38:
		tmp = t_3
	elif b <= -1.9e-117:
		tmp = t_1
	elif b <= -7.2e-166:
		tmp = y * (x * z)
	elif b <= -5.8e-167:
		tmp = t_1
	elif b <= 4.3e-141:
		tmp = t_2
	elif b <= 6.5e-60:
		tmp = i * (y * -j)
	elif b <= 3.1e-19:
		tmp = t_2
	elif b <= 3.1e+20:
		tmp = c * ((a * j) - (z * b))
	elif b <= 2.55e+66:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-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 <= -5.2e+38)
		tmp = t_3;
	elseif (b <= -1.9e-117)
		tmp = t_1;
	elseif (b <= -7.2e-166)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= -5.8e-167)
		tmp = t_1;
	elseif (b <= 4.3e-141)
		tmp = t_2;
	elseif (b <= 6.5e-60)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 3.1e-19)
		tmp = t_2;
	elseif (b <= 3.1e+20)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 2.55e+66)
		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 = y * (i * -j);
	t_2 = a * ((c * j) - (x * t));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.2e+38)
		tmp = t_3;
	elseif (b <= -1.9e-117)
		tmp = t_1;
	elseif (b <= -7.2e-166)
		tmp = y * (x * z);
	elseif (b <= -5.8e-167)
		tmp = t_1;
	elseif (b <= 4.3e-141)
		tmp = t_2;
	elseif (b <= 6.5e-60)
		tmp = i * (y * -j);
	elseif (b <= 3.1e-19)
		tmp = t_2;
	elseif (b <= 3.1e+20)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 2.55e+66)
		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[(y * N[(i * (-j)), $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, -5.2e+38], t$95$3, If[LessEqual[b, -1.9e-117], t$95$1, If[LessEqual[b, -7.2e-166], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-167], t$95$1, If[LessEqual[b, 4.3e-141], t$95$2, If[LessEqual[b, 6.5e-60], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-19], t$95$2, If[LessEqual[b, 3.1e+20], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e+66], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.1999999999999998e38 or 2.55000000000000004e66 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 68.8%

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

   if -5.1999999999999998e38 < b < -1.89999999999999986e-117 or -7.2000000000000002e-166 < b < -5.80000000000000005e-167

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. *-commutative 48.4%

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

      3. distribute-rgt-neg-in 48.4%

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

   8. Simplified 48.4%

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

   if -1.89999999999999986e-117 < b < -7.2000000000000002e-166

   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. Add Preprocessing

   3. Taylor expanded in y around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. mul-1-neg 87.3%

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

      3. unsub-neg 87.3%

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

      4. *-commutative 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in x around inf 75.0%

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

   if -5.80000000000000005e-167 < b < 4.29999999999999974e-141 or 6.49999999999999995e-60 < b < 3.0999999999999999e-19 or 3.1e20 < b < 2.55000000000000004e66

   1. Initial program 69.1%

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

   3. Taylor expanded in a around inf 58.7%

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

      1. +-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

      4. *-commutative 58.7%

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

      5. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   if 4.29999999999999974e-141 < b < 6.49999999999999995e-60

   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. Add Preprocessing

   3. Taylor expanded in y around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in x around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. *-commutative 54.7%

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

      3. distribute-rgt-neg-in 54.7%

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

   8. Simplified 54.7%

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

   if 3.0999999999999999e-19 < b < 3.1e20

   1. Initial program 74.9%

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

   3. Taylor expanded in c around inf 55.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.8 \cdot 10^{+164}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (- (* z (* x y)) (* a (- (* x t) (* c j)))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -3.8e+164)
     t_3
     (if (<= i -4.8e+42)
       (* y (- (* x z) (* i j)))
       (if (<= i -1.25e+17)
         t_1
         (if (<= i -1.35e-91)
           t_2
           (if (<= i -4.4e-163)
             t_1
             (if (<= i 5e-178)
               t_2
               (if (<= i 2.8e+32)
                 (* z (- (* x y) (* b c)))
                 (if (<= i 5.2e+116)
                   (- (* a (* c j)) (* i (* y j)))
                   (if (<= i 2.3e+150) 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 = b * ((t * i) - (z * c));
	double t_2 = (z * (x * y)) - (a * ((x * t) - (c * j)));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.8e+164) {
		tmp = t_3;
	} else if (i <= -4.8e+42) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -1.25e+17) {
		tmp = t_1;
	} else if (i <= -1.35e-91) {
		tmp = t_2;
	} else if (i <= -4.4e-163) {
		tmp = t_1;
	} else if (i <= 5e-178) {
		tmp = t_2;
	} else if (i <= 2.8e+32) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 5.2e+116) {
		tmp = (a * (c * j)) - (i * (y * j));
	} else if (i <= 2.3e+150) {
		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 = b * ((t * i) - (z * c))
    t_2 = (z * (x * y)) - (a * ((x * t) - (c * j)))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-3.8d+164)) then
        tmp = t_3
    else if (i <= (-4.8d+42)) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= (-1.25d+17)) then
        tmp = t_1
    else if (i <= (-1.35d-91)) then
        tmp = t_2
    else if (i <= (-4.4d-163)) then
        tmp = t_1
    else if (i <= 5d-178) then
        tmp = t_2
    else if (i <= 2.8d+32) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 5.2d+116) then
        tmp = (a * (c * j)) - (i * (y * j))
    else if (i <= 2.3d+150) 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 = b * ((t * i) - (z * c));
	double t_2 = (z * (x * y)) - (a * ((x * t) - (c * j)));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.8e+164) {
		tmp = t_3;
	} else if (i <= -4.8e+42) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -1.25e+17) {
		tmp = t_1;
	} else if (i <= -1.35e-91) {
		tmp = t_2;
	} else if (i <= -4.4e-163) {
		tmp = t_1;
	} else if (i <= 5e-178) {
		tmp = t_2;
	} else if (i <= 2.8e+32) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 5.2e+116) {
		tmp = (a * (c * j)) - (i * (y * j));
	} else if (i <= 2.3e+150) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (z * (x * y)) - (a * ((x * t) - (c * j)))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.8e+164:
		tmp = t_3
	elif i <= -4.8e+42:
		tmp = y * ((x * z) - (i * j))
	elif i <= -1.25e+17:
		tmp = t_1
	elif i <= -1.35e-91:
		tmp = t_2
	elif i <= -4.4e-163:
		tmp = t_1
	elif i <= 5e-178:
		tmp = t_2
	elif i <= 2.8e+32:
		tmp = z * ((x * y) - (b * c))
	elif i <= 5.2e+116:
		tmp = (a * (c * j)) - (i * (y * j))
	elif i <= 2.3e+150:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(z * Float64(x * y)) - Float64(a * Float64(Float64(x * t) - Float64(c * j))))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.8e+164)
		tmp = t_3;
	elseif (i <= -4.8e+42)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= -1.25e+17)
		tmp = t_1;
	elseif (i <= -1.35e-91)
		tmp = t_2;
	elseif (i <= -4.4e-163)
		tmp = t_1;
	elseif (i <= 5e-178)
		tmp = t_2;
	elseif (i <= 2.8e+32)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 5.2e+116)
		tmp = Float64(Float64(a * Float64(c * j)) - Float64(i * Float64(y * j)));
	elseif (i <= 2.3e+150)
		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 = b * ((t * i) - (z * c));
	t_2 = (z * (x * y)) - (a * ((x * t) - (c * j)));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.8e+164)
		tmp = t_3;
	elseif (i <= -4.8e+42)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= -1.25e+17)
		tmp = t_1;
	elseif (i <= -1.35e-91)
		tmp = t_2;
	elseif (i <= -4.4e-163)
		tmp = t_1;
	elseif (i <= 5e-178)
		tmp = t_2;
	elseif (i <= 2.8e+32)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 5.2e+116)
		tmp = (a * (c * j)) - (i * (y * j));
	elseif (i <= 2.3e+150)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.8e+164], t$95$3, If[LessEqual[i, -4.8e+42], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.25e+17], t$95$1, If[LessEqual[i, -1.35e-91], t$95$2, If[LessEqual[i, -4.4e-163], t$95$1, If[LessEqual[i, 5e-178], t$95$2, If[LessEqual[i, 2.8e+32], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+116], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e+150], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.80000000000000021e164 or 2.30000000000000001e150 < i

   1. Initial program 65.2%

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

   3. Taylor expanded in a around -inf 71.6%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in i around inf 85.2%

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

      1. +-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

      4. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   if -3.80000000000000021e164 < i < -4.7999999999999997e42

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. +-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

      4. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   if -4.7999999999999997e42 < i < -1.25e17 or -1.3499999999999999e-91 < i < -4.40000000000000022e-163 or 5.19999999999999973e116 < i < 2.30000000000000001e150

   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. Add Preprocessing

   3. Taylor expanded in b around inf 70.1%

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

   if -1.25e17 < i < -1.3499999999999999e-91 or -4.40000000000000022e-163 < i < 4.99999999999999976e-178

   1. Initial program 81.7%

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

   3. Taylor expanded in a around -inf 78.0%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in b around 0 73.5%

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

   7. Taylor expanded in x around inf 66.1%

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

      1. associate-*r* 70.5%

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

   9. Simplified 70.5%

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

   if 4.99999999999999976e-178 < i < 2.8e32

   1. Initial program 82.9%

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

   3. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

      2. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if 2.8e32 < i < 5.19999999999999973e116

   1. Initial program 61.9%

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

   3. Taylor expanded in a around -inf 80.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in b around 0 90.0%

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

   7. Taylor expanded in x around 0 81.2%

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

      1. distribute-lft-out-- 81.2%

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

   9. Simplified 81.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right) - a \cdot \left(c \cdot j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+164}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-178}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+150}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -9.2 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-24}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.14 \cdot 10^{-182}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= i -9.2e+93)
     t_1
     (if (<= i -2.1e+48)
       t_2
       (if (<= i -1.6e+41)
         (* i (* y (- j)))
         (if (<= i -3.7e-24)
           t_3
           (if (<= i -2.3e-85)
             t_2
             (if (<= i -1.14e-182)
               t_3
               (if (<= i 1.05e-177)
                 t_2
                 (if (<= i 1.3e+50) (* c (- (* a j) (* z 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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (i <= -9.2e+93) {
		tmp = t_1;
	} else if (i <= -2.1e+48) {
		tmp = t_2;
	} else if (i <= -1.6e+41) {
		tmp = i * (y * -j);
	} else if (i <= -3.7e-24) {
		tmp = t_3;
	} else if (i <= -2.3e-85) {
		tmp = t_2;
	} else if (i <= -1.14e-182) {
		tmp = t_3;
	} else if (i <= 1.05e-177) {
		tmp = t_2;
	} else if (i <= 1.3e+50) {
		tmp = c * ((a * j) - (z * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = b * ((t * i) - (z * c))
    if (i <= (-9.2d+93)) then
        tmp = t_1
    else if (i <= (-2.1d+48)) then
        tmp = t_2
    else if (i <= (-1.6d+41)) then
        tmp = i * (y * -j)
    else if (i <= (-3.7d-24)) then
        tmp = t_3
    else if (i <= (-2.3d-85)) then
        tmp = t_2
    else if (i <= (-1.14d-182)) then
        tmp = t_3
    else if (i <= 1.05d-177) then
        tmp = t_2
    else if (i <= 1.3d+50) then
        tmp = c * ((a * j) - (z * 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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (i <= -9.2e+93) {
		tmp = t_1;
	} else if (i <= -2.1e+48) {
		tmp = t_2;
	} else if (i <= -1.6e+41) {
		tmp = i * (y * -j);
	} else if (i <= -3.7e-24) {
		tmp = t_3;
	} else if (i <= -2.3e-85) {
		tmp = t_2;
	} else if (i <= -1.14e-182) {
		tmp = t_3;
	} else if (i <= 1.05e-177) {
		tmp = t_2;
	} else if (i <= 1.3e+50) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if i <= -9.2e+93:
		tmp = t_1
	elif i <= -2.1e+48:
		tmp = t_2
	elif i <= -1.6e+41:
		tmp = i * (y * -j)
	elif i <= -3.7e-24:
		tmp = t_3
	elif i <= -2.3e-85:
		tmp = t_2
	elif i <= -1.14e-182:
		tmp = t_3
	elif i <= 1.05e-177:
		tmp = t_2
	elif i <= 1.3e+50:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	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(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (i <= -9.2e+93)
		tmp = t_1;
	elseif (i <= -2.1e+48)
		tmp = t_2;
	elseif (i <= -1.6e+41)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (i <= -3.7e-24)
		tmp = t_3;
	elseif (i <= -2.3e-85)
		tmp = t_2;
	elseif (i <= -1.14e-182)
		tmp = t_3;
	elseif (i <= 1.05e-177)
		tmp = t_2;
	elseif (i <= 1.3e+50)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * 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 = i * ((t * b) - (y * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (i <= -9.2e+93)
		tmp = t_1;
	elseif (i <= -2.1e+48)
		tmp = t_2;
	elseif (i <= -1.6e+41)
		tmp = i * (y * -j);
	elseif (i <= -3.7e-24)
		tmp = t_3;
	elseif (i <= -2.3e-85)
		tmp = t_2;
	elseif (i <= -1.14e-182)
		tmp = t_3;
	elseif (i <= 1.05e-177)
		tmp = t_2;
	elseif (i <= 1.3e+50)
		tmp = c * ((a * j) - (z * 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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * 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[i, -9.2e+93], t$95$1, If[LessEqual[i, -2.1e+48], t$95$2, If[LessEqual[i, -1.6e+41], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.7e-24], t$95$3, If[LessEqual[i, -2.3e-85], t$95$2, If[LessEqual[i, -1.14e-182], t$95$3, If[LessEqual[i, 1.05e-177], t$95$2, If[LessEqual[i, 1.3e+50], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -9.2000000000000006e93 or 1.3000000000000001e50 < i

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 70.7%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in i around inf 78.1%

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

      1. +-commutative 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. *-commutative 78.1%

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

   8. Simplified 78.1%

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

   if -9.2000000000000006e93 < i < -2.0999999999999998e48 or -3.69999999999999981e-24 < i < -2.3e-85 or -1.14000000000000006e-182 < i < 1.05e-177

   1. Initial program 80.6%

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

   3. Taylor expanded in a around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if -2.0999999999999998e48 < i < -1.60000000000000005e41

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. +-commutative 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   8. Simplified 100.0%

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

   if -1.60000000000000005e41 < i < -3.69999999999999981e-24 or -2.3e-85 < i < -1.14000000000000006e-182

   1. Initial program 81.6%

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

   3. Taylor expanded in b around inf 56.6%

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

   if 1.05e-177 < i < 1.3000000000000001e50

   1. Initial program 81.6%

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

   3. Taylor expanded in c around inf 55.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{+93}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.14 \cdot 10^{-182}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-177}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1960000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z)))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.7e+151)
     t_2
     (if (<= b -1.2e-47)
       t_1
       (if (<= b -1.6e-150)
         (* y (- (* x z) (* i j)))
         (if (<= b 1960000.0)
           t_1
           (if (<= b 2.3e+14)
             (* b (* z (- c)))
             (if (<= b 1.2e+67) 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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.7e+151) {
		tmp = t_2;
	} else if (b <= -1.2e-47) {
		tmp = t_1;
	} else if (b <= -1.6e-150) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1960000.0) {
		tmp = t_1;
	} else if (b <= 2.3e+14) {
		tmp = b * (z * -c);
	} else if (b <= 1.2e+67) {
		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 = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.7d+151)) then
        tmp = t_2
    else if (b <= (-1.2d-47)) then
        tmp = t_1
    else if (b <= (-1.6d-150)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1960000.0d0) then
        tmp = t_1
    else if (b <= 2.3d+14) then
        tmp = b * (z * -c)
    else if (b <= 1.2d+67) 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 = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.7e+151) {
		tmp = t_2;
	} else if (b <= -1.2e-47) {
		tmp = t_1;
	} else if (b <= -1.6e-150) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1960000.0) {
		tmp = t_1;
	} else if (b <= 2.3e+14) {
		tmp = b * (z * -c);
	} else if (b <= 1.2e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.7e+151:
		tmp = t_2
	elif b <= -1.2e-47:
		tmp = t_1
	elif b <= -1.6e-150:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1960000.0:
		tmp = t_1
	elif b <= 2.3e+14:
		tmp = b * (z * -c)
	elif b <= 1.2e+67:
		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(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.7e+151)
		tmp = t_2;
	elseif (b <= -1.2e-47)
		tmp = t_1;
	elseif (b <= -1.6e-150)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1960000.0)
		tmp = t_1;
	elseif (b <= 2.3e+14)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (b <= 1.2e+67)
		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 = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.7e+151)
		tmp = t_2;
	elseif (b <= -1.2e-47)
		tmp = t_1;
	elseif (b <= -1.6e-150)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1960000.0)
		tmp = t_1;
	elseif (b <= 2.3e+14)
		tmp = b * (z * -c);
	elseif (b <= 1.2e+67)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e+151], t$95$2, If[LessEqual[b, -1.2e-47], t$95$1, If[LessEqual[b, -1.6e-150], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1960000.0], t$95$1, If[LessEqual[b, 2.3e+14], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+67], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.7e151 or 1.20000000000000001e67 < 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. Add Preprocessing

   3. Taylor expanded in b around inf 77.4%

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

   if -1.7e151 < b < -1.2e-47 or -1.5999999999999999e-150 < b < 1.96e6 or 2.3e14 < b < 1.20000000000000001e67

   1. Initial program 79.2%

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

   3. Taylor expanded in b around 0 70.3%

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

   if -1.2e-47 < b < -1.5999999999999999e-150

   1. Initial program 57.6%

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

   3. Taylor expanded in y around inf 82.8%

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

      1. +-commutative 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

      4. *-commutative 82.8%

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

   5. Simplified 82.8%

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

   if 1.96e6 < b < 2.3e14

   1. Initial program 40.0%

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

      1. prod-diff 40.0%

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

      2. *-commutative 40.0%

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

      3. fma-neg 40.0%

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

      4. distribute-rgt-in 40.0%

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

      5. *-commutative 40.0%

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

      6. fma-neg 40.0%

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

      7. distribute-rgt-neg-in 40.0%

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

   4. Applied egg-rr 40.0%

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

   5. Taylor expanded in b around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. *-commutative 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in t around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. *-commutative 81.0%

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

      3. distribute-rgt-neg-in 81.0%

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

   10. Simplified 81.0%

       \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1960000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-288}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -2.35e-6)
     t_2
     (if (<= z -1.6e-96)
       (* x (- (* y z) (* t a)))
       (if (<= z -2.6e-288)
         (* i (- (* t b) (* y j)))
         (if (<= z 9e-219)
           t_1
           (if (<= z 2.1e-100)
             (* t (- (* b i) (* x a)))
             (if (<= z 7.2e-44) 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 * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.35e-6) {
		tmp = t_2;
	} else if (z <= -1.6e-96) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -2.6e-288) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 9e-219) {
		tmp = t_1;
	} else if (z <= 2.1e-100) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 7.2e-44) {
		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 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-2.35d-6)) then
        tmp = t_2
    else if (z <= (-1.6d-96)) then
        tmp = x * ((y * z) - (t * a))
    else if (z <= (-2.6d-288)) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 9d-219) then
        tmp = t_1
    else if (z <= 2.1d-100) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 7.2d-44) 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 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.35e-6) {
		tmp = t_2;
	} else if (z <= -1.6e-96) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -2.6e-288) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 9e-219) {
		tmp = t_1;
	} else if (z <= 2.1e-100) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 7.2e-44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.35e-6:
		tmp = t_2
	elif z <= -1.6e-96:
		tmp = x * ((y * z) - (t * a))
	elif z <= -2.6e-288:
		tmp = i * ((t * b) - (y * j))
	elif z <= 9e-219:
		tmp = t_1
	elif z <= 2.1e-100:
		tmp = t * ((b * i) - (x * a))
	elif z <= 7.2e-44:
		tmp = 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(a * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.35e-6)
		tmp = t_2;
	elseif (z <= -1.6e-96)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (z <= -2.6e-288)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 9e-219)
		tmp = t_1;
	elseif (z <= 2.1e-100)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 7.2e-44)
		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 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.35e-6)
		tmp = t_2;
	elseif (z <= -1.6e-96)
		tmp = x * ((y * z) - (t * a));
	elseif (z <= -2.6e-288)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 9e-219)
		tmp = t_1;
	elseif (z <= 2.1e-100)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 7.2e-44)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e-6], t$95$2, If[LessEqual[z, -1.6e-96], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-288], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-219], t$95$1, If[LessEqual[z, 2.1e-100], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-44], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.34999999999999995e-6 or 7.1999999999999998e-44 < z

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -2.34999999999999995e-6 < z < -1.60000000000000006e-96

   1. Initial program 88.9%

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

   3. Taylor expanded in a around -inf 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in x around inf 62.4%

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

   if -1.60000000000000006e-96 < z < -2.59999999999999989e-288

   1. Initial program 81.1%

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

   3. Taylor expanded in a around -inf 89.1%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in i around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

   8. Simplified 74.2%

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

   if -2.59999999999999989e-288 < z < 9.00000000000000029e-219 or 2.10000000000000009e-100 < z < 7.1999999999999998e-44

   1. Initial program 90.3%

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

      1. prod-diff 85.2%

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

      2. *-commutative 85.2%

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

      3. fma-neg 85.2%

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

      4. distribute-rgt-in 82.7%

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

      5. *-commutative 82.7%

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

      6. fma-neg 82.7%

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

      7. distribute-rgt-neg-in 82.7%

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

   4. Applied egg-rr 82.7%

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

   5. Taylor expanded in j around inf 70.9%

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

      1. sub-neg 70.9%

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

      2. *-commutative 70.9%

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

      3. sub-neg 70.9%

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

   7. Simplified 70.9%

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

   if 9.00000000000000029e-219 < z < 2.10000000000000009e-100

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 90.1%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in t around inf 65.6%

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

      1. *-commutative 65.6%

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

   8. Simplified 65.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-288}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-219}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) + t\_1\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-87}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ (* b (- (* t i) (* z c))) t_1)))
   (if (<= y -2.5e-87)
     (- t_1 (* x (- (* t a) (* y z))))
     (if (<= y 1.12e-117)
       t_2
       (if (<= y 6.2e-30)
         (* t (- (* b i) (* x a)))
         (if (<= y 1.16e+122) t_2 (* 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 t_1 = j * ((a * c) - (y * i));
	double t_2 = (b * ((t * i) - (z * c))) + t_1;
	double tmp;
	if (y <= -2.5e-87) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (y <= 1.12e-117) {
		tmp = t_2;
	} else if (y <= 6.2e-30) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.16e+122) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (b * ((t * i) - (z * c))) + t_1
    if (y <= (-2.5d-87)) then
        tmp = t_1 - (x * ((t * a) - (y * z)))
    else if (y <= 1.12d-117) then
        tmp = t_2
    else if (y <= 6.2d-30) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 1.16d+122) then
        tmp = t_2
    else
        tmp = 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 t_1 = j * ((a * c) - (y * i));
	double t_2 = (b * ((t * i) - (z * c))) + t_1;
	double tmp;
	if (y <= -2.5e-87) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (y <= 1.12e-117) {
		tmp = t_2;
	} else if (y <= 6.2e-30) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.16e+122) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (b * ((t * i) - (z * c))) + t_1
	tmp = 0
	if y <= -2.5e-87:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	elif y <= 1.12e-117:
		tmp = t_2
	elif y <= 6.2e-30:
		tmp = t * ((b * i) - (x * a))
	elif y <= 1.16e+122:
		tmp = t_2
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + t_1)
	tmp = 0.0
	if (y <= -2.5e-87)
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (y <= 1.12e-117)
		tmp = t_2;
	elseif (y <= 6.2e-30)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 1.16e+122)
		tmp = t_2;
	else
		tmp = 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)
	t_1 = j * ((a * c) - (y * i));
	t_2 = (b * ((t * i) - (z * c))) + t_1;
	tmp = 0.0;
	if (y <= -2.5e-87)
		tmp = t_1 - (x * ((t * a) - (y * z)));
	elseif (y <= 1.12e-117)
		tmp = t_2;
	elseif (y <= 6.2e-30)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 1.16e+122)
		tmp = t_2;
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $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]}, If[LessEqual[y, -2.5e-87], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-117], t$95$2, If[LessEqual[y, 6.2e-30], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e+122], t$95$2, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.50000000000000021e-87

   1. Initial program 76.9%

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

   3. Taylor expanded in b around 0 70.5%

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

   if -2.50000000000000021e-87 < y < 1.12e-117 or 6.19999999999999982e-30 < y < 1.16e122

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 69.5%

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

   if 1.12e-117 < y < 6.19999999999999982e-30

   1. Initial program 67.7%

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

   3. Taylor expanded in a around -inf 80.2%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in t around inf 74.5%

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

      1. *-commutative 74.5%

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

   8. Simplified 74.5%

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

   if 1.16e122 < y

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 82.3%

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

      1. +-commutative 82.3%

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

      2. mul-1-neg 82.3%

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

      3. unsub-neg 82.3%

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

      4. *-commutative 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-87}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-47}:\\ \;\;\;\;t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+63}:\\ \;\;\;\;t\_1 + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4.4e+153)
     t_3
     (if (<= b -1.3e-47)
       (- t_2 (* x (- (* t a) (* y z))))
       (if (<= b -4.8e-132)
         t_1
         (if (<= b 9e+63) (+ t_1 (* a (- (* c j) (* x t)))) (+ t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.4e+153) {
		tmp = t_3;
	} else if (b <= -1.3e-47) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else if (b <= -4.8e-132) {
		tmp = t_1;
	} else if (b <= 9e+63) {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	} else {
		tmp = t_3 + 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) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = j * ((a * c) - (y * i))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4.4d+153)) then
        tmp = t_3
    else if (b <= (-1.3d-47)) then
        tmp = t_2 - (x * ((t * a) - (y * z)))
    else if (b <= (-4.8d-132)) then
        tmp = t_1
    else if (b <= 9d+63) then
        tmp = t_1 + (a * ((c * j) - (x * t)))
    else
        tmp = t_3 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.4e+153) {
		tmp = t_3;
	} else if (b <= -1.3e-47) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else if (b <= -4.8e-132) {
		tmp = t_1;
	} else if (b <= 9e+63) {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	} else {
		tmp = t_3 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = j * ((a * c) - (y * i))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.4e+153:
		tmp = t_3
	elif b <= -1.3e-47:
		tmp = t_2 - (x * ((t * a) - (y * z)))
	elif b <= -4.8e-132:
		tmp = t_1
	elif b <= 9e+63:
		tmp = t_1 + (a * ((c * j) - (x * t)))
	else:
		tmp = t_3 + t_2
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.4e+153)
		tmp = t_3;
	elseif (b <= -1.3e-47)
		tmp = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (b <= -4.8e-132)
		tmp = t_1;
	elseif (b <= 9e+63)
		tmp = Float64(t_1 + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	else
		tmp = Float64(t_3 + t_2);
	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 = j * ((a * c) - (y * i));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.4e+153)
		tmp = t_3;
	elseif (b <= -1.3e-47)
		tmp = t_2 - (x * ((t * a) - (y * z)));
	elseif (b <= -4.8e-132)
		tmp = t_1;
	elseif (b <= 9e+63)
		tmp = t_1 + (a * ((c * j) - (x * t)));
	else
		tmp = t_3 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+153], t$95$3, If[LessEqual[b, -1.3e-47], N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-132], t$95$1, If[LessEqual[b, 9e+63], N[(t$95$1 + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$3 + t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.3999999999999999e153

   1. Initial program 55.6%

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

   3. Taylor expanded in b around inf 81.7%

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

   if -4.3999999999999999e153 < b < -1.3e-47

   1. Initial program 91.6%

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

   3. Taylor expanded in b around 0 71.3%

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

   if -1.3e-47 < b < -4.80000000000000031e-132

   1. Initial program 55.8%

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

   3. Taylor expanded in y around inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

      4. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -4.80000000000000031e-132 < b < 9.00000000000000034e63

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 73.5%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in b around 0 74.7%

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

   if 9.00000000000000034e63 < b

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 81.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;i \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= i -7.2e+106)
     (* y (* i (- j)))
     (if (<= i 1.7e-177)
       t_2
       (if (<= i 1.95e+31)
         t_1
         (if (<= i 5e+124)
           t_2
           (if (<= i 1.2e+150)
             t_1
             (if (<= i 1.02e+226) (* i (* t b)) (* 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 t_1 = b * (z * -c);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (i <= -7.2e+106) {
		tmp = y * (i * -j);
	} else if (i <= 1.7e-177) {
		tmp = t_2;
	} else if (i <= 1.95e+31) {
		tmp = t_1;
	} else if (i <= 5e+124) {
		tmp = t_2;
	} else if (i <= 1.2e+150) {
		tmp = t_1;
	} else if (i <= 1.02e+226) {
		tmp = i * (t * b);
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = a * ((c * j) - (x * t))
    if (i <= (-7.2d+106)) then
        tmp = y * (i * -j)
    else if (i <= 1.7d-177) then
        tmp = t_2
    else if (i <= 1.95d+31) then
        tmp = t_1
    else if (i <= 5d+124) then
        tmp = t_2
    else if (i <= 1.2d+150) then
        tmp = t_1
    else if (i <= 1.02d+226) then
        tmp = i * (t * b)
    else
        tmp = 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 t_1 = b * (z * -c);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (i <= -7.2e+106) {
		tmp = y * (i * -j);
	} else if (i <= 1.7e-177) {
		tmp = t_2;
	} else if (i <= 1.95e+31) {
		tmp = t_1;
	} else if (i <= 5e+124) {
		tmp = t_2;
	} else if (i <= 1.2e+150) {
		tmp = t_1;
	} else if (i <= 1.02e+226) {
		tmp = i * (t * b);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if i <= -7.2e+106:
		tmp = y * (i * -j)
	elif i <= 1.7e-177:
		tmp = t_2
	elif i <= 1.95e+31:
		tmp = t_1
	elif i <= 5e+124:
		tmp = t_2
	elif i <= 1.2e+150:
		tmp = t_1
	elif i <= 1.02e+226:
		tmp = i * (t * b)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (i <= -7.2e+106)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= 1.7e-177)
		tmp = t_2;
	elseif (i <= 1.95e+31)
		tmp = t_1;
	elseif (i <= 5e+124)
		tmp = t_2;
	elseif (i <= 1.2e+150)
		tmp = t_1;
	elseif (i <= 1.02e+226)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (i <= -7.2e+106)
		tmp = y * (i * -j);
	elseif (i <= 1.7e-177)
		tmp = t_2;
	elseif (i <= 1.95e+31)
		tmp = t_1;
	elseif (i <= 5e+124)
		tmp = t_2;
	elseif (i <= 1.2e+150)
		tmp = t_1;
	elseif (i <= 1.02e+226)
		tmp = i * (t * b);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.2e+106], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e-177], t$95$2, If[LessEqual[i, 1.95e+31], t$95$1, If[LessEqual[i, 5e+124], t$95$2, If[LessEqual[i, 1.2e+150], t$95$1, If[LessEqual[i, 1.02e+226], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -7.2000000000000002e106

   1. Initial program 70.2%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

      4. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in x around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. *-commutative 68.2%

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

      3. distribute-rgt-neg-in 68.2%

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

   8. Simplified 68.2%

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

   if -7.2000000000000002e106 < i < 1.7e-177 or 1.95e31 < i < 4.9999999999999996e124

   1. Initial program 78.4%

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

   3. Taylor expanded in a around inf 47.0%

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

      1. +-commutative 47.0%

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

      2. mul-1-neg 47.0%

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

      3. unsub-neg 47.0%

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

      4. *-commutative 47.0%

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

      5. *-commutative 47.0%

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

   5. Simplified 47.0%

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

   if 1.7e-177 < i < 1.95e31 or 4.9999999999999996e124 < i < 1.20000000000000001e150

   1. Initial program 77.7%

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

      1. prod-diff 71.1%

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

      2. *-commutative 71.1%

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

      3. fma-neg 71.1%

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

      4. distribute-rgt-in 66.6%

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

      5. *-commutative 66.6%

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

      6. fma-neg 66.6%

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

      7. distribute-rgt-neg-in 66.6%

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

   4. Applied egg-rr 66.6%

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

   5. Taylor expanded in b around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. *-commutative 56.7%

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

   7. Simplified 56.7%

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

   8. Taylor expanded in t around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. *-commutative 46.8%

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

      3. distribute-rgt-neg-in 46.8%

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

   10. Simplified 46.8%

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

   if 1.20000000000000001e150 < i < 1.02e226

   1. Initial program 59.2%

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

   3. Taylor expanded in a around -inf 65.3%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in i around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. mul-1-neg 88.6%

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

      3. unsub-neg 88.6%

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

      4. *-commutative 88.6%

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

   8. Simplified 88.6%

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

   9. Taylor expanded in t around inf 54.3%

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

       1. *-commutative 54.3%

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

   11. Simplified 54.3%

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

   if 1.02e226 < i

   1. Initial program 63.1%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in x around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-177}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.8 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -9.8e+102)
     t_2
     (if (<= j -2.6e+44)
       t_1
       (if (<= j -1.05e-32)
         (* i (- (* t b) (* y j)))
         (if (<= j 2.4e-222)
           (* x (- (* y z) (* t a)))
           (if (<= j 1.15e+52) 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));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.8e+102) {
		tmp = t_2;
	} else if (j <= -2.6e+44) {
		tmp = t_1;
	} else if (j <= -1.05e-32) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 2.4e-222) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.15e+52) {
		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))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-9.8d+102)) then
        tmp = t_2
    else if (j <= (-2.6d+44)) then
        tmp = t_1
    else if (j <= (-1.05d-32)) then
        tmp = i * ((t * b) - (y * j))
    else if (j <= 2.4d-222) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 1.15d+52) 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));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.8e+102) {
		tmp = t_2;
	} else if (j <= -2.6e+44) {
		tmp = t_1;
	} else if (j <= -1.05e-32) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 2.4e-222) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.15e+52) {
		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))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -9.8e+102:
		tmp = t_2
	elif j <= -2.6e+44:
		tmp = t_1
	elif j <= -1.05e-32:
		tmp = i * ((t * b) - (y * j))
	elif j <= 2.4e-222:
		tmp = x * ((y * z) - (t * a))
	elif j <= 1.15e+52:
		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(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -9.8e+102)
		tmp = t_2;
	elseif (j <= -2.6e+44)
		tmp = t_1;
	elseif (j <= -1.05e-32)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (j <= 2.4e-222)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 1.15e+52)
		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));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -9.8e+102)
		tmp = t_2;
	elseif (j <= -2.6e+44)
		tmp = t_1;
	elseif (j <= -1.05e-32)
		tmp = i * ((t * b) - (y * j));
	elseif (j <= 2.4e-222)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 1.15e+52)
		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[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.8e+102], t$95$2, If[LessEqual[j, -2.6e+44], t$95$1, If[LessEqual[j, -1.05e-32], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e-222], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e+52], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.80000000000000089e102 or 1.15e52 < j

   1. Initial program 75.1%

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

      1. prod-diff 72.8%

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

      2. *-commutative 72.8%

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

      3. fma-neg 72.8%

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

      4. distribute-rgt-in 72.8%

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

      5. *-commutative 72.8%

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

      6. fma-neg 72.8%

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

      7. distribute-rgt-neg-in 72.8%

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

   4. Applied egg-rr 72.8%

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

   5. Taylor expanded in j around inf 72.4%

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

      1. sub-neg 72.4%

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

      2. *-commutative 72.4%

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

      3. sub-neg 72.4%

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

   7. Simplified 72.4%

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

   if -9.80000000000000089e102 < j < -2.5999999999999999e44 or 2.39999999999999993e-222 < j < 1.15e52

   1. Initial program 70.6%

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

   3. Taylor expanded in b around inf 56.3%

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

   if -2.5999999999999999e44 < j < -1.05e-32

   1. Initial program 91.7%

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

   3. Taylor expanded in a around -inf 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in i around inf 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. *-commutative 83.6%

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

   8. Simplified 83.6%

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

   if -1.05e-32 < j < 2.39999999999999993e-222

   1. Initial program 74.3%

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

   3. Taylor expanded in a around -inf 78.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in x around inf 50.8%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.8 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+30}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -2.35e+30)
     t_3
     (if (<= y -4.6e-86)
       t_2
       (if (<= y 1.65e-100)
         t_1
         (if (<= y 8.2e-71) t_2 (if (<= y 6.5e+49) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.35e+30) {
		tmp = t_3;
	} else if (y <= -4.6e-86) {
		tmp = t_2;
	} else if (y <= 1.65e-100) {
		tmp = t_1;
	} else if (y <= 8.2e-71) {
		tmp = t_2;
	} else if (y <= 6.5e+49) {
		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 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-2.35d+30)) then
        tmp = t_3
    else if (y <= (-4.6d-86)) then
        tmp = t_2
    else if (y <= 1.65d-100) then
        tmp = t_1
    else if (y <= 8.2d-71) then
        tmp = t_2
    else if (y <= 6.5d+49) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.35e+30) {
		tmp = t_3;
	} else if (y <= -4.6e-86) {
		tmp = t_2;
	} else if (y <= 1.65e-100) {
		tmp = t_1;
	} else if (y <= 8.2e-71) {
		tmp = t_2;
	} else if (y <= 6.5e+49) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.35e+30:
		tmp = t_3
	elif y <= -4.6e-86:
		tmp = t_2
	elif y <= 1.65e-100:
		tmp = t_1
	elif y <= 8.2e-71:
		tmp = t_2
	elif y <= 6.5e+49:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.35e+30)
		tmp = t_3;
	elseif (y <= -4.6e-86)
		tmp = t_2;
	elseif (y <= 1.65e-100)
		tmp = t_1;
	elseif (y <= 8.2e-71)
		tmp = t_2;
	elseif (y <= 6.5e+49)
		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 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.35e+30)
		tmp = t_3;
	elseif (y <= -4.6e-86)
		tmp = t_2;
	elseif (y <= 1.65e-100)
		tmp = t_1;
	elseif (y <= 8.2e-71)
		tmp = t_2;
	elseif (y <= 6.5e+49)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.35e+30], t$95$3, If[LessEqual[y, -4.6e-86], t$95$2, If[LessEqual[y, 1.65e-100], t$95$1, If[LessEqual[y, 8.2e-71], t$95$2, If[LessEqual[y, 6.5e+49], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.34999999999999995e30 or 6.5000000000000005e49 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 70.0%

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

      1. +-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   if -2.34999999999999995e30 < y < -4.59999999999999992e-86 or 1.64999999999999998e-100 < y < 8.19999999999999987e-71

   1. Initial program 86.2%

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

   3. Taylor expanded in a around -inf 83.3%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in x around inf 63.7%

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

   if -4.59999999999999992e-86 < y < 1.64999999999999998e-100 or 8.19999999999999987e-71 < y < 6.5000000000000005e49

   1. Initial program 77.7%

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

   3. Taylor expanded in b around inf 58.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;i \leq -2.25 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))) (t_2 (* b (* z (- c)))))
   (if (<= i -2.25e+17)
     t_1
     (if (<= i -4.5e-74)
       (* a (* t (- x)))
       (if (<= i -1.25e-298)
         t_2
         (if (<= i 4.8e-234) (* y (* x z)) (if (<= i 5.5e+47) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double t_2 = b * (z * -c);
	double tmp;
	if (i <= -2.25e+17) {
		tmp = t_1;
	} else if (i <= -4.5e-74) {
		tmp = a * (t * -x);
	} else if (i <= -1.25e-298) {
		tmp = t_2;
	} else if (i <= 4.8e-234) {
		tmp = y * (x * z);
	} else if (i <= 5.5e+47) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (i * -j)
    t_2 = b * (z * -c)
    if (i <= (-2.25d+17)) then
        tmp = t_1
    else if (i <= (-4.5d-74)) then
        tmp = a * (t * -x)
    else if (i <= (-1.25d-298)) then
        tmp = t_2
    else if (i <= 4.8d-234) then
        tmp = y * (x * z)
    else if (i <= 5.5d+47) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double t_2 = b * (z * -c);
	double tmp;
	if (i <= -2.25e+17) {
		tmp = t_1;
	} else if (i <= -4.5e-74) {
		tmp = a * (t * -x);
	} else if (i <= -1.25e-298) {
		tmp = t_2;
	} else if (i <= 4.8e-234) {
		tmp = y * (x * z);
	} else if (i <= 5.5e+47) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = b * (z * -c)
	tmp = 0
	if i <= -2.25e+17:
		tmp = t_1
	elif i <= -4.5e-74:
		tmp = a * (t * -x)
	elif i <= -1.25e-298:
		tmp = t_2
	elif i <= 4.8e-234:
		tmp = y * (x * z)
	elif i <= 5.5e+47:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	t_2 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (i <= -2.25e+17)
		tmp = t_1;
	elseif (i <= -4.5e-74)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= -1.25e-298)
		tmp = t_2;
	elseif (i <= 4.8e-234)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 5.5e+47)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	t_2 = b * (z * -c);
	tmp = 0.0;
	if (i <= -2.25e+17)
		tmp = t_1;
	elseif (i <= -4.5e-74)
		tmp = a * (t * -x);
	elseif (i <= -1.25e-298)
		tmp = t_2;
	elseif (i <= 4.8e-234)
		tmp = y * (x * z);
	elseif (i <= 5.5e+47)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.25e+17], t$95$1, If[LessEqual[i, -4.5e-74], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.25e-298], t$95$2, If[LessEqual[i, 4.8e-234], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+47], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.25e17 or 5.4999999999999998e47 < i

   1. Initial program 65.2%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in x around 0 50.5%

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

      1. mul-1-neg 50.5%

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

      2. *-commutative 50.5%

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

      3. distribute-rgt-neg-in 50.5%

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

   8. Simplified 50.5%

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

   if -2.25e17 < i < -4.4999999999999999e-74

   1. Initial program 88.2%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

      5. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in j around 0 54.6%

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

      1. associate-*r* 54.6%

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

      2. mul-1-neg 54.6%

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

   8. Simplified 54.6%

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

   if -4.4999999999999999e-74 < i < -1.25000000000000005e-298 or 4.7999999999999998e-234 < i < 5.4999999999999998e47

   1. Initial program 82.8%

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

      1. prod-diff 78.8%

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

      2. *-commutative 78.8%

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

      3. fma-neg 78.8%

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

      4. distribute-rgt-in 76.8%

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

      5. *-commutative 76.8%

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

      6. fma-neg 76.8%

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

      7. distribute-rgt-neg-in 76.8%

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

   4. Applied egg-rr 76.8%

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

   5. Taylor expanded in b around inf 47.0%

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

      1. *-commutative 47.0%

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

      2. *-commutative 47.0%

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

   7. Simplified 47.0%

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

   8. Taylor expanded in t around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. *-commutative 37.2%

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

      3. distribute-rgt-neg-in 37.2%

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

   10. Simplified 37.2%

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

   if -1.25000000000000005e-298 < i < 4.7999999999999998e-234

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in x around inf 58.1%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.25 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-298}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= i -4e+14)
     (* y (* i (- j)))
     (if (<= i -6.4e-74)
       (* a (* t (- x)))
       (if (<= i -6e-300)
         t_1
         (if (<= i 7.5e-236)
           (* y (* x z))
           (if (<= i 5.2e+49) t_1 (* 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 t_1 = b * (z * -c);
	double tmp;
	if (i <= -4e+14) {
		tmp = y * (i * -j);
	} else if (i <= -6.4e-74) {
		tmp = a * (t * -x);
	} else if (i <= -6e-300) {
		tmp = t_1;
	} else if (i <= 7.5e-236) {
		tmp = y * (x * z);
	} else if (i <= 5.2e+49) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = b * (z * -c)
    if (i <= (-4d+14)) then
        tmp = y * (i * -j)
    else if (i <= (-6.4d-74)) then
        tmp = a * (t * -x)
    else if (i <= (-6d-300)) then
        tmp = t_1
    else if (i <= 7.5d-236) then
        tmp = y * (x * z)
    else if (i <= 5.2d+49) then
        tmp = t_1
    else
        tmp = 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 t_1 = b * (z * -c);
	double tmp;
	if (i <= -4e+14) {
		tmp = y * (i * -j);
	} else if (i <= -6.4e-74) {
		tmp = a * (t * -x);
	} else if (i <= -6e-300) {
		tmp = t_1;
	} else if (i <= 7.5e-236) {
		tmp = y * (x * z);
	} else if (i <= 5.2e+49) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if i <= -4e+14:
		tmp = y * (i * -j)
	elif i <= -6.4e-74:
		tmp = a * (t * -x)
	elif i <= -6e-300:
		tmp = t_1
	elif i <= 7.5e-236:
		tmp = y * (x * z)
	elif i <= 5.2e+49:
		tmp = t_1
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (i <= -4e+14)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -6.4e-74)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= -6e-300)
		tmp = t_1;
	elseif (i <= 7.5e-236)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 5.2e+49)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (i <= -4e+14)
		tmp = y * (i * -j);
	elseif (i <= -6.4e-74)
		tmp = a * (t * -x);
	elseif (i <= -6e-300)
		tmp = t_1;
	elseif (i <= 7.5e-236)
		tmp = y * (x * z);
	elseif (i <= 5.2e+49)
		tmp = t_1;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+14], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.4e-74], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6e-300], t$95$1, If[LessEqual[i, 7.5e-236], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+49], t$95$1, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4e14

   1. Initial program 71.0%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in x around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. *-commutative 58.2%

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

      3. distribute-rgt-neg-in 58.2%

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

   8. Simplified 58.2%

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

   if -4e14 < i < -6.3999999999999997e-74

   1. Initial program 88.2%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

      5. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in j around 0 54.6%

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

      1. associate-*r* 54.6%

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

      2. mul-1-neg 54.6%

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

   8. Simplified 54.6%

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

   if -6.3999999999999997e-74 < i < -6.00000000000000048e-300 or 7.4999999999999997e-236 < i < 5.19999999999999977e49

   1. Initial program 82.8%

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

      1. prod-diff 78.8%

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

      2. *-commutative 78.8%

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

      3. fma-neg 78.8%

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

      4. distribute-rgt-in 76.8%

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

      5. *-commutative 76.8%

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

      6. fma-neg 76.8%

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

      7. distribute-rgt-neg-in 76.8%

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

   4. Applied egg-rr 76.8%

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

   5. Taylor expanded in b around inf 47.0%

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

      1. *-commutative 47.0%

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

      2. *-commutative 47.0%

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

   7. Simplified 47.0%

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

   8. Taylor expanded in t around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. *-commutative 37.2%

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

      3. distribute-rgt-neg-in 37.2%

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

   10. Simplified 37.2%

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

   if -6.00000000000000048e-300 < i < 7.4999999999999997e-236

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in x around inf 58.1%

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

   if 5.19999999999999977e49 < i

   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. Add Preprocessing

   3. Taylor expanded in y around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in x around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. *-commutative 43.3%

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

      3. distribute-rgt-neg-in 43.3%

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

   8. Simplified 43.3%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+46}:\\ \;\;\;\;t\_1 + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + \left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -4.1e+46)
     (+ t_1 (* a (- (* c j) (* x t))))
     (if (<= y 9e+120)
       (+ (* b (- (* t i) (* z c))) (- (* a (* c j)) (* a (* x t))))
       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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.1e+46) {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	} else if (y <= 9e+120) {
		tmp = (b * ((t * i) - (z * c))) + ((a * (c * j)) - (a * (x * t)));
	} 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 = y * ((x * z) - (i * j))
    if (y <= (-4.1d+46)) then
        tmp = t_1 + (a * ((c * j) - (x * t)))
    else if (y <= 9d+120) then
        tmp = (b * ((t * i) - (z * c))) + ((a * (c * j)) - (a * (x * t)))
    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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.1e+46) {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	} else if (y <= 9e+120) {
		tmp = (b * ((t * i) - (z * c))) + ((a * (c * j)) - (a * (x * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.1e+46:
		tmp = t_1 + (a * ((c * j) - (x * t)))
	elif y <= 9e+120:
		tmp = (b * ((t * i) - (z * c))) + ((a * (c * j)) - (a * (x * t)))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (y <= -4.1e+46)
		tmp = Float64(t_1 + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	elseif (y <= 9e+120)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(Float64(a * Float64(c * j)) - Float64(a * Float64(x * t))));
	else
		tmp = t_1;
	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));
	tmp = 0.0;
	if (y <= -4.1e+46)
		tmp = t_1 + (a * ((c * j) - (x * t)));
	elseif (y <= 9e+120)
		tmp = (b * ((t * i) - (z * c))) + ((a * (c * j)) - (a * (x * t)));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+46], N[(t$95$1 + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+120], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1e46

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 69.3%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in b around 0 79.2%

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

   if -4.1e46 < y < 8.99999999999999953e120

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 70.1%

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

   if 8.99999999999999953e120 < y

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 82.3%

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

      1. +-commutative 82.3%

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

      2. mul-1-neg 82.3%

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

      3. unsub-neg 82.3%

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

      4. *-commutative 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + \left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -5 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -5e-37)
     t_1
     (if (<= j -2.35e-153)
       (* y (* x z))
       (if (<= j 4.4e-102)
         (* x (* t (- a)))
         (if (<= j 2.1e+52) (* 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 = y * (i * -j);
	double tmp;
	if (j <= -5e-37) {
		tmp = t_1;
	} else if (j <= -2.35e-153) {
		tmp = y * (x * z);
	} else if (j <= 4.4e-102) {
		tmp = x * (t * -a);
	} else if (j <= 2.1e+52) {
		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 = y * (i * -j)
    if (j <= (-5d-37)) then
        tmp = t_1
    else if (j <= (-2.35d-153)) then
        tmp = y * (x * z)
    else if (j <= 4.4d-102) then
        tmp = x * (t * -a)
    else if (j <= 2.1d+52) 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 = y * (i * -j);
	double tmp;
	if (j <= -5e-37) {
		tmp = t_1;
	} else if (j <= -2.35e-153) {
		tmp = y * (x * z);
	} else if (j <= 4.4e-102) {
		tmp = x * (t * -a);
	} else if (j <= 2.1e+52) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if j <= -5e-37:
		tmp = t_1
	elif j <= -2.35e-153:
		tmp = y * (x * z)
	elif j <= 4.4e-102:
		tmp = x * (t * -a)
	elif j <= 2.1e+52:
		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(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -5e-37)
		tmp = t_1;
	elseif (j <= -2.35e-153)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 4.4e-102)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 2.1e+52)
		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 = y * (i * -j);
	tmp = 0.0;
	if (j <= -5e-37)
		tmp = t_1;
	elseif (j <= -2.35e-153)
		tmp = y * (x * z);
	elseif (j <= 4.4e-102)
		tmp = x * (t * -a);
	elseif (j <= 2.1e+52)
		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[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5e-37], t$95$1, If[LessEqual[j, -2.35e-153], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-102], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.1e+52], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.9999999999999997e-37 or 2.1e52 < j

   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. Add Preprocessing

   3. Taylor expanded in y around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in x around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. *-commutative 51.3%

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

      3. distribute-rgt-neg-in 51.3%

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

   8. Simplified 51.3%

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

   if -4.9999999999999997e-37 < j < -2.35e-153

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in x around inf 42.1%

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

   if -2.35e-153 < j < 4.40000000000000026e-102

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 78.2%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x around inf 46.3%

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

   7. Taylor expanded in y around 0 32.7%

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

      1. neg-mul-1 32.7%

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

      2. distribute-rgt-neg-in 32.7%

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

   9. Simplified 32.7%

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

   if 4.40000000000000026e-102 < j < 2.1e52

   1. Initial program 72.2%

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

   3. Taylor expanded in a around -inf 74.5%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in i around inf 42.6%

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

      1. +-commutative 42.6%

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

      2. mul-1-neg 42.6%

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

      3. unsub-neg 42.6%

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

      4. *-commutative 42.6%

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

   8. Simplified 42.6%

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

   9. Taylor expanded in t around inf 30.8%

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

       1. *-commutative 30.8%

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

   11. Simplified 30.8%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -2.8e+35)
     t_1
     (if (<= z 2.25e-99)
       (* b (* t i))
       (if (<= z 3.6e+36)
         (* a (* c j))
         (if (<= z 3.2e+82) (* 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 = x * (y * z);
	double tmp;
	if (z <= -2.8e+35) {
		tmp = t_1;
	} else if (z <= 2.25e-99) {
		tmp = b * (t * i);
	} else if (z <= 3.6e+36) {
		tmp = a * (c * j);
	} else if (z <= 3.2e+82) {
		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 = x * (y * z)
    if (z <= (-2.8d+35)) then
        tmp = t_1
    else if (z <= 2.25d-99) then
        tmp = b * (t * i)
    else if (z <= 3.6d+36) then
        tmp = a * (c * j)
    else if (z <= 3.2d+82) 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 = x * (y * z);
	double tmp;
	if (z <= -2.8e+35) {
		tmp = t_1;
	} else if (z <= 2.25e-99) {
		tmp = b * (t * i);
	} else if (z <= 3.6e+36) {
		tmp = a * (c * j);
	} else if (z <= 3.2e+82) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -2.8e+35:
		tmp = t_1
	elif z <= 2.25e-99:
		tmp = b * (t * i)
	elif z <= 3.6e+36:
		tmp = a * (c * j)
	elif z <= 3.2e+82:
		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(x * Float64(y * z))
	tmp = 0.0
	if (z <= -2.8e+35)
		tmp = t_1;
	elseif (z <= 2.25e-99)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 3.6e+36)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 3.2e+82)
		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 = x * (y * z);
	tmp = 0.0;
	if (z <= -2.8e+35)
		tmp = t_1;
	elseif (z <= 2.25e-99)
		tmp = b * (t * i);
	elseif (z <= 3.6e+36)
		tmp = a * (c * j);
	elseif (z <= 3.2e+82)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+35], t$95$1, If[LessEqual[z, 2.25e-99], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+36], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+82], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.79999999999999999e35 or 3.19999999999999975e82 < z

   1. Initial program 65.5%

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

   3. Taylor expanded in y around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in x around inf 40.6%

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

   if -2.79999999999999999e35 < z < 2.2500000000000001e-99

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 83.5%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in i around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in t around inf 31.8%

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

       1. *-commutative 31.8%

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

   11. Simplified 31.8%

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

   if 2.2500000000000001e-99 < z < 3.5999999999999997e36

   1. Initial program 77.0%

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

   3. Taylor expanded in a around inf 44.2%

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

      1. +-commutative 44.2%

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

      2. mul-1-neg 44.2%

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

      3. unsub-neg 44.2%

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

      4. *-commutative 44.2%

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

      5. *-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in j around inf 33.3%

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

   if 3.5999999999999997e36 < z < 3.19999999999999975e82

   1. Initial program 70.7%

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

   3. Taylor expanded in a around -inf 70.7%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in i around inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

      4. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in t around inf 41.0%

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

       1. *-commutative 41.0%

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

   11. Simplified 41.0%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -3.1e+35)
     t_1
     (if (<= z 1.2e-99)
       (* t (* b i))
       (if (<= z 6.4e+35)
         (* a (* c j))
         (if (<= z 1.8e+82) (* 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 = x * (y * z);
	double tmp;
	if (z <= -3.1e+35) {
		tmp = t_1;
	} else if (z <= 1.2e-99) {
		tmp = t * (b * i);
	} else if (z <= 6.4e+35) {
		tmp = a * (c * j);
	} else if (z <= 1.8e+82) {
		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 = x * (y * z)
    if (z <= (-3.1d+35)) then
        tmp = t_1
    else if (z <= 1.2d-99) then
        tmp = t * (b * i)
    else if (z <= 6.4d+35) then
        tmp = a * (c * j)
    else if (z <= 1.8d+82) 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 = x * (y * z);
	double tmp;
	if (z <= -3.1e+35) {
		tmp = t_1;
	} else if (z <= 1.2e-99) {
		tmp = t * (b * i);
	} else if (z <= 6.4e+35) {
		tmp = a * (c * j);
	} else if (z <= 1.8e+82) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -3.1e+35:
		tmp = t_1
	elif z <= 1.2e-99:
		tmp = t * (b * i)
	elif z <= 6.4e+35:
		tmp = a * (c * j)
	elif z <= 1.8e+82:
		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(x * Float64(y * z))
	tmp = 0.0
	if (z <= -3.1e+35)
		tmp = t_1;
	elseif (z <= 1.2e-99)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 6.4e+35)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 1.8e+82)
		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 = x * (y * z);
	tmp = 0.0;
	if (z <= -3.1e+35)
		tmp = t_1;
	elseif (z <= 1.2e-99)
		tmp = t * (b * i);
	elseif (z <= 6.4e+35)
		tmp = a * (c * j);
	elseif (z <= 1.8e+82)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+35], t$95$1, If[LessEqual[z, 1.2e-99], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+35], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+82], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.09999999999999987e35 or 1.80000000000000007e82 < z

   1. Initial program 65.5%

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

   3. Taylor expanded in y around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in x around inf 40.6%

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

   if -3.09999999999999987e35 < z < 1.2e-99

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 83.5%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in i around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in t around inf 31.8%

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

       1. associate-*r* 32.6%

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

       2. *-commutative 32.6%

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

   11. Simplified 32.6%

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

   if 1.2e-99 < z < 6.39999999999999965e35

   1. Initial program 77.0%

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

   3. Taylor expanded in a around inf 44.2%

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

      1. +-commutative 44.2%

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

      2. mul-1-neg 44.2%

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

      3. unsub-neg 44.2%

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

      4. *-commutative 44.2%

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

      5. *-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in j around inf 33.3%

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

   if 6.39999999999999965e35 < z < 1.80000000000000007e82

   1. Initial program 70.7%

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

   3. Taylor expanded in a around -inf 70.7%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in i around inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

      4. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in t around inf 41.0%

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

       1. *-commutative 41.0%

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

   11. Simplified 41.0%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -1.95e+90)
     t_1
     (if (<= t 3.8e-34)
       (* c (- (* a j) (* z b)))
       (if (<= t 5.8e+23) (* i (- (* t b) (* y j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.95e+90) {
		tmp = t_1;
	} else if (t <= 3.8e-34) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 5.8e+23) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-1.95d+90)) then
        tmp = t_1
    else if (t <= 3.8d-34) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 5.8d+23) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.95e+90) {
		tmp = t_1;
	} else if (t <= 3.8e-34) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 5.8e+23) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.95e+90:
		tmp = t_1
	elif t <= 3.8e-34:
		tmp = c * ((a * j) - (z * b))
	elif t <= 5.8e+23:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (t <= -1.95e+90)
		tmp = t_1;
	elseif (t <= 3.8e-34)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 5.8e+23)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.95e+90)
		tmp = t_1;
	elseif (t <= 3.8e-34)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 5.8e+23)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e+90], t$95$1, If[LessEqual[t, 3.8e-34], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+23], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9500000000000001e90 or 5.80000000000000025e23 < t

   1. Initial program 62.9%

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

   3. Taylor expanded in a around -inf 62.8%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in t around inf 67.1%

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

      1. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   if -1.9500000000000001e90 < t < 3.8000000000000001e-34

   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. Add Preprocessing

   3. Taylor expanded in c around inf 46.6%

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

   if 3.8000000000000001e-34 < t < 5.80000000000000025e23

   1. Initial program 62.3%

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

   3. Taylor expanded in a around -inf 68.6%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in i around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

      4. *-commutative 63.7%

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

   8. Simplified 63.7%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -2.4e-33)
     t_1
     (if (<= j -3.7e-159)
       (* y (* x z))
       (if (<= j 3.5e-25) (* a (* t (- x))) 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 = y * (i * -j);
	double tmp;
	if (j <= -2.4e-33) {
		tmp = t_1;
	} else if (j <= -3.7e-159) {
		tmp = y * (x * z);
	} else if (j <= 3.5e-25) {
		tmp = a * (t * -x);
	} 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 = y * (i * -j)
    if (j <= (-2.4d-33)) then
        tmp = t_1
    else if (j <= (-3.7d-159)) then
        tmp = y * (x * z)
    else if (j <= 3.5d-25) then
        tmp = a * (t * -x)
    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 = y * (i * -j);
	double tmp;
	if (j <= -2.4e-33) {
		tmp = t_1;
	} else if (j <= -3.7e-159) {
		tmp = y * (x * z);
	} else if (j <= 3.5e-25) {
		tmp = a * (t * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if j <= -2.4e-33:
		tmp = t_1
	elif j <= -3.7e-159:
		tmp = y * (x * z)
	elif j <= 3.5e-25:
		tmp = a * (t * -x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -2.4e-33)
		tmp = t_1;
	elseif (j <= -3.7e-159)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 3.5e-25)
		tmp = Float64(a * Float64(t * Float64(-x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	tmp = 0.0;
	if (j <= -2.4e-33)
		tmp = t_1;
	elseif (j <= -3.7e-159)
		tmp = y * (x * z);
	elseif (j <= 3.5e-25)
		tmp = a * (t * -x);
	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[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.4e-33], t$95$1, If[LessEqual[j, -3.7e-159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-25], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.4e-33 or 3.5000000000000002e-25 < j

   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. Add Preprocessing

   3. Taylor expanded in y around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in x around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

   8. Simplified 47.3%

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

   if -2.4e-33 < j < -3.6999999999999999e-159

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in x around inf 42.1%

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

   if -3.6999999999999999e-159 < j < 3.5000000000000002e-25

   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. Add Preprocessing

   3. Taylor expanded in a around inf 35.5%

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

      1. +-commutative 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. *-commutative 35.5%

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

      5. *-commutative 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in j around 0 31.9%

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

      1. associate-*r* 31.9%

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

      2. mul-1-neg 31.9%

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

   8. Simplified 31.9%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 31.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -520000000000 \lor \neg \left(t \leq 2.9 \cdot 10^{-21}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -520000000000.0) (not (<= t 2.9e-21)))
   (* b (* t i))
   (* a (* c 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 <= -520000000000.0) || !(t <= 2.9e-21)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * 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 <= (-520000000000.0d0)) .or. (.not. (t <= 2.9d-21))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * 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 <= -520000000000.0) || !(t <= 2.9e-21)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -520000000000.0) or not (t <= 2.9e-21):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -520000000000.0) || !(t <= 2.9e-21))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -520000000000.0) || ~((t <= 2.9e-21)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -520000000000.0], N[Not[LessEqual[t, 2.9e-21]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e11 or 2.9e-21 < t

   1. Initial program 66.9%

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

   3. Taylor expanded in a around -inf 67.6%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in i around inf 45.9%

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

      1. +-commutative 45.9%

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

      2. mul-1-neg 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   9. Taylor expanded in t around inf 34.0%

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

       1. *-commutative 34.0%

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

   11. Simplified 34.0%

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

   if -5.2e11 < t < 2.9e-21

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 29.3%

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

      1. +-commutative 29.3%

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

      2. mul-1-neg 29.3%

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

      3. unsub-neg 29.3%

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

      4. *-commutative 29.3%

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

      5. *-commutative 29.3%

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

   5. Simplified 29.3%

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

   6. Taylor expanded in j around inf 26.0%

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

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -520000000000 \lor \neg \left(t \leq 2.9 \cdot 10^{-21}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -65000000000000:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -65000000000000.0)
   (* i (* t b))
   (if (<= t 6.1e-21) (* 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 (t <= -65000000000000.0) {
		tmp = i * (t * b);
	} else if (t <= 6.1e-21) {
		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 (t <= (-65000000000000.0d0)) then
        tmp = i * (t * b)
    else if (t <= 6.1d-21) 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 (t <= -65000000000000.0) {
		tmp = i * (t * b);
	} else if (t <= 6.1e-21) {
		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 t <= -65000000000000.0:
		tmp = i * (t * b)
	elif t <= 6.1e-21:
		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 (t <= -65000000000000.0)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 6.1e-21)
		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 (t <= -65000000000000.0)
		tmp = i * (t * b);
	elseif (t <= 6.1e-21)
		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[LessEqual[t, -65000000000000.0], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e-21], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5e13

   1. Initial program 72.5%

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

   3. Taylor expanded in a around -inf 72.4%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in i around inf 39.6%

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

      1. +-commutative 39.6%

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

      2. mul-1-neg 39.6%

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

      3. unsub-neg 39.6%

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

      4. *-commutative 39.6%

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

   8. Simplified 39.6%

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

   9. Taylor expanded in t around inf 29.3%

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

       1. *-commutative 29.3%

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

   11. Simplified 29.3%

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

   if -6.5e13 < t < 6.10000000000000013e-21

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 29.3%

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

      1. +-commutative 29.3%

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

      2. mul-1-neg 29.3%

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

      3. unsub-neg 29.3%

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

      4. *-commutative 29.3%

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

      5. *-commutative 29.3%

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

   5. Simplified 29.3%

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

   6. Taylor expanded in j around inf 26.0%

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

   if 6.10000000000000013e-21 < t

   1. Initial program 63.0%

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

   3. Taylor expanded in a around -inf 64.2%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in i around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

   8. Simplified 50.4%

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

   9. Taylor expanded in t around inf 38.6%

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

       1. *-commutative 38.6%

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

   11. Simplified 38.6%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -65000000000000:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.2% 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 74.3%

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

3. Taylor expanded in a around inf 35.1%

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

   1. +-commutative 35.1%

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

   2. mul-1-neg 35.1%

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

   3. unsub-neg 35.1%

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

   4. *-commutative 35.1%

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

   5. *-commutative 35.1%

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

5. Simplified 35.1%

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

6. Taylor expanded in j around inf 18.9%

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

7. Final simplification 18.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 59.1% 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 2024027 
(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)))))