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

Percentage Accurate: 73.0% → 75.8%

Time: 26.9s

Alternatives: 23

Speedup: 0.5×

• 58.0% 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: 73.0% 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: 75.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, i \cdot b\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \left(\left(\mathsf{fma}\left(x, y, \left(c \cdot a - y \cdot i\right) \cdot \frac{j}{z}\right) + \frac{t \cdot t\_1}{z}\right) - c \cdot b\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-158}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-50}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(t, \frac{t\_1}{z}, \mathsf{fma}\left(x, y, \frac{j}{z} \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)\right)\right) - c \cdot b\right)}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- a) x (* i b))))
   (if (<= z -1.5e-107)
     (*
      z
      (-
       (+ (fma x y (* (- (* c a) (* y i)) (/ j z))) (/ (* t t_1) z))
       (* c b)))
     (if (<= z 6.4e-158)
       (- (* t (- (* i b) (* x a))) (* j (- (* y i) (* c a))))
       (if (<= z 6.8e-50)
         (+ (- (* a (* c j)) (* a (* x t))) (* b (- (* i t) (* z c))))
         (pow
          (cbrt
           (*
            z
            (-
             (fma t (/ t_1 z) (fma x y (* (/ j z) (fma c a (* i (- y))))))
             (* c b))))
          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 = fma(-a, x, (i * b));
	double tmp;
	if (z <= -1.5e-107) {
		tmp = z * ((fma(x, y, (((c * a) - (y * i)) * (j / z))) + ((t * t_1) / z)) - (c * b));
	} else if (z <= 6.4e-158) {
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	} else if (z <= 6.8e-50) {
		tmp = ((a * (c * j)) - (a * (x * t))) + (b * ((i * t) - (z * c)));
	} else {
		tmp = pow(cbrt((z * (fma(t, (t_1 / z), fma(x, y, ((j / z) * fma(c, a, (i * -y))))) - (c * b)))), 3.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-a), x, Float64(i * b))
	tmp = 0.0
	if (z <= -1.5e-107)
		tmp = Float64(z * Float64(Float64(fma(x, y, Float64(Float64(Float64(c * a) - Float64(y * i)) * Float64(j / z))) + Float64(Float64(t * t_1) / z)) - Float64(c * b)));
	elseif (z <= 6.4e-158)
		tmp = Float64(Float64(t * Float64(Float64(i * b) - Float64(x * a))) - Float64(j * Float64(Float64(y * i) - Float64(c * a))));
	elseif (z <= 6.8e-50)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(a * Float64(x * t))) + Float64(b * Float64(Float64(i * t) - Float64(z * c))));
	else
		tmp = cbrt(Float64(z * Float64(fma(t, Float64(t_1 / z), fma(x, y, Float64(Float64(j / z) * fma(c, a, Float64(i * Float64(-y)))))) - Float64(c * b)))) ^ 3.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-107], N[(z * N[(N[(N[(x * y + N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-158], N[(N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-50], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(z * N[(N[(t * N[(t$95$1 / z), $MachinePrecision] + N[(x * y + N[(N[(j / z), $MachinePrecision] * N[(c * a + N[(i * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4999999999999999e-107

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. fma-define 65.0%

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

      3. *-commutative 65.0%

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

      4. *-commutative 65.0%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in z around inf 73.6%

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

   7. Simplified 81.1%

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

   if -1.4999999999999999e-107 < z < 6.39999999999999993e-158

   1. Initial program 73.4%

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

   3. Taylor expanded in t around -inf 84.5%

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

   if 6.39999999999999993e-158 < z < 6.80000000000000029e-50

   1. Initial program 77.2%

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

      1. +-commutative 77.2%

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

      2. fma-define 77.2%

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

      3. *-commutative 77.2%

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

      4. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in y around 0 90.4%

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

   if 6.80000000000000029e-50 < z

   1. Initial program 60.7%

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

      1. +-commutative 60.7%

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

      2. fma-define 62.0%

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

      3. *-commutative 62.0%

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

      4. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in z around inf 70.4%

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

   7. Simplified 75.4%

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

      1. add-cube-cbrt 75.0%

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

      2. pow3 75.0%

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

   9. Applied egg-rr 80.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(-a, x, i \cdot b\right)}{z}, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, a, \left(-i\right) \cdot y\right) \cdot \frac{j}{z}\right)\right) - c \cdot b\right)}\right)}^{3}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \left(\left(\mathsf{fma}\left(x, y, \left(c \cdot a - y \cdot i\right) \cdot \frac{j}{z}\right) + \frac{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)}{z}\right) - c \cdot b\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-158}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-50}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(t, \frac{\mathsf{fma}\left(-a, x, i \cdot b\right)}{z}, \mathsf{fma}\left(x, y, \frac{j}{z} \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)\right)\right) - c \cdot b\right)}\right)}^{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(a * t), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 + N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(i * b), $MachinePrecision] - N[(c * N[(N[(z * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(z * N[(N[(j * N[(N[(N[(c * a), $MachinePrecision] / z), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * b), $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 78.2%

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

   3. Taylor expanded in t around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. +-commutative 84.6%

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

      3. unsub-neg 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-*l* 85.9%

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

      6. *-commutative 85.9%

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

      7. associate-/l* 85.9%

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

   5. Simplified 85.9%

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

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

   1. Initial program 86.3%

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

      1. +-commutative 0.0%

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

      2. fma-define 3.8%

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

      3. *-commutative 3.8%

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

      4. *-commutative 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 26.9%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in j around inf 52.1%

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

4. Final simplification 79.2%

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

Alternative 3: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(a * t), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(j * N[(N[(N[(c * a), $MachinePrecision] / z), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * b), $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 83.5%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 3.8%

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

      3. *-commutative 3.8%

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

      4. *-commutative 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 26.9%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in j around inf 52.1%

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

4. Final simplification 77.1%

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

Alternative 4: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a - y \cdot i\right) \cdot j\\ t_2 := t\_1 + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+140}:\\ \;\;\;\;t\_1 + x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-121}:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \left(i \cdot b - b \cdot \left(c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* c a) (* y i)) j))
        (t_2 (+ t_1 (* b (- (* i t) (* z c))))))
   (if (<= x -5.8e+140)
     (+ t_1 (* x (- (* z y) (* a t))))
     (if (<= x -6.8e-277)
       t_2
       (if (<= x 9.5e-121)
         (+ t_1 (* z (- (* x y) (* c b))))
         (if (<= x 2.3e-46)
           (* t (- (* i b) (* b (* c (/ z t)))))
           (if (<= x 4.3e+122) t_2 (* x (* z (- y (* a (/ t z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((c * a) - (y * i)) * j;
	double t_2 = t_1 + (b * ((i * t) - (z * c)));
	double tmp;
	if (x <= -5.8e+140) {
		tmp = t_1 + (x * ((z * y) - (a * t)));
	} else if (x <= -6.8e-277) {
		tmp = t_2;
	} else if (x <= 9.5e-121) {
		tmp = t_1 + (z * ((x * y) - (c * b)));
	} else if (x <= 2.3e-46) {
		tmp = t * ((i * b) - (b * (c * (z / t))));
	} else if (x <= 4.3e+122) {
		tmp = t_2;
	} else {
		tmp = x * (z * (y - (a * (t / z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((c * a) - (y * i)) * j
    t_2 = t_1 + (b * ((i * t) - (z * c)))
    if (x <= (-5.8d+140)) then
        tmp = t_1 + (x * ((z * y) - (a * t)))
    else if (x <= (-6.8d-277)) then
        tmp = t_2
    else if (x <= 9.5d-121) then
        tmp = t_1 + (z * ((x * y) - (c * b)))
    else if (x <= 2.3d-46) then
        tmp = t * ((i * b) - (b * (c * (z / t))))
    else if (x <= 4.3d+122) then
        tmp = t_2
    else
        tmp = x * (z * (y - (a * (t / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((c * a) - (y * i)) * j;
	double t_2 = t_1 + (b * ((i * t) - (z * c)));
	double tmp;
	if (x <= -5.8e+140) {
		tmp = t_1 + (x * ((z * y) - (a * t)));
	} else if (x <= -6.8e-277) {
		tmp = t_2;
	} else if (x <= 9.5e-121) {
		tmp = t_1 + (z * ((x * y) - (c * b)));
	} else if (x <= 2.3e-46) {
		tmp = t * ((i * b) - (b * (c * (z / t))));
	} else if (x <= 4.3e+122) {
		tmp = t_2;
	} else {
		tmp = x * (z * (y - (a * (t / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((c * a) - (y * i)) * j
	t_2 = t_1 + (b * ((i * t) - (z * c)))
	tmp = 0
	if x <= -5.8e+140:
		tmp = t_1 + (x * ((z * y) - (a * t)))
	elif x <= -6.8e-277:
		tmp = t_2
	elif x <= 9.5e-121:
		tmp = t_1 + (z * ((x * y) - (c * b)))
	elif x <= 2.3e-46:
		tmp = t * ((i * b) - (b * (c * (z / t))))
	elif x <= 4.3e+122:
		tmp = t_2
	else:
		tmp = x * (z * (y - (a * (t / z))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(c * a) - Float64(y * i)) * j)
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(i * t) - Float64(z * c))))
	tmp = 0.0
	if (x <= -5.8e+140)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(z * y) - Float64(a * t))));
	elseif (x <= -6.8e-277)
		tmp = t_2;
	elseif (x <= 9.5e-121)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(c * b))));
	elseif (x <= 2.3e-46)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(b * Float64(c * Float64(z / t)))));
	elseif (x <= 4.3e+122)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(z * Float64(y - Float64(a * Float64(t / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((c * a) - (y * i)) * j;
	t_2 = t_1 + (b * ((i * t) - (z * c)));
	tmp = 0.0;
	if (x <= -5.8e+140)
		tmp = t_1 + (x * ((z * y) - (a * t)));
	elseif (x <= -6.8e-277)
		tmp = t_2;
	elseif (x <= 9.5e-121)
		tmp = t_1 + (z * ((x * y) - (c * b)));
	elseif (x <= 2.3e-46)
		tmp = t * ((i * b) - (b * (c * (z / t))));
	elseif (x <= 4.3e+122)
		tmp = t_2;
	else
		tmp = x * (z * (y - (a * (t / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+140], N[(t$95$1 + N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.8e-277], t$95$2, If[LessEqual[x, 9.5e-121], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-46], N[(t * N[(N[(i * b), $MachinePrecision] - N[(b * N[(c * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+122], t$95$2, N[(x * N[(z * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.7999999999999998e140

   1. Initial program 74.0%

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

      1. +-commutative 74.0%

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

      2. fma-define 74.0%

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

      3. *-commutative 74.0%

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

      4. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in b around 0 85.6%

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

   if -5.7999999999999998e140 < x < -6.79999999999999964e-277 or 2.2999999999999999e-46 < x < 4.29999999999999971e122

   1. Initial program 73.9%

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

      1. +-commutative 73.9%

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

      2. fma-define 74.8%

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

      3. *-commutative 74.8%

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

      4. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in x around 0 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   if -6.79999999999999964e-277 < x < 9.4999999999999994e-121

   1. Initial program 60.6%

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

   3. Taylor expanded in z around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   if 9.4999999999999994e-121 < x < 2.2999999999999999e-46

   1. Initial program 42.4%

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

      1. +-commutative 42.4%

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

      2. fma-define 42.4%

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

      3. *-commutative 42.4%

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

      4. *-commutative 42.4%

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

   3. Simplified 42.4%

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

   5. Taylor expanded in z around inf 73.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in b around inf 67.5%

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

   9. Taylor expanded in t around -inf 61.9%

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

       1. mul-1-neg 61.9%

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

       2. *-commutative 61.9%

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

       3. distribute-rgt-neg-in 61.9%

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

       4. +-commutative 61.9%

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

       5. mul-1-neg 61.9%

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

       6. unsub-neg 61.9%

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

       7. associate-/l* 61.9%

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

       8. associate-/l* 80.6%

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

   11. Simplified 80.6%

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

   if 4.29999999999999971e122 < x

   1. Initial program 55.9%

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

      1. +-commutative 55.9%

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

      2. fma-define 58.7%

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

      3. *-commutative 58.7%

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

      4. *-commutative 58.7%

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

   3. Simplified 58.7%

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

   5. Taylor expanded in z around inf 51.9%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in x around -inf 66.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(z \cdot \left(-1 \cdot y + \frac{a \cdot t}{z}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 66.5%

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

      2. *-commutative 66.5%

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

      3. distribute-rgt-neg-in 66.5%

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

      4. +-commutative 66.5%

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

      5. neg-mul-1 66.5%

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

      6. unsub-neg 66.5%

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

      7. associate-/l* 72.2%

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

   10. Simplified 72.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+140}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-277}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-121}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \left(i \cdot b - b \cdot \left(c \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+122}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(j \cdot \left(\frac{c \cdot a}{z} - \frac{y \cdot i}{z}\right) - c \cdot b\right)\\ t_2 := \left(c \cdot a - y \cdot i\right) \cdot j\\ t_3 := t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+107}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-100}:\\ \;\;\;\;t\_2 + x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+109}:\\ \;\;\;\;t\_2 + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+264}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* j (- (/ (* c a) z) (/ (* y i) z))) (* c b))))
        (t_2 (* (- (* c a) (* y i)) j))
        (t_3 (* t (- (* i b) (* x a)))))
   (if (<= t -9.2e+107)
     t_3
     (if (<= t -5e+36)
       t_1
       (if (<= t -1e-100)
         (+ t_2 (* x (- (* z y) (* a t))))
         (if (<= t 9e+109)
           (+ t_2 (* z (- (* x y) (* c b))))
           (if (<= t 1.05e+264) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b));
	double t_2 = ((c * a) - (y * i)) * j;
	double t_3 = t * ((i * b) - (x * a));
	double tmp;
	if (t <= -9.2e+107) {
		tmp = t_3;
	} else if (t <= -5e+36) {
		tmp = t_1;
	} else if (t <= -1e-100) {
		tmp = t_2 + (x * ((z * y) - (a * t)));
	} else if (t <= 9e+109) {
		tmp = t_2 + (z * ((x * y) - (c * b)));
	} else if (t <= 1.05e+264) {
		tmp = t_3;
	} 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 = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b))
    t_2 = ((c * a) - (y * i)) * j
    t_3 = t * ((i * b) - (x * a))
    if (t <= (-9.2d+107)) then
        tmp = t_3
    else if (t <= (-5d+36)) then
        tmp = t_1
    else if (t <= (-1d-100)) then
        tmp = t_2 + (x * ((z * y) - (a * t)))
    else if (t <= 9d+109) then
        tmp = t_2 + (z * ((x * y) - (c * b)))
    else if (t <= 1.05d+264) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b));
	double t_2 = ((c * a) - (y * i)) * j;
	double t_3 = t * ((i * b) - (x * a));
	double tmp;
	if (t <= -9.2e+107) {
		tmp = t_3;
	} else if (t <= -5e+36) {
		tmp = t_1;
	} else if (t <= -1e-100) {
		tmp = t_2 + (x * ((z * y) - (a * t)));
	} else if (t <= 9e+109) {
		tmp = t_2 + (z * ((x * y) - (c * b)));
	} else if (t <= 1.05e+264) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b))
	t_2 = ((c * a) - (y * i)) * j
	t_3 = t * ((i * b) - (x * a))
	tmp = 0
	if t <= -9.2e+107:
		tmp = t_3
	elif t <= -5e+36:
		tmp = t_1
	elif t <= -1e-100:
		tmp = t_2 + (x * ((z * y) - (a * t)))
	elif t <= 9e+109:
		tmp = t_2 + (z * ((x * y) - (c * b)))
	elif t <= 1.05e+264:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(j * Float64(Float64(Float64(c * a) / z) - Float64(Float64(y * i) / z))) - Float64(c * b)))
	t_2 = Float64(Float64(Float64(c * a) - Float64(y * i)) * j)
	t_3 = Float64(t * Float64(Float64(i * b) - Float64(x * a)))
	tmp = 0.0
	if (t <= -9.2e+107)
		tmp = t_3;
	elseif (t <= -5e+36)
		tmp = t_1;
	elseif (t <= -1e-100)
		tmp = Float64(t_2 + Float64(x * Float64(Float64(z * y) - Float64(a * t))));
	elseif (t <= 9e+109)
		tmp = Float64(t_2 + Float64(z * Float64(Float64(x * y) - Float64(c * b))));
	elseif (t <= 1.05e+264)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b));
	t_2 = ((c * a) - (y * i)) * j;
	t_3 = t * ((i * b) - (x * a));
	tmp = 0.0;
	if (t <= -9.2e+107)
		tmp = t_3;
	elseif (t <= -5e+36)
		tmp = t_1;
	elseif (t <= -1e-100)
		tmp = t_2 + (x * ((z * y) - (a * t)));
	elseif (t <= 9e+109)
		tmp = t_2 + (z * ((x * y) - (c * b)));
	elseif (t <= 1.05e+264)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(j * N[(N[(N[(c * a), $MachinePrecision] / z), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+107], t$95$3, If[LessEqual[t, -5e+36], t$95$1, If[LessEqual[t, -1e-100], N[(t$95$2 + N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+109], N[(t$95$2 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+264], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.2000000000000001e107 or 8.9999999999999992e109 < t < 1.05000000000000005e264

   1. Initial program 53.3%

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

      1. +-commutative 53.3%

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

      2. fma-define 54.7%

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

      3. *-commutative 54.7%

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

      4. *-commutative 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in z around inf 50.4%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in t around -inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

      4. *-commutative 71.1%

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

   10. Simplified 71.1%

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

   if -9.2000000000000001e107 < t < -4.99999999999999977e36 or 1.05000000000000005e264 < t

   1. Initial program 44.6%

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

      1. +-commutative 44.6%

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

      2. fma-define 44.6%

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

      3. *-commutative 44.6%

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

      4. *-commutative 44.6%

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

   3. Simplified 44.6%

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

   5. Taylor expanded in z around inf 48.9%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in j around inf 73.3%

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

   if -4.99999999999999977e36 < t < -1e-100

   1. Initial program 74.0%

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

      1. +-commutative 74.0%

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

      2. fma-define 74.0%

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

      3. *-commutative 74.0%

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

      4. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in b around 0 66.3%

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

   if -1e-100 < t < 8.9999999999999992e109

   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 z around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(j \cdot \left(\frac{c \cdot a}{z} - \frac{y \cdot i}{z}\right) - c \cdot b\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-100}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+109}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+264}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(j \cdot \left(\frac{c \cdot a}{z} - \frac{y \cdot i}{z}\right) - c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;b \leq -320000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(j \cdot \left(\frac{c \cdot a}{z} - \frac{y \cdot i}{z}\right) - c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(i \cdot \frac{t}{z} - c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* (- (* c a) (* y i)) j) (* x (- (* z y) (* a t))))))
   (if (<= b -4.1e+79)
     (* b (- (* i t) (* z c)))
     (if (<= b -320000000.0)
       t_1
       (if (<= b -5.7e-61)
         (* t (- (* i b) (* x a)))
         (if (<= b 3.1e-166)
           t_1
           (if (<= b 6.4e+158)
             (* z (- (* j (- (/ (* c a) z) (/ (* y i) z))) (* c b)))
             (* (* z b) (- (* i (/ t z)) c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (((c * a) - (y * i)) * j) + (x * ((z * y) - (a * t)));
	double tmp;
	if (b <= -4.1e+79) {
		tmp = b * ((i * t) - (z * c));
	} else if (b <= -320000000.0) {
		tmp = t_1;
	} else if (b <= -5.7e-61) {
		tmp = t * ((i * b) - (x * a));
	} else if (b <= 3.1e-166) {
		tmp = t_1;
	} else if (b <= 6.4e+158) {
		tmp = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b));
	} else {
		tmp = (z * b) * ((i * (t / z)) - c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((c * a) - (y * i)) * j) + (x * ((z * y) - (a * t)))
    if (b <= (-4.1d+79)) then
        tmp = b * ((i * t) - (z * c))
    else if (b <= (-320000000.0d0)) then
        tmp = t_1
    else if (b <= (-5.7d-61)) then
        tmp = t * ((i * b) - (x * a))
    else if (b <= 3.1d-166) then
        tmp = t_1
    else if (b <= 6.4d+158) then
        tmp = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b))
    else
        tmp = (z * b) * ((i * (t / z)) - c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (((c * a) - (y * i)) * j) + (x * ((z * y) - (a * t)));
	double tmp;
	if (b <= -4.1e+79) {
		tmp = b * ((i * t) - (z * c));
	} else if (b <= -320000000.0) {
		tmp = t_1;
	} else if (b <= -5.7e-61) {
		tmp = t * ((i * b) - (x * a));
	} else if (b <= 3.1e-166) {
		tmp = t_1;
	} else if (b <= 6.4e+158) {
		tmp = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b));
	} else {
		tmp = (z * b) * ((i * (t / z)) - c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (((c * a) - (y * i)) * j) + (x * ((z * y) - (a * t)))
	tmp = 0
	if b <= -4.1e+79:
		tmp = b * ((i * t) - (z * c))
	elif b <= -320000000.0:
		tmp = t_1
	elif b <= -5.7e-61:
		tmp = t * ((i * b) - (x * a))
	elif b <= 3.1e-166:
		tmp = t_1
	elif b <= 6.4e+158:
		tmp = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b))
	else:
		tmp = (z * b) * ((i * (t / z)) - c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(Float64(c * a) - Float64(y * i)) * j) + Float64(x * Float64(Float64(z * y) - Float64(a * t))))
	tmp = 0.0
	if (b <= -4.1e+79)
		tmp = Float64(b * Float64(Float64(i * t) - Float64(z * c)));
	elseif (b <= -320000000.0)
		tmp = t_1;
	elseif (b <= -5.7e-61)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (b <= 3.1e-166)
		tmp = t_1;
	elseif (b <= 6.4e+158)
		tmp = Float64(z * Float64(Float64(j * Float64(Float64(Float64(c * a) / z) - Float64(Float64(y * i) / z))) - Float64(c * b)));
	else
		tmp = Float64(Float64(z * b) * Float64(Float64(i * Float64(t / z)) - c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (((c * a) - (y * i)) * j) + (x * ((z * y) - (a * t)));
	tmp = 0.0;
	if (b <= -4.1e+79)
		tmp = b * ((i * t) - (z * c));
	elseif (b <= -320000000.0)
		tmp = t_1;
	elseif (b <= -5.7e-61)
		tmp = t * ((i * b) - (x * a));
	elseif (b <= 3.1e-166)
		tmp = t_1;
	elseif (b <= 6.4e+158)
		tmp = z * ((j * (((c * a) / z) - ((y * i) / z))) - (c * b));
	else
		tmp = (z * b) * ((i * (t / z)) - c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision] + N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+79], N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -320000000.0], t$95$1, If[LessEqual[b, -5.7e-61], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-166], t$95$1, If[LessEqual[b, 6.4e+158], N[(z * N[(N[(j * N[(N[(N[(c * a), $MachinePrecision] / z), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * b), $MachinePrecision] * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.1e79

   1. Initial program 81.0%

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

      1. +-commutative 81.0%

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

      2. fma-define 83.1%

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

      3. *-commutative 83.1%

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

      4. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around 0 85.0%

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

      1. *-commutative 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in b around inf 73.3%

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

      1. *-commutative 73.3%

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

   10. Simplified 73.3%

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

   if -4.1e79 < b < -3.2e8 or -5.70000000000000005e-61 < b < 3.09999999999999984e-166

   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. Step-by-step derivation

      1. +-commutative 62.3%

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

      2. fma-define 62.3%

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

      3. *-commutative 62.3%

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

      4. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in b around 0 67.6%

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

   if -3.2e8 < b < -5.70000000000000005e-61

   1. Initial program 53.8%

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

      1. +-commutative 53.8%

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

      2. fma-define 53.8%

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

      3. *-commutative 53.8%

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

      4. *-commutative 53.8%

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

   3. Simplified 53.8%

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

   5. Taylor expanded in z around inf 57.4%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in t around -inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

      4. *-commutative 60.9%

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

   10. Simplified 60.9%

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

   if 3.09999999999999984e-166 < b < 6.39999999999999989e158

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. fma-define 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around inf 80.6%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in j around inf 64.6%

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

   if 6.39999999999999989e158 < b

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. fma-define 65.0%

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

      3. *-commutative 65.0%

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

      4. *-commutative 65.0%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in z around inf 42.9%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in b around inf 73.1%

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

      1. associate-*r* 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-/l* 77.9%

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

   10. Simplified 77.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;b \leq -320000000:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-166}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(j \cdot \left(\frac{c \cdot a}{z} - \frac{y \cdot i}{z}\right) - c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(i \cdot \frac{t}{z} - c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(i \cdot t - z \cdot c\right)\\ t_2 := \left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{if}\;j \leq -3.6 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-209}:\\ \;\;\;\;t\_1 - \left(i \cdot \left(y \cdot j\right) - x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-89}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t\_1\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* i t) (* z c))))
        (t_2 (+ (* (- (* c a) (* y i)) j) (* z (- (* x y) (* c b))))))
   (if (<= j -3.6e-31)
     t_2
     (if (<= j -1.05e-209)
       (- t_1 (- (* i (* y j)) (* x (* z y))))
       (if (<= j 1.15e-89)
         (+ (- (* a (* c j)) (* a (* x t))) t_1)
         (if (<= j 6.4e+110)
           t_2
           (- (* t (- (* i b) (* x a))) (* j (- (* y i) (* c a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (z * c));
	double t_2 = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	double tmp;
	if (j <= -3.6e-31) {
		tmp = t_2;
	} else if (j <= -1.05e-209) {
		tmp = t_1 - ((i * (y * j)) - (x * (z * y)));
	} else if (j <= 1.15e-89) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	} else if (j <= 6.4e+110) {
		tmp = t_2;
	} else {
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((i * t) - (z * c))
    t_2 = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)))
    if (j <= (-3.6d-31)) then
        tmp = t_2
    else if (j <= (-1.05d-209)) then
        tmp = t_1 - ((i * (y * j)) - (x * (z * y)))
    else if (j <= 1.15d-89) then
        tmp = ((a * (c * j)) - (a * (x * t))) + t_1
    else if (j <= 6.4d+110) then
        tmp = t_2
    else
        tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (z * c));
	double t_2 = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	double tmp;
	if (j <= -3.6e-31) {
		tmp = t_2;
	} else if (j <= -1.05e-209) {
		tmp = t_1 - ((i * (y * j)) - (x * (z * y)));
	} else if (j <= 1.15e-89) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	} else if (j <= 6.4e+110) {
		tmp = t_2;
	} else {
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((i * t) - (z * c))
	t_2 = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)))
	tmp = 0
	if j <= -3.6e-31:
		tmp = t_2
	elif j <= -1.05e-209:
		tmp = t_1 - ((i * (y * j)) - (x * (z * y)))
	elif j <= 1.15e-89:
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1
	elif j <= 6.4e+110:
		tmp = t_2
	else:
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(i * t) - Float64(z * c)))
	t_2 = Float64(Float64(Float64(Float64(c * a) - Float64(y * i)) * j) + Float64(z * Float64(Float64(x * y) - Float64(c * b))))
	tmp = 0.0
	if (j <= -3.6e-31)
		tmp = t_2;
	elseif (j <= -1.05e-209)
		tmp = Float64(t_1 - Float64(Float64(i * Float64(y * j)) - Float64(x * Float64(z * y))));
	elseif (j <= 1.15e-89)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(a * Float64(x * t))) + t_1);
	elseif (j <= 6.4e+110)
		tmp = t_2;
	else
		tmp = Float64(Float64(t * Float64(Float64(i * b) - Float64(x * a))) - Float64(j * Float64(Float64(y * i) - Float64(c * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((i * t) - (z * c));
	t_2 = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	tmp = 0.0;
	if (j <= -3.6e-31)
		tmp = t_2;
	elseif (j <= -1.05e-209)
		tmp = t_1 - ((i * (y * j)) - (x * (z * y)));
	elseif (j <= 1.15e-89)
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	elseif (j <= 6.4e+110)
		tmp = t_2;
	else
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.6e-31], t$95$2, If[LessEqual[j, -1.05e-209], N[(t$95$1 - N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e-89], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 6.4e+110], t$95$2, N[(N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.60000000000000004e-31 or 1.15e-89 < j < 6.39999999999999988e110

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 81.7%

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

      1. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -3.60000000000000004e-31 < j < -1.04999999999999998e-209

   1. Initial program 62.1%

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

      1. +-commutative 62.1%

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

      2. fma-define 62.1%

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

      3. *-commutative 62.1%

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

      4. *-commutative 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in a around 0 71.9%

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

   if -1.04999999999999998e-209 < j < 1.15e-89

   1. Initial program 61.8%

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

      1. +-commutative 61.8%

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

      2. fma-define 61.8%

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

      3. *-commutative 61.8%

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

      4. *-commutative 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in y around 0 75.2%

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

   if 6.39999999999999988e110 < j

   1. Initial program 61.5%

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

   3. Taylor expanded in t around -inf 75.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{-31}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-209}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-89}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+110}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \mathbf{if}\;i \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{-307}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;i \leq 38000:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (- (* i b) (* x a))) (* j (- (* y i) (* c a))))))
   (if (<= i -2.1e-15)
     t_1
     (if (<= i 5.6e-307)
       (+ (- (* a (* c j)) (* a (* x t))) (* b (- (* i t) (* z c))))
       (if (<= i 38000.0)
         (+ (* (- (* c a) (* y i)) j) (* z (- (* x y) (* c b))))
         (if (<= i 1.65e+205) 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 = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	double tmp;
	if (i <= -2.1e-15) {
		tmp = t_1;
	} else if (i <= 5.6e-307) {
		tmp = ((a * (c * j)) - (a * (x * t))) + (b * ((i * t) - (z * c)));
	} else if (i <= 38000.0) {
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	} else if (i <= 1.65e+205) {
		tmp = t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)))
    if (i <= (-2.1d-15)) then
        tmp = t_1
    else if (i <= 5.6d-307) then
        tmp = ((a * (c * j)) - (a * (x * t))) + (b * ((i * t) - (z * c)))
    else if (i <= 38000.0d0) then
        tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)))
    else if (i <= 1.65d+205) then
        tmp = t_1
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	double tmp;
	if (i <= -2.1e-15) {
		tmp = t_1;
	} else if (i <= 5.6e-307) {
		tmp = ((a * (c * j)) - (a * (x * t))) + (b * ((i * t) - (z * c)));
	} else if (i <= 38000.0) {
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	} else if (i <= 1.65e+205) {
		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 = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)))
	tmp = 0
	if i <= -2.1e-15:
		tmp = t_1
	elif i <= 5.6e-307:
		tmp = ((a * (c * j)) - (a * (x * t))) + (b * ((i * t) - (z * c)))
	elif i <= 38000.0:
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)))
	elif i <= 1.65e+205:
		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(t * Float64(Float64(i * b) - Float64(x * a))) - Float64(j * Float64(Float64(y * i) - Float64(c * a))))
	tmp = 0.0
	if (i <= -2.1e-15)
		tmp = t_1;
	elseif (i <= 5.6e-307)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(a * Float64(x * t))) + Float64(b * Float64(Float64(i * t) - Float64(z * c))));
	elseif (i <= 38000.0)
		tmp = Float64(Float64(Float64(Float64(c * a) - Float64(y * i)) * j) + Float64(z * Float64(Float64(x * y) - Float64(c * b))));
	elseif (i <= 1.65e+205)
		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 = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	tmp = 0.0;
	if (i <= -2.1e-15)
		tmp = t_1;
	elseif (i <= 5.6e-307)
		tmp = ((a * (c * j)) - (a * (x * t))) + (b * ((i * t) - (z * c)));
	elseif (i <= 38000.0)
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	elseif (i <= 1.65e+205)
		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[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.1e-15], t$95$1, If[LessEqual[i, 5.6e-307], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 38000.0], N[(N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.65e+205], t$95$1, N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.09999999999999981e-15 or 38000 < i < 1.6500000000000001e205

   1. Initial program 66.4%

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

   3. Taylor expanded in t around -inf 72.3%

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

   if -2.09999999999999981e-15 < i < 5.6e-307

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. fma-define 75.5%

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

      3. *-commutative 75.5%

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

      4. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in y around 0 79.4%

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

   if 5.6e-307 < i < 38000

   1. Initial program 68.2%

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

   3. Taylor expanded in z around inf 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if 1.6500000000000001e205 < i

   1. Initial program 47.2%

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

      1. +-commutative 47.2%

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

      2. fma-define 47.2%

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

      3. *-commutative 47.2%

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

      4. *-commutative 47.2%

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

   3. Simplified 47.2%

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

   5. Taylor expanded in i around inf 84.2%

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

      1. distribute-lft-out-- 84.2%

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

   7. Simplified 84.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{-307}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;i \leq 38000:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -110000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-167}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-85}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 8.4 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.2e+92)
   (* (* y i) (- j))
   (if (<= i -110000.0)
     (* a (* x (- t)))
     (if (<= i 2.2e-184)
       (* z (* c (- b)))
       (if (<= i 2.4e-167)
         (* (* c a) j)
         (if (<= i 1.65e-85)
           (* c (* z (- b)))
           (if (<= i 8.4e+166) (* b (* i t)) (* i (* y (- j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5.2e+92) {
		tmp = (y * i) * -j;
	} else if (i <= -110000.0) {
		tmp = a * (x * -t);
	} else if (i <= 2.2e-184) {
		tmp = z * (c * -b);
	} else if (i <= 2.4e-167) {
		tmp = (c * a) * j;
	} else if (i <= 1.65e-85) {
		tmp = c * (z * -b);
	} else if (i <= 8.4e+166) {
		tmp = b * (i * t);
	} 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) :: tmp
    if (i <= (-5.2d+92)) then
        tmp = (y * i) * -j
    else if (i <= (-110000.0d0)) then
        tmp = a * (x * -t)
    else if (i <= 2.2d-184) then
        tmp = z * (c * -b)
    else if (i <= 2.4d-167) then
        tmp = (c * a) * j
    else if (i <= 1.65d-85) then
        tmp = c * (z * -b)
    else if (i <= 8.4d+166) then
        tmp = b * (i * t)
    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 tmp;
	if (i <= -5.2e+92) {
		tmp = (y * i) * -j;
	} else if (i <= -110000.0) {
		tmp = a * (x * -t);
	} else if (i <= 2.2e-184) {
		tmp = z * (c * -b);
	} else if (i <= 2.4e-167) {
		tmp = (c * a) * j;
	} else if (i <= 1.65e-85) {
		tmp = c * (z * -b);
	} else if (i <= 8.4e+166) {
		tmp = b * (i * t);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5.2e+92:
		tmp = (y * i) * -j
	elif i <= -110000.0:
		tmp = a * (x * -t)
	elif i <= 2.2e-184:
		tmp = z * (c * -b)
	elif i <= 2.4e-167:
		tmp = (c * a) * j
	elif i <= 1.65e-85:
		tmp = c * (z * -b)
	elif i <= 8.4e+166:
		tmp = b * (i * t)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.2e+92)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (i <= -110000.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 2.2e-184)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 2.4e-167)
		tmp = Float64(Float64(c * a) * j);
	elseif (i <= 1.65e-85)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= 8.4e+166)
		tmp = Float64(b * Float64(i * t));
	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)
	tmp = 0.0;
	if (i <= -5.2e+92)
		tmp = (y * i) * -j;
	elseif (i <= -110000.0)
		tmp = a * (x * -t);
	elseif (i <= 2.2e-184)
		tmp = z * (c * -b);
	elseif (i <= 2.4e-167)
		tmp = (c * a) * j;
	elseif (i <= 1.65e-85)
		tmp = c * (z * -b);
	elseif (i <= 8.4e+166)
		tmp = b * (i * t);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.2e+92], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[i, -110000.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.2e-184], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e-167], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[i, 1.65e-85], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.4e+166], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -5.1999999999999998e92

   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 i around inf 66.1%

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

   4. Taylor expanded in y around inf 42.6%

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

      1. associate-*r* 42.6%

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

      2. neg-mul-1 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in i around 0 42.6%

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

      1. associate-*r* 42.6%

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

      2. neg-mul-1 42.6%

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

      3. *-commutative 42.6%

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

      4. associate-*r* 43.7%

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

      5. *-commutative 43.7%

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

   9. Simplified 43.7%

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

   if -5.1999999999999998e92 < i < -1.1e5

   1. Initial program 41.3%

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

      1. +-commutative 41.3%

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

      2. fma-define 51.3%

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

      3. *-commutative 51.3%

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

      4. *-commutative 51.3%

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

   3. Simplified 51.3%

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

   5. Taylor expanded in a around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in c around 0 41.4%

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

      1. associate-*r* 41.4%

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

      2. neg-mul-1 41.4%

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

   10. Simplified 41.4%

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

   if -1.1e5 < i < 2.19999999999999992e-184

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. fma-define 72.4%

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

      3. *-commutative 72.4%

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

      4. *-commutative 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in z around inf 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in b around inf 44.7%

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

   9. Taylor expanded in i around 0 43.0%

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

       1. associate-*r* 43.0%

          \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

       2. mul-1-neg 43.0%

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

   11. Simplified 43.0%

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

   if 2.19999999999999992e-184 < i < 2.39999999999999993e-167

   1. Initial program 56.9%

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

      1. +-commutative 56.9%

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

      2. fma-define 56.9%

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

      3. *-commutative 56.9%

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

      4. *-commutative 56.9%

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

   3. Simplified 56.9%

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

   5. Taylor expanded in a around inf 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

   7. Simplified 72.0%

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

   8. Taylor expanded in c around inf 72.5%

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

      1. associate-*r* 72.5%

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

   10. Simplified 72.5%

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

   if 2.39999999999999993e-167 < i < 1.64999999999999986e-85

   1. Initial program 72.1%

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

      1. +-commutative 72.1%

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

      2. fma-define 72.1%

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

      3. *-commutative 72.1%

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

      4. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. *-commutative 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in z around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. *-commutative 33.8%

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

      3. associate-*r* 42.6%

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

      4. *-commutative 42.6%

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

      5. distribute-rgt-neg-in 42.6%

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

      6. distribute-rgt-neg-in 42.6%

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

   10. Simplified 42.6%

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

   if 1.64999999999999986e-85 < i < 8.4000000000000002e166

   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 i around inf 60.1%

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

   4. Taylor expanded in b around inf 36.7%

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

   if 8.4000000000000002e166 < i

   1. Initial program 48.6%

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

   3. Taylor expanded in i around inf 56.3%

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

   4. Taylor expanded in y around inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. neg-mul-1 51.2%

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

   6. Simplified 51.2%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -110000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-167}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-85}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 8.4 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 28.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -550:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-169}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-86}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 1.62 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= i -5.5e+92)
     t_1
     (if (<= i -550.0)
       (* a (* x (- t)))
       (if (<= i 4.4e-184)
         (* z (* c (- b)))
         (if (<= i 6.6e-169)
           (* (* c a) j)
           (if (<= i 9.5e-86)
             (* c (* z (- b)))
             (if (<= i 1.62e+168) (* b (* i 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 = i * (y * -j);
	double tmp;
	if (i <= -5.5e+92) {
		tmp = t_1;
	} else if (i <= -550.0) {
		tmp = a * (x * -t);
	} else if (i <= 4.4e-184) {
		tmp = z * (c * -b);
	} else if (i <= 6.6e-169) {
		tmp = (c * a) * j;
	} else if (i <= 9.5e-86) {
		tmp = c * (z * -b);
	} else if (i <= 1.62e+168) {
		tmp = b * (i * 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 = i * (y * -j)
    if (i <= (-5.5d+92)) then
        tmp = t_1
    else if (i <= (-550.0d0)) then
        tmp = a * (x * -t)
    else if (i <= 4.4d-184) then
        tmp = z * (c * -b)
    else if (i <= 6.6d-169) then
        tmp = (c * a) * j
    else if (i <= 9.5d-86) then
        tmp = c * (z * -b)
    else if (i <= 1.62d+168) then
        tmp = b * (i * 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 = i * (y * -j);
	double tmp;
	if (i <= -5.5e+92) {
		tmp = t_1;
	} else if (i <= -550.0) {
		tmp = a * (x * -t);
	} else if (i <= 4.4e-184) {
		tmp = z * (c * -b);
	} else if (i <= 6.6e-169) {
		tmp = (c * a) * j;
	} else if (i <= 9.5e-86) {
		tmp = c * (z * -b);
	} else if (i <= 1.62e+168) {
		tmp = b * (i * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if i <= -5.5e+92:
		tmp = t_1
	elif i <= -550.0:
		tmp = a * (x * -t)
	elif i <= 4.4e-184:
		tmp = z * (c * -b)
	elif i <= 6.6e-169:
		tmp = (c * a) * j
	elif i <= 9.5e-86:
		tmp = c * (z * -b)
	elif i <= 1.62e+168:
		tmp = b * (i * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (i <= -5.5e+92)
		tmp = t_1;
	elseif (i <= -550.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 4.4e-184)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 6.6e-169)
		tmp = Float64(Float64(c * a) * j);
	elseif (i <= 9.5e-86)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= 1.62e+168)
		tmp = Float64(b * Float64(i * 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 = i * (y * -j);
	tmp = 0.0;
	if (i <= -5.5e+92)
		tmp = t_1;
	elseif (i <= -550.0)
		tmp = a * (x * -t);
	elseif (i <= 4.4e-184)
		tmp = z * (c * -b);
	elseif (i <= 6.6e-169)
		tmp = (c * a) * j;
	elseif (i <= 9.5e-86)
		tmp = c * (z * -b);
	elseif (i <= 1.62e+168)
		tmp = b * (i * 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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.5e+92], t$95$1, If[LessEqual[i, -550.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e-184], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.6e-169], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[i, 9.5e-86], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.62e+168], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.50000000000000053e92 or 1.6199999999999999e168 < i

   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 i around inf 61.1%

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

   4. Taylor expanded in y around inf 46.9%

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

      1. associate-*r* 46.9%

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

      2. neg-mul-1 46.9%

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

   6. Simplified 46.9%

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

   if -5.50000000000000053e92 < i < -550

   1. Initial program 41.3%

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

      1. +-commutative 41.3%

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

      2. fma-define 51.3%

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

      3. *-commutative 51.3%

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

      4. *-commutative 51.3%

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

   3. Simplified 51.3%

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

   5. Taylor expanded in a around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in c around 0 41.4%

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

      1. associate-*r* 41.4%

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

      2. neg-mul-1 41.4%

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

   10. Simplified 41.4%

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

   if -550 < i < 4.39999999999999984e-184

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. fma-define 72.4%

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

      3. *-commutative 72.4%

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

      4. *-commutative 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in z around inf 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in b around inf 44.7%

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

   9. Taylor expanded in i around 0 43.0%

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

       1. associate-*r* 43.0%

          \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

       2. mul-1-neg 43.0%

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

   11. Simplified 43.0%

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

   if 4.39999999999999984e-184 < i < 6.60000000000000052e-169

   1. Initial program 56.9%

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

      1. +-commutative 56.9%

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

      2. fma-define 56.9%

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

      3. *-commutative 56.9%

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

      4. *-commutative 56.9%

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

   3. Simplified 56.9%

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

   5. Taylor expanded in a around inf 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

   7. Simplified 72.0%

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

   8. Taylor expanded in c around inf 72.5%

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

      1. associate-*r* 72.5%

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

   10. Simplified 72.5%

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

   if 6.60000000000000052e-169 < i < 9.4999999999999996e-86

   1. Initial program 72.1%

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

      1. +-commutative 72.1%

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

      2. fma-define 72.1%

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

      3. *-commutative 72.1%

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

      4. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. *-commutative 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in z around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. *-commutative 33.8%

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

      3. associate-*r* 42.6%

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

      4. *-commutative 42.6%

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

      5. distribute-rgt-neg-in 42.6%

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

      6. distribute-rgt-neg-in 42.6%

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

   10. Simplified 42.6%

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

   if 9.4999999999999996e-86 < i < 1.6199999999999999e168

   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 i around inf 60.1%

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

   4. Taylor expanded in b around inf 36.7%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -550:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-169}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-86}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 1.62 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(i \cdot t\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* b (* i t))))
   (if (<= z -3.5e+33)
     (* y (* z x))
     (if (<= z -9e-79)
       t_1
       (if (<= z -1.05e-218)
         t_2
         (if (<= z 7.2e-264)
           t_1
           (if (<= z 1.7e-150)
             t_2
             (if (<= z 2.9e+141) t_1 (* c (* z (- b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = b * (i * t);
	double tmp;
	if (z <= -3.5e+33) {
		tmp = y * (z * x);
	} else if (z <= -9e-79) {
		tmp = t_1;
	} else if (z <= -1.05e-218) {
		tmp = t_2;
	} else if (z <= 7.2e-264) {
		tmp = t_1;
	} else if (z <= 1.7e-150) {
		tmp = t_2;
	} else if (z <= 2.9e+141) {
		tmp = t_1;
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = b * (i * t)
    if (z <= (-3.5d+33)) then
        tmp = y * (z * x)
    else if (z <= (-9d-79)) then
        tmp = t_1
    else if (z <= (-1.05d-218)) then
        tmp = t_2
    else if (z <= 7.2d-264) then
        tmp = t_1
    else if (z <= 1.7d-150) then
        tmp = t_2
    else if (z <= 2.9d+141) then
        tmp = t_1
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = b * (i * t);
	double tmp;
	if (z <= -3.5e+33) {
		tmp = y * (z * x);
	} else if (z <= -9e-79) {
		tmp = t_1;
	} else if (z <= -1.05e-218) {
		tmp = t_2;
	} else if (z <= 7.2e-264) {
		tmp = t_1;
	} else if (z <= 1.7e-150) {
		tmp = t_2;
	} else if (z <= 2.9e+141) {
		tmp = t_1;
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = b * (i * t)
	tmp = 0
	if z <= -3.5e+33:
		tmp = y * (z * x)
	elif z <= -9e-79:
		tmp = t_1
	elif z <= -1.05e-218:
		tmp = t_2
	elif z <= 7.2e-264:
		tmp = t_1
	elif z <= 1.7e-150:
		tmp = t_2
	elif z <= 2.9e+141:
		tmp = t_1
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(b * Float64(i * t))
	tmp = 0.0
	if (z <= -3.5e+33)
		tmp = Float64(y * Float64(z * x));
	elseif (z <= -9e-79)
		tmp = t_1;
	elseif (z <= -1.05e-218)
		tmp = t_2;
	elseif (z <= 7.2e-264)
		tmp = t_1;
	elseif (z <= 1.7e-150)
		tmp = t_2;
	elseif (z <= 2.9e+141)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = b * (i * t);
	tmp = 0.0;
	if (z <= -3.5e+33)
		tmp = y * (z * x);
	elseif (z <= -9e-79)
		tmp = t_1;
	elseif (z <= -1.05e-218)
		tmp = t_2;
	elseif (z <= 7.2e-264)
		tmp = t_1;
	elseif (z <= 1.7e-150)
		tmp = t_2;
	elseif (z <= 2.9e+141)
		tmp = t_1;
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+33], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-79], t$95$1, If[LessEqual[z, -1.05e-218], t$95$2, If[LessEqual[z, 7.2e-264], t$95$1, If[LessEqual[z, 1.7e-150], t$95$2, If[LessEqual[z, 2.9e+141], t$95$1, N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5000000000000001e33

   1. Initial program 58.0%

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

      1. +-commutative 58.0%

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

      2. fma-define 59.9%

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

      3. *-commutative 59.9%

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

      4. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in y around inf 44.9%

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

      1. +-commutative 44.9%

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

      2. mul-1-neg 44.9%

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

      3. unsub-neg 44.9%

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

      4. *-commutative 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in z around inf 36.9%

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

   if -3.5000000000000001e33 < z < -9.0000000000000006e-79 or -1.04999999999999997e-218 < z < 7.2000000000000004e-264 or 1.7e-150 < z < 2.90000000000000007e141

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. fma-define 71.0%

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

      3. *-commutative 71.0%

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

      4. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in a around inf 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

   7. Simplified 48.2%

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

   8. Taylor expanded in c around inf 38.0%

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

      1. *-commutative 38.0%

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

   10. Simplified 38.0%

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

   if -9.0000000000000006e-79 < z < -1.04999999999999997e-218 or 7.2000000000000004e-264 < z < 1.7e-150

   1. Initial program 73.2%

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

   3. Taylor expanded in i around inf 66.2%

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

   4. Taylor expanded in b around inf 36.4%

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

   if 2.90000000000000007e141 < z

   1. Initial program 58.9%

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

      1. +-commutative 58.9%

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

      2. fma-define 58.9%

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

      3. *-commutative 58.9%

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

      4. *-commutative 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. *-commutative 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in z around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*r* 59.0%

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

      4. *-commutative 59.0%

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

      5. distribute-rgt-neg-in 59.0%

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

      6. distribute-rgt-neg-in 59.0%

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

   10. Simplified 59.0%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-150}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{if}\;i \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+96}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* i b) (* x a)))))
   (if (<= i -4.6e-15)
     t_1
     (if (<= i 2.7e-44)
       (* c (- (* a j) (* z b)))
       (if (<= i 4.6e+86)
         t_1
         (if (<= i 3.9e+96)
           (* (- (* c a) (* y i)) j)
           (if (<= i 6.8e+166)
             (* b (- (* i t) (* z c)))
             (* y (- (* z x) (* 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 = t * ((i * b) - (x * a));
	double tmp;
	if (i <= -4.6e-15) {
		tmp = t_1;
	} else if (i <= 2.7e-44) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 4.6e+86) {
		tmp = t_1;
	} else if (i <= 3.9e+96) {
		tmp = ((c * a) - (y * i)) * j;
	} else if (i <= 6.8e+166) {
		tmp = b * ((i * t) - (z * c));
	} else {
		tmp = y * ((z * x) - (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) :: tmp
    t_1 = t * ((i * b) - (x * a))
    if (i <= (-4.6d-15)) then
        tmp = t_1
    else if (i <= 2.7d-44) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 4.6d+86) then
        tmp = t_1
    else if (i <= 3.9d+96) then
        tmp = ((c * a) - (y * i)) * j
    else if (i <= 6.8d+166) then
        tmp = b * ((i * t) - (z * c))
    else
        tmp = y * ((z * x) - (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 = t * ((i * b) - (x * a));
	double tmp;
	if (i <= -4.6e-15) {
		tmp = t_1;
	} else if (i <= 2.7e-44) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 4.6e+86) {
		tmp = t_1;
	} else if (i <= 3.9e+96) {
		tmp = ((c * a) - (y * i)) * j;
	} else if (i <= 6.8e+166) {
		tmp = b * ((i * t) - (z * c));
	} else {
		tmp = y * ((z * x) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((i * b) - (x * a))
	tmp = 0
	if i <= -4.6e-15:
		tmp = t_1
	elif i <= 2.7e-44:
		tmp = c * ((a * j) - (z * b))
	elif i <= 4.6e+86:
		tmp = t_1
	elif i <= 3.9e+96:
		tmp = ((c * a) - (y * i)) * j
	elif i <= 6.8e+166:
		tmp = b * ((i * t) - (z * c))
	else:
		tmp = y * ((z * x) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(i * b) - Float64(x * a)))
	tmp = 0.0
	if (i <= -4.6e-15)
		tmp = t_1;
	elseif (i <= 2.7e-44)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 4.6e+86)
		tmp = t_1;
	elseif (i <= 3.9e+96)
		tmp = Float64(Float64(Float64(c * a) - Float64(y * i)) * j);
	elseif (i <= 6.8e+166)
		tmp = Float64(b * Float64(Float64(i * t) - Float64(z * c)));
	else
		tmp = Float64(y * Float64(Float64(z * x) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((i * b) - (x * a));
	tmp = 0.0;
	if (i <= -4.6e-15)
		tmp = t_1;
	elseif (i <= 2.7e-44)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 4.6e+86)
		tmp = t_1;
	elseif (i <= 3.9e+96)
		tmp = ((c * a) - (y * i)) * j;
	elseif (i <= 6.8e+166)
		tmp = b * ((i * t) - (z * c));
	else
		tmp = y * ((z * x) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.6e-15], t$95$1, If[LessEqual[i, 2.7e-44], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.6e+86], t$95$1, If[LessEqual[i, 3.9e+96], N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[i, 6.8e+166], N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z * x), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.59999999999999981e-15 or 2.6999999999999999e-44 < i < 4.59999999999999979e86

   1. Initial program 65.8%

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

      1. +-commutative 65.8%

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

      2. fma-define 68.3%

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

      3. *-commutative 68.3%

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

      4. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 56.9%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in t around -inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

      4. *-commutative 53.9%

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

   10. Simplified 53.9%

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

   if -4.59999999999999981e-15 < i < 2.6999999999999999e-44

   1. Initial program 71.8%

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

      1. +-commutative 71.8%

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

      2. fma-define 71.8%

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

      3. *-commutative 71.8%

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

      4. *-commutative 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in c around inf 71.1%

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

      1. *-commutative 71.1%

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

   7. Simplified 71.1%

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

   if 4.59999999999999979e86 < i < 3.9e96

   1. Initial program 76.7%

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

      1. +-commutative 76.7%

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

      2. fma-define 76.7%

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

      3. *-commutative 76.7%

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

      4. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in z around inf 53.3%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in j around -inf 99.6%

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

   if 3.9e96 < i < 6.8000000000000001e166

   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. Step-by-step derivation

      1. +-commutative 74.3%

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

      2. fma-define 74.3%

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

      3. *-commutative 74.3%

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

      4. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in x around 0 70.5%

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

      1. *-commutative 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in b around inf 58.1%

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

      1. *-commutative 58.1%

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

   10. Simplified 58.1%

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

   if 6.8000000000000001e166 < i

   1. Initial program 48.6%

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

      1. +-commutative 48.6%

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

      2. fma-define 48.6%

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

      3. *-commutative 48.6%

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

      4. *-commutative 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in y around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   7. Simplified 59.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+96}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -65000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* i t) (* z c)))))
   (if (<= b -1.35e+49)
     t_2
     (if (<= b -65000000000000.0)
       t_1
       (if (<= b -8e-74)
         t_2
         (if (<= b 4.1e-39) t_1 (if (<= b 5.2e+53) (* (* y i) (- j)) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((i * t) - (z * c));
	double tmp;
	if (b <= -1.35e+49) {
		tmp = t_2;
	} else if (b <= -65000000000000.0) {
		tmp = t_1;
	} else if (b <= -8e-74) {
		tmp = t_2;
	} else if (b <= 4.1e-39) {
		tmp = t_1;
	} else if (b <= 5.2e+53) {
		tmp = (y * i) * -j;
	} 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 = a * ((c * j) - (x * t))
    t_2 = b * ((i * t) - (z * c))
    if (b <= (-1.35d+49)) then
        tmp = t_2
    else if (b <= (-65000000000000.0d0)) then
        tmp = t_1
    else if (b <= (-8d-74)) then
        tmp = t_2
    else if (b <= 4.1d-39) then
        tmp = t_1
    else if (b <= 5.2d+53) then
        tmp = (y * i) * -j
    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 = a * ((c * j) - (x * t));
	double t_2 = b * ((i * t) - (z * c));
	double tmp;
	if (b <= -1.35e+49) {
		tmp = t_2;
	} else if (b <= -65000000000000.0) {
		tmp = t_1;
	} else if (b <= -8e-74) {
		tmp = t_2;
	} else if (b <= 4.1e-39) {
		tmp = t_1;
	} else if (b <= 5.2e+53) {
		tmp = (y * i) * -j;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((i * t) - (z * c))
	tmp = 0
	if b <= -1.35e+49:
		tmp = t_2
	elif b <= -65000000000000.0:
		tmp = t_1
	elif b <= -8e-74:
		tmp = t_2
	elif b <= 4.1e-39:
		tmp = t_1
	elif b <= 5.2e+53:
		tmp = (y * i) * -j
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(i * t) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.35e+49)
		tmp = t_2;
	elseif (b <= -65000000000000.0)
		tmp = t_1;
	elseif (b <= -8e-74)
		tmp = t_2;
	elseif (b <= 4.1e-39)
		tmp = t_1;
	elseif (b <= 5.2e+53)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((i * t) - (z * c));
	tmp = 0.0;
	if (b <= -1.35e+49)
		tmp = t_2;
	elseif (b <= -65000000000000.0)
		tmp = t_1;
	elseif (b <= -8e-74)
		tmp = t_2;
	elseif (b <= 4.1e-39)
		tmp = t_1;
	elseif (b <= 5.2e+53)
		tmp = (y * i) * -j;
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e+49], t$95$2, If[LessEqual[b, -65000000000000.0], t$95$1, If[LessEqual[b, -8e-74], t$95$2, If[LessEqual[b, 4.1e-39], t$95$1, If[LessEqual[b, 5.2e+53], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.35000000000000005e49 or -6.5e13 < b < -7.99999999999999966e-74 or 5.19999999999999996e53 < b

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. fma-define 72.1%

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

      3. *-commutative 72.1%

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

      4. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in x around 0 72.8%

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

      1. *-commutative 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in b around inf 64.5%

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

      1. *-commutative 64.5%

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

   10. Simplified 64.5%

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

   if -1.35000000000000005e49 < b < -6.5e13 or -7.99999999999999966e-74 < b < 4.1e-39

   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. Step-by-step derivation

      1. +-commutative 59.7%

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

      2. fma-define 60.7%

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

      3. *-commutative 60.7%

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

      4. *-commutative 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in a around inf 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

   7. Simplified 45.1%

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

   if 4.1e-39 < b < 5.19999999999999996e53

   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 i around inf 79.9%

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

   4. Taylor expanded in y around inf 63.9%

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

      1. associate-*r* 63.9%

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

      2. neg-mul-1 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in i around 0 63.9%

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

      1. associate-*r* 63.9%

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

      2. neg-mul-1 63.9%

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

      3. *-commutative 63.9%

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

      4. associate-*r* 71.9%

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

      5. *-commutative 71.9%

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

   9. Simplified 71.9%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;b \leq -65000000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-74}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot i\right) \cdot \left(-j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-287}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.78 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* y i) (- j))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -3.2e-64)
     t_2
     (if (<= a -3e-253)
       t_1
       (if (<= a 5.5e-287)
         (* z (* c (- b)))
         (if (<= a 1.02e-153) t_1 (if (<= a 1.78e-62) (* b (* i t)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * i) * -j;
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e-64) {
		tmp = t_2;
	} else if (a <= -3e-253) {
		tmp = t_1;
	} else if (a <= 5.5e-287) {
		tmp = z * (c * -b);
	} else if (a <= 1.02e-153) {
		tmp = t_1;
	} else if (a <= 1.78e-62) {
		tmp = b * (i * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * i) * -j
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-3.2d-64)) then
        tmp = t_2
    else if (a <= (-3d-253)) then
        tmp = t_1
    else if (a <= 5.5d-287) then
        tmp = z * (c * -b)
    else if (a <= 1.02d-153) then
        tmp = t_1
    else if (a <= 1.78d-62) then
        tmp = b * (i * t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * i) * -j;
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e-64) {
		tmp = t_2;
	} else if (a <= -3e-253) {
		tmp = t_1;
	} else if (a <= 5.5e-287) {
		tmp = z * (c * -b);
	} else if (a <= 1.02e-153) {
		tmp = t_1;
	} else if (a <= 1.78e-62) {
		tmp = b * (i * t);
	} else {
		tmp = t_2;
	}
	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))
	tmp = 0
	if a <= -3.2e-64:
		tmp = t_2
	elif a <= -3e-253:
		tmp = t_1
	elif a <= 5.5e-287:
		tmp = z * (c * -b)
	elif a <= 1.02e-153:
		tmp = t_1
	elif a <= 1.78e-62:
		tmp = b * (i * t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * i) * Float64(-j))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.2e-64)
		tmp = t_2;
	elseif (a <= -3e-253)
		tmp = t_1;
	elseif (a <= 5.5e-287)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (a <= 1.02e-153)
		tmp = t_1;
	elseif (a <= 1.78e-62)
		tmp = Float64(b * Float64(i * t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * i) * -j;
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.2e-64)
		tmp = t_2;
	elseif (a <= -3e-253)
		tmp = t_1;
	elseif (a <= 5.5e-287)
		tmp = z * (c * -b);
	elseif (a <= 1.02e-153)
		tmp = t_1;
	elseif (a <= 1.78e-62)
		tmp = b * (i * t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e-64], t$95$2, If[LessEqual[a, -3e-253], t$95$1, If[LessEqual[a, 5.5e-287], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-153], t$95$1, If[LessEqual[a, 1.78e-62], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.19999999999999975e-64 or 1.77999999999999998e-62 < a

   1. Initial program 62.0%

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

      1. +-commutative 62.0%

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

      2. fma-define 63.3%

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

      3. *-commutative 63.3%

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

      4. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in a around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

   7. Simplified 53.1%

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

   if -3.19999999999999975e-64 < a < -3.0000000000000002e-253 or 5.4999999999999998e-287 < a < 1.02e-153

   1. Initial program 67.5%

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

   3. Taylor expanded in i around inf 57.4%

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

   4. Taylor expanded in y around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. neg-mul-1 38.5%

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

   6. Simplified 38.5%

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

   7. Taylor expanded in i around 0 38.5%

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

      1. associate-*r* 38.5%

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

      2. neg-mul-1 38.5%

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

      3. *-commutative 38.5%

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

      4. associate-*r* 42.2%

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

      5. *-commutative 42.2%

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

   9. Simplified 42.2%

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

   if -3.0000000000000002e-253 < a < 5.4999999999999998e-287

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. fma-define 86.1%

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

      3. *-commutative 86.1%

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

      4. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 76.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in b around inf 58.3%

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

   9. Taylor expanded in i around 0 48.8%

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

       1. associate-*r* 48.8%

          \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

       2. mul-1-neg 48.8%

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

   11. Simplified 48.8%

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

   if 1.02e-153 < a < 1.77999999999999998e-62

   1. Initial program 74.4%

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

   3. Taylor expanded in i around inf 51.6%

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

   4. Taylor expanded in b around inf 44.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-253}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-287}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-153}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 1.78 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-278}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-279}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* z x))))
   (if (<= x -5.2e+161)
     t_1
     (if (<= x -4.8e-77)
       (* c (* z (- b)))
       (if (<= x -5.3e-278)
         (* (* c a) j)
         (if (<= x 2.7e-279)
           (* z (* c (- b)))
           (if (<= x 1.15e+96) (* a (* c 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 = y * (z * x);
	double tmp;
	if (x <= -5.2e+161) {
		tmp = t_1;
	} else if (x <= -4.8e-77) {
		tmp = c * (z * -b);
	} else if (x <= -5.3e-278) {
		tmp = (c * a) * j;
	} else if (x <= 2.7e-279) {
		tmp = z * (c * -b);
	} else if (x <= 1.15e+96) {
		tmp = a * (c * 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 = y * (z * x)
    if (x <= (-5.2d+161)) then
        tmp = t_1
    else if (x <= (-4.8d-77)) then
        tmp = c * (z * -b)
    else if (x <= (-5.3d-278)) then
        tmp = (c * a) * j
    else if (x <= 2.7d-279) then
        tmp = z * (c * -b)
    else if (x <= 1.15d+96) then
        tmp = a * (c * 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 = y * (z * x);
	double tmp;
	if (x <= -5.2e+161) {
		tmp = t_1;
	} else if (x <= -4.8e-77) {
		tmp = c * (z * -b);
	} else if (x <= -5.3e-278) {
		tmp = (c * a) * j;
	} else if (x <= 2.7e-279) {
		tmp = z * (c * -b);
	} else if (x <= 1.15e+96) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (z * x)
	tmp = 0
	if x <= -5.2e+161:
		tmp = t_1
	elif x <= -4.8e-77:
		tmp = c * (z * -b)
	elif x <= -5.3e-278:
		tmp = (c * a) * j
	elif x <= 2.7e-279:
		tmp = z * (c * -b)
	elif x <= 1.15e+96:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(z * x))
	tmp = 0.0
	if (x <= -5.2e+161)
		tmp = t_1;
	elseif (x <= -4.8e-77)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (x <= -5.3e-278)
		tmp = Float64(Float64(c * a) * j);
	elseif (x <= 2.7e-279)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (x <= 1.15e+96)
		tmp = Float64(a * Float64(c * 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 = y * (z * x);
	tmp = 0.0;
	if (x <= -5.2e+161)
		tmp = t_1;
	elseif (x <= -4.8e-77)
		tmp = c * (z * -b);
	elseif (x <= -5.3e-278)
		tmp = (c * a) * j;
	elseif (x <= 2.7e-279)
		tmp = z * (c * -b);
	elseif (x <= 1.15e+96)
		tmp = a * (c * 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[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+161], t$95$1, If[LessEqual[x, -4.8e-77], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.3e-278], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[x, 2.7e-279], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+96], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.1999999999999996e161 or 1.15000000000000008e96 < x

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. fma-define 67.0%

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

      3. *-commutative 67.0%

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

      4. *-commutative 67.0%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in y around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in z around inf 49.2%

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

   if -5.1999999999999996e161 < x < -4.7999999999999998e-77

   1. Initial program 72.6%

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

      1. +-commutative 72.6%

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

      2. fma-define 72.6%

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

      3. *-commutative 72.6%

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

      4. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around 0 67.5%

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

      1. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in z around inf 36.0%

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

      1. mul-1-neg 36.0%

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

      2. *-commutative 36.0%

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

      3. associate-*r* 38.6%

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

      4. *-commutative 38.6%

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

      5. distribute-rgt-neg-in 38.6%

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

      6. distribute-rgt-neg-in 38.6%

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

   10. Simplified 38.6%

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

   if -4.7999999999999998e-77 < x < -5.3e-278

   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. Step-by-step derivation

      1. +-commutative 67.7%

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

      2. fma-define 67.7%

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

      3. *-commutative 67.7%

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

      4. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in a around inf 40.8%

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

      1. +-commutative 40.8%

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

      2. mul-1-neg 40.8%

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

      3. unsub-neg 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in c around inf 32.3%

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

      1. associate-*r* 34.7%

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

   10. Simplified 34.7%

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

   if -5.3e-278 < x < 2.7000000000000001e-279

   1. Initial program 71.2%

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

      1. +-commutative 71.2%

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

      2. fma-define 71.2%

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

      3. *-commutative 71.2%

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

      4. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in z around inf 70.3%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in b around inf 51.1%

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

   9. Taylor expanded in i around 0 65.9%

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

       1. associate-*r* 65.9%

          \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

       2. mul-1-neg 65.9%

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

   11. Simplified 65.9%

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

   if 2.7000000000000001e-279 < x < 1.15000000000000008e96

   1. Initial program 63.5%

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

      1. +-commutative 63.5%

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

      2. fma-define 64.5%

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

      3. *-commutative 64.5%

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

      4. *-commutative 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in a around inf 39.1%

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

      1. +-commutative 39.1%

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

      2. mul-1-neg 39.1%

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

      3. unsub-neg 39.1%

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

   7. Simplified 39.1%

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

   8. Taylor expanded in c around inf 32.2%

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

      1. *-commutative 32.2%

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

   10. Simplified 32.2%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-278}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-279}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7.8 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -6.6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{a \cdot t}{y}\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -7.8e+71)
     t_1
     (if (<= i -6.6e+45)
       (* x (* y (- z (/ (* a t) y))))
       (if (<= i -2.6e-13)
         (* t (- (* i b) (* x a)))
         (if (<= i 1.08e-41) (* 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 tmp;
	if (i <= -7.8e+71) {
		tmp = t_1;
	} else if (i <= -6.6e+45) {
		tmp = x * (y * (z - ((a * t) / y)));
	} else if (i <= -2.6e-13) {
		tmp = t * ((i * b) - (x * a));
	} else if (i <= 1.08e-41) {
		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) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-7.8d+71)) then
        tmp = t_1
    else if (i <= (-6.6d+45)) then
        tmp = x * (y * (z - ((a * t) / y)))
    else if (i <= (-2.6d-13)) then
        tmp = t * ((i * b) - (x * a))
    else if (i <= 1.08d-41) 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 tmp;
	if (i <= -7.8e+71) {
		tmp = t_1;
	} else if (i <= -6.6e+45) {
		tmp = x * (y * (z - ((a * t) / y)));
	} else if (i <= -2.6e-13) {
		tmp = t * ((i * b) - (x * a));
	} else if (i <= 1.08e-41) {
		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))
	tmp = 0
	if i <= -7.8e+71:
		tmp = t_1
	elif i <= -6.6e+45:
		tmp = x * (y * (z - ((a * t) / y)))
	elif i <= -2.6e-13:
		tmp = t * ((i * b) - (x * a))
	elif i <= 1.08e-41:
		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)))
	tmp = 0.0
	if (i <= -7.8e+71)
		tmp = t_1;
	elseif (i <= -6.6e+45)
		tmp = Float64(x * Float64(y * Float64(z - Float64(Float64(a * t) / y))));
	elseif (i <= -2.6e-13)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (i <= 1.08e-41)
		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));
	tmp = 0.0;
	if (i <= -7.8e+71)
		tmp = t_1;
	elseif (i <= -6.6e+45)
		tmp = x * (y * (z - ((a * t) / y)));
	elseif (i <= -2.6e-13)
		tmp = t * ((i * b) - (x * a));
	elseif (i <= 1.08e-41)
		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]}, If[LessEqual[i, -7.8e+71], t$95$1, If[LessEqual[i, -6.6e+45], N[(x * N[(y * N[(z - N[(N[(a * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.6e-13], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.08e-41], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -7.8000000000000002e71 or 1.08e-41 < 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. Step-by-step derivation

      1. +-commutative 65.2%

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

      2. fma-define 65.2%

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

      3. *-commutative 65.2%

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

      4. *-commutative 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in i around inf 67.2%

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

      1. distribute-lft-out-- 67.2%

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

   7. Simplified 67.2%

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

   if -7.8000000000000002e71 < i < -6.6000000000000001e45

   1. Initial program 44.3%

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

      1. +-commutative 44.3%

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

      2. fma-define 55.4%

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

      3. *-commutative 55.4%

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

      4. *-commutative 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in z around inf 44.3%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in x around -inf 67.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(z \cdot \left(-1 \cdot y + \frac{a \cdot t}{z}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. +-commutative 67.6%

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

      5. neg-mul-1 67.6%

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

      6. unsub-neg 67.6%

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

      7. associate-/l* 67.6%

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

   10. Simplified 67.6%

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

   11. Taylor expanded in y around inf 78.4%

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

   if -6.6000000000000001e45 < i < -2.6e-13

   1. Initial program 46.8%

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

      1. +-commutative 46.8%

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

      2. fma-define 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in z around inf 35.9%

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

   7. Simplified 47.3%

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

   8. Taylor expanded in t around -inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   10. Simplified 55.9%

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

   if -2.6e-13 < i < 1.08e-41

   1. Initial program 71.8%

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

      1. +-commutative 71.8%

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

      2. fma-define 71.8%

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

      3. *-commutative 71.8%

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

      4. *-commutative 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in c around inf 71.1%

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

      1. *-commutative 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.8 \cdot 10^{+71}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6.6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{a \cdot t}{y}\right)\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.08 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.26 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -5.2e+92)
     t_1
     (if (<= i -1.8e+49)
       (* a (- (* c j) (* x t)))
       (if (<= i -6.4e-16)
         (* t (- (* i b) (* x a)))
         (if (<= i 1.26e-51) (* 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 tmp;
	if (i <= -5.2e+92) {
		tmp = t_1;
	} else if (i <= -1.8e+49) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -6.4e-16) {
		tmp = t * ((i * b) - (x * a));
	} else if (i <= 1.26e-51) {
		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) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-5.2d+92)) then
        tmp = t_1
    else if (i <= (-1.8d+49)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= (-6.4d-16)) then
        tmp = t * ((i * b) - (x * a))
    else if (i <= 1.26d-51) 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 tmp;
	if (i <= -5.2e+92) {
		tmp = t_1;
	} else if (i <= -1.8e+49) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -6.4e-16) {
		tmp = t * ((i * b) - (x * a));
	} else if (i <= 1.26e-51) {
		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))
	tmp = 0
	if i <= -5.2e+92:
		tmp = t_1
	elif i <= -1.8e+49:
		tmp = a * ((c * j) - (x * t))
	elif i <= -6.4e-16:
		tmp = t * ((i * b) - (x * a))
	elif i <= 1.26e-51:
		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)))
	tmp = 0.0
	if (i <= -5.2e+92)
		tmp = t_1;
	elseif (i <= -1.8e+49)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= -6.4e-16)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (i <= 1.26e-51)
		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));
	tmp = 0.0;
	if (i <= -5.2e+92)
		tmp = t_1;
	elseif (i <= -1.8e+49)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= -6.4e-16)
		tmp = t * ((i * b) - (x * a));
	elseif (i <= 1.26e-51)
		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]}, If[LessEqual[i, -5.2e+92], t$95$1, If[LessEqual[i, -1.8e+49], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.4e-16], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.26e-51], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -5.1999999999999998e92 or 1.2600000000000001e-51 < i

   1. Initial program 65.9%

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

      1. +-commutative 65.9%

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

      2. fma-define 65.9%

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

      3. *-commutative 65.9%

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

      4. *-commutative 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in i around inf 67.9%

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

      1. distribute-lft-out-- 67.9%

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

   7. Simplified 67.9%

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

   if -5.1999999999999998e92 < i < -1.79999999999999998e49

   1. Initial program 36.8%

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

      1. +-commutative 36.8%

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

      2. fma-define 45.8%

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

      3. *-commutative 45.8%

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

      4. *-commutative 45.8%

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

   3. Simplified 45.8%

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

   5. Taylor expanded in a around inf 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

   7. Simplified 73.5%

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

   if -1.79999999999999998e49 < i < -6.40000000000000046e-16

   1. Initial program 52.1%

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

      1. +-commutative 52.1%

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

      2. fma-define 62.1%

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

      3. *-commutative 62.1%

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

      4. *-commutative 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in z around inf 42.3%

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

   7. Simplified 52.5%

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

   8. Taylor expanded in t around -inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   10. Simplified 50.6%

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

   if -6.40000000000000046e-16 < i < 1.2600000000000001e-51

   1. Initial program 71.8%

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

      1. +-commutative 71.8%

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

      2. fma-define 71.8%

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

      3. *-commutative 71.8%

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

      4. *-commutative 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in c around inf 71.1%

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

      1. *-commutative 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.26 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{if}\;i \leq -4.2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* i t) (* z c)))))
   (if (<= i -4.2e+92)
     t_1
     (if (<= i -3.2e+14)
       (* a (- (* c j) (* x t)))
       (if (<= i 1.45e-62)
         (* c (- (* a j) (* z b)))
         (if (<= i 1.06e+168) 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 * ((i * t) - (z * c));
	double tmp;
	if (i <= -4.2e+92) {
		tmp = t_1;
	} else if (i <= -3.2e+14) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.45e-62) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.06e+168) {
		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 * ((i * t) - (z * c))
    if (i <= (-4.2d+92)) then
        tmp = t_1
    else if (i <= (-3.2d+14)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.45d-62) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1.06d+168) 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 * ((i * t) - (z * c));
	double tmp;
	if (i <= -4.2e+92) {
		tmp = t_1;
	} else if (i <= -3.2e+14) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.45e-62) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.06e+168) {
		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 * ((i * t) - (z * c))
	tmp = 0
	if i <= -4.2e+92:
		tmp = t_1
	elif i <= -3.2e+14:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.45e-62:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1.06e+168:
		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(Float64(i * t) - Float64(z * c)))
	tmp = 0.0
	if (i <= -4.2e+92)
		tmp = t_1;
	elseif (i <= -3.2e+14)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.45e-62)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1.06e+168)
		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 * ((i * t) - (z * c));
	tmp = 0.0;
	if (i <= -4.2e+92)
		tmp = t_1;
	elseif (i <= -3.2e+14)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.45e-62)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1.06e+168)
		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[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.2e+92], t$95$1, If[LessEqual[i, -3.2e+14], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.45e-62], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.06e+168], t$95$1, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.19999999999999972e92 or 1.44999999999999993e-62 < i < 1.0599999999999999e168

   1. Initial program 74.0%

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

      1. +-commutative 74.0%

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

      2. fma-define 74.0%

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

      3. *-commutative 74.0%

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

      4. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in x around 0 71.2%

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

      1. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in b around inf 51.0%

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

      1. *-commutative 51.0%

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

   10. Simplified 51.0%

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

   if -4.19999999999999972e92 < i < -3.2e14

   1. Initial program 40.3%

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

      1. +-commutative 40.3%

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

      2. fma-define 51.4%

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

      3. *-commutative 51.4%

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

      4. *-commutative 51.4%

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

   3. Simplified 51.4%

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

   5. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

   7. Simplified 56.5%

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

   if -3.2e14 < i < 1.44999999999999993e-62

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. fma-define 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in c around inf 69.8%

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

      1. *-commutative 69.8%

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

   7. Simplified 69.8%

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

   if 1.0599999999999999e168 < i

   1. Initial program 48.6%

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

   3. Taylor expanded in i around inf 56.3%

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

   4. Taylor expanded in y around inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. neg-mul-1 51.2%

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

   6. Simplified 51.2%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-16} \lor \neg \left(t \leq 3 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.5e-16) (not (<= t 3e+69)))
   (- (* t (- (* i b) (* x a))) (* j (- (* y i) (* c a))))
   (+ (* (- (* c a) (* y i)) j) (* z (- (* x y) (* c b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.5e-16) || !(t <= 3e+69)) {
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	} else {
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.5d-16)) .or. (.not. (t <= 3d+69))) then
        tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)))
    else
        tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.5e-16) || !(t <= 3e+69)) {
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	} else {
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.5e-16) or not (t <= 3e+69):
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)))
	else:
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.5e-16) || !(t <= 3e+69))
		tmp = Float64(Float64(t * Float64(Float64(i * b) - Float64(x * a))) - Float64(j * Float64(Float64(y * i) - Float64(c * a))));
	else
		tmp = Float64(Float64(Float64(Float64(c * a) - Float64(y * i)) * j) + Float64(z * Float64(Float64(x * y) - Float64(c * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.5e-16) || ~((t <= 3e+69)))
		tmp = (t * ((i * b) - (x * a))) - (j * ((y * i) - (c * a)));
	else
		tmp = (((c * a) - (y * i)) * j) + (z * ((x * y) - (c * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.5e-16], N[Not[LessEqual[t, 3e+69]], $MachinePrecision]], N[(N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999997e-16 or 2.99999999999999983e69 < t

   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 t around -inf 71.6%

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

   if -1.49999999999999997e-16 < t < 2.99999999999999983e69

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. *-commutative 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-16} \lor \neg \left(t \leq 3 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right) - j \cdot \left(y \cdot i - c \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j + z \cdot \left(x \cdot y - c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(i \cdot t\right)\\ \mathbf{if}\;i \leq -6 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+219} \lor \neg \left(i \leq 7.8 \cdot 10^{+285}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* i t))))
   (if (<= i -6e+71)
     t_1
     (if (<= i 1.5e-62)
       (* a (* c j))
       (if (or (<= i 5.1e+219) (not (<= i 7.8e+285))) t_1 (* x (* z y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (i * t);
	double tmp;
	if (i <= -6e+71) {
		tmp = t_1;
	} else if (i <= 1.5e-62) {
		tmp = a * (c * j);
	} else if ((i <= 5.1e+219) || !(i <= 7.8e+285)) {
		tmp = t_1;
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (i * t)
    if (i <= (-6d+71)) then
        tmp = t_1
    else if (i <= 1.5d-62) then
        tmp = a * (c * j)
    else if ((i <= 5.1d+219) .or. (.not. (i <= 7.8d+285))) then
        tmp = t_1
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (i * t);
	double tmp;
	if (i <= -6e+71) {
		tmp = t_1;
	} else if (i <= 1.5e-62) {
		tmp = a * (c * j);
	} else if ((i <= 5.1e+219) || !(i <= 7.8e+285)) {
		tmp = t_1;
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (i * t)
	tmp = 0
	if i <= -6e+71:
		tmp = t_1
	elif i <= 1.5e-62:
		tmp = a * (c * j)
	elif (i <= 5.1e+219) or not (i <= 7.8e+285):
		tmp = t_1
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(i * t))
	tmp = 0.0
	if (i <= -6e+71)
		tmp = t_1;
	elseif (i <= 1.5e-62)
		tmp = Float64(a * Float64(c * j));
	elseif ((i <= 5.1e+219) || !(i <= 7.8e+285))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (i * t);
	tmp = 0.0;
	if (i <= -6e+71)
		tmp = t_1;
	elseif (i <= 1.5e-62)
		tmp = a * (c * j);
	elseif ((i <= 5.1e+219) || ~((i <= 7.8e+285)))
		tmp = t_1;
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6e+71], t$95$1, If[LessEqual[i, 1.5e-62], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 5.1e+219], N[Not[LessEqual[i, 7.8e+285]], $MachinePrecision]], t$95$1, N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.00000000000000025e71 or 1.5000000000000001e-62 < i < 5.09999999999999993e219 or 7.7999999999999998e285 < i

   1. Initial program 67.8%

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

   3. Taylor expanded in i around inf 60.0%

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

   4. Taylor expanded in b around inf 37.9%

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

   if -6.00000000000000025e71 < i < 1.5000000000000001e-62

   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. Step-by-step derivation

      1. +-commutative 67.7%

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

      2. fma-define 69.3%

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

      3. *-commutative 69.3%

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

      4. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in a around inf 46.7%

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

      1. +-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

   7. Simplified 46.7%

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

   8. Taylor expanded in c around inf 34.1%

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

      1. *-commutative 34.1%

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

   10. Simplified 34.1%

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

   if 5.09999999999999993e219 < i < 7.7999999999999998e285

   1. Initial program 47.4%

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

      1. +-commutative 47.4%

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

      2. fma-define 47.4%

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

      3. *-commutative 47.4%

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

      4. *-commutative 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y around inf 89.1%

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

      1. +-commutative 89.1%

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

      2. mul-1-neg 89.1%

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

      3. unsub-neg 89.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 89.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 89.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 47.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+219} \lor \neg \left(i \leq 7.8 \cdot 10^{+285}\right):\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{-64}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4.6e-64)
   (* (- (* c a) (* y i)) j)
   (if (<= j 4e-85) (* b (- (* i t) (* z c))) (* c (- (* a j) (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -4.6e-64) {
		tmp = ((c * a) - (y * i)) * j;
	} else if (j <= 4e-85) {
		tmp = b * ((i * t) - (z * c));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-4.6d-64)) then
        tmp = ((c * a) - (y * i)) * j
    else if (j <= 4d-85) then
        tmp = b * ((i * t) - (z * c))
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -4.6e-64) {
		tmp = ((c * a) - (y * i)) * j;
	} else if (j <= 4e-85) {
		tmp = b * ((i * t) - (z * c));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -4.6e-64:
		tmp = ((c * a) - (y * i)) * j
	elif j <= 4e-85:
		tmp = b * ((i * t) - (z * c))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4.6e-64)
		tmp = Float64(Float64(Float64(c * a) - Float64(y * i)) * j);
	elseif (j <= 4e-85)
		tmp = Float64(b * Float64(Float64(i * t) - Float64(z * c)));
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -4.6e-64)
		tmp = ((c * a) - (y * i)) * j;
	elseif (j <= 4e-85)
		tmp = b * ((i * t) - (z * c));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -4.6e-64], N[(N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[j, 4e-85], N[(b * N[(N[(i * t), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.6000000000000003e-64

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 72.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.5%

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z} + \left(x \cdot y + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right)\right) - \left(-1 \cdot \frac{b \cdot \left(i \cdot t\right)}{z} + b \cdot c\right)\right)} \]

   7. Simplified 73.0%

      \[\leadsto \color{blue}{z \cdot \left(\left(\mathsf{fma}\left(x, y, \left(c \cdot a - i \cdot y\right) \cdot \frac{j}{z}\right) + \frac{t \cdot \mathsf{fma}\left(-a, x, b \cdot i\right)}{z}\right) - b \cdot c\right)} \]

   8. Taylor expanded in j around -inf 66.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -4.6000000000000003e-64 < j < 3.9999999999999999e-85

   1. Initial program 61.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 61.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 61.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 61.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 61.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 52.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   7. Simplified 52.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   8. Taylor expanded in b around inf 53.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 53.5%

         \[\leadsto b \cdot \left(i \cdot t - \color{blue}{z \cdot c}\right) \]

   10. Simplified 53.5%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t - z \cdot c\right)} \]

   if 3.9999999999999999e-85 < j

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 69.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 56.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   7. Simplified 56.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{-64}:\\ \;\;\;\;\left(c \cdot a - y \cdot i\right) \cdot j\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(i \cdot t - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+72} \lor \neg \left(i \leq 5.1 \cdot 10^{-61}\right):\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -4.2e+72) (not (<= i 5.1e-61))) (* b (* i t)) (* 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 ((i <= -4.2e+72) || !(i <= 5.1e-61)) {
		tmp = b * (i * t);
	} 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 ((i <= (-4.2d+72)) .or. (.not. (i <= 5.1d-61))) then
        tmp = b * (i * t)
    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 ((i <= -4.2e+72) || !(i <= 5.1e-61)) {
		tmp = b * (i * t);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -4.2e+72) or not (i <= 5.1e-61):
		tmp = b * (i * t)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -4.2e+72) || !(i <= 5.1e-61))
		tmp = Float64(b * Float64(i * t));
	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 ((i <= -4.2e+72) || ~((i <= 5.1e-61)))
		tmp = b * (i * t);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -4.2e+72], N[Not[LessEqual[i, 5.1e-61]], $MachinePrecision]], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4.2000000000000003e72 or 5.09999999999999968e-61 < i

   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 i around inf 60.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in b around inf 35.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -4.2000000000000003e72 < i < 5.09999999999999968e-61

   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. Step-by-step derivation

      1. +-commutative 67.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 69.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 69.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 46.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 46.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   7. Simplified 46.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   8. Taylor expanded in c around inf 34.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.1%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   10. Simplified 34.1%

       \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+72} \lor \neg \left(i \leq 5.1 \cdot 10^{-61}\right):\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.9% 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 66.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. +-commutative 66.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   2. fma-define 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   3. *-commutative 67.3%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

   4. *-commutative 67.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

3. Simplified 67.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 36.1%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
6. Step-by-step derivation

   1. +-commutative 36.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.1%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

7. Simplified 36.1%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

8. Taylor expanded in c around inf 23.8%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
9. Step-by-step derivation

   1. *-commutative 23.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

10. Simplified 23.8%

    \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

11. Final simplification 23.8%

    \[\leadsto a \cdot \left(c \cdot j\right) \]
12. Add Preprocessing

Developer target: 59.0% 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 2024087 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (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)))))