Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 96.0% → 98.4%

Time: 11.7s

Alternatives: 11

Speedup: 0.8×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x \cdot \left(y + -1\right), z, x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-247}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* x (+ y -1.0)) z x)))
   (if (<= z -2e-17) t_0 (if (<= z 2.65e-247) (fma (* y z) x x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((x * (y + -1.0)), z, x);
	double tmp;
	if (z <= -2e-17) {
		tmp = t_0;
	} else if (z <= 2.65e-247) {
		tmp = fma((y * z), x, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(x * Float64(y + -1.0)), z, x)
	tmp = 0.0
	if (z <= -2e-17)
		tmp = t_0;
	elseif (z <= 2.65e-247)
		tmp = fma(Float64(y * z), x, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -2e-17], t$95$0, If[LessEqual[z, 2.65e-247], N[(N[(y * z), $MachinePrecision] * x + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000014e-17 or 2.6499999999999999e-247 < z

   1. Initial program 94.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 100.0%

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

   if -2.00000000000000014e-17 < z < 2.6499999999999999e-247

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 85.5%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 85.5%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 99.9

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

   9. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, x, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;1 - y \leq -2 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= (- 1.0 y) -2e+40)
     t_0
     (if (<= (- 1.0 y) 1e+35) (fma (- 0.0 z) x x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if ((1.0 - y) <= -2e+40) {
		tmp = t_0;
	} else if ((1.0 - y) <= 1e+35) {
		tmp = fma((0.0 - z), x, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (Float64(1.0 - y) <= -2e+40)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 1e+35)
		tmp = fma(Float64(0.0 - z), x, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+40], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 1e+35], N[(N[(0.0 - z), $MachinePrecision] * x + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -2.00000000000000006e40 or 9.9999999999999997e34 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 90.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-rgt-identity N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + 0\right)} \]

      2. *-commutative N/A

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} + 0\right) \]

      3. accelerator-lowering-fma.f64 74.1

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, y, 0\right)} \]

   5. Simplified 74.1%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-lowering-*.f64 74.1

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

   7. Applied egg-rr 74.1%

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

   if -2.00000000000000006e40 < (-.f64 #s(literal 1 binary64) y) < 9.9999999999999997e34

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 99.4

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

   5. Simplified 99.4%

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

      1. sub-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot x + \left(\mathsf{neg}\left(z\right)\right) \cdot x} \]

      3. *-lft-identity N/A

         \[\leadsto \color{blue}{x} + \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot x + x} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), x, x\right)} \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

      7. --lowering--.f64 99.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

   7. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0 - z, x, x\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, x, x\right) \]

      2. neg-lowering-neg.f64 99.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]

   9. Applied egg-rr 99.4%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;1 - y \leq 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\mathsf{fma}\left(x \cdot y, z, x\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0)
   (fma (* x y) z x)
   (if (<= y 2e-6) (fma (- 0.0 z) x x) (fma y (* x z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = fma((x * y), z, x);
	} else if (y <= 2e-6) {
		tmp = fma((0.0 - z), x, x);
	} else {
		tmp = fma(y, (x * z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = fma(Float64(x * y), z, x);
	elseif (y <= 2e-6)
		tmp = fma(Float64(0.0 - z), x, x);
	else
		tmp = fma(y, Float64(x * z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(N[(x * y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[y, 2e-6], N[(N[(0.0 - z), $MachinePrecision] * x + x), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 91.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 92.0%

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

   if -1 < y < 1.99999999999999991e-6

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 100.0

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

   5. Simplified 100.0%

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

      1. sub-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot x + \left(\mathsf{neg}\left(z\right)\right) \cdot x} \]

      3. *-lft-identity N/A

         \[\leadsto \color{blue}{x} + \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot x + x} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), x, x\right)} \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

      7. --lowering--.f64 100.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

   7. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0 - z, x, x\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, x, x\right) \]

      2. neg-lowering-neg.f64 100.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]

   9. Applied egg-rr 100.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]

   if 1.99999999999999991e-6 < y

   1. Initial program 90.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 98.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\mathsf{fma}\left(x \cdot y, z, x\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y, x \cdot z, x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma y (* x z) x)))
   (if (<= y -1.0) t_0 (if (<= y 2e-6) (fma (- 0.0 z) x x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(y, (x * z), x);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2e-6) {
		tmp = fma((0.0 - z), x, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(y, Float64(x * z), x)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2e-6)
		tmp = fma(Float64(0.0 - z), x, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 2e-6], N[(N[(0.0 - z), $MachinePrecision] * x + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.99999999999999991e-6 < y

   1. Initial program 91.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 94.6%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 94.0%

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

   if -1 < y < 1.99999999999999991e-6

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 100.0

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

   5. Simplified 100.0%

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

      1. sub-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot x + \left(\mathsf{neg}\left(z\right)\right) \cdot x} \]

      3. *-lft-identity N/A

         \[\leadsto \color{blue}{x} + \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot x + x} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), x, x\right)} \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

      7. --lowering--.f64 100.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

   7. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0 - z, x, x\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, x, x\right) \]

      2. neg-lowering-neg.f64 100.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]

   9. Applied egg-rr 100.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot z, x\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x \cdot z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x y))))
   (if (<= y -3.5e+43) t_0 (if (<= y 1.5e+36) (fma (- 0.0 z) x x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -3.5e+43) {
		tmp = t_0;
	} else if (y <= 1.5e+36) {
		tmp = fma((0.0 - z), x, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -3.5e+43)
		tmp = t_0;
	elseif (y <= 1.5e+36)
		tmp = fma(Float64(0.0 - z), x, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+43], t$95$0, If[LessEqual[y, 1.5e+36], N[(N[(0.0 - z), $MachinePrecision] * x + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000001e43 or 1.5e36 < y

   1. Initial program 90.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-rgt-identity N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + 0\right)} \]

      2. *-commutative N/A

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} + 0\right) \]

      3. accelerator-lowering-fma.f64 74.1

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, y, 0\right)} \]

   5. Simplified 74.1%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 81.5

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

   7. Applied egg-rr 81.5%

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

   if -3.5000000000000001e43 < y < 1.5e36

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 99.4

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

   5. Simplified 99.4%

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

      1. sub-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot x + \left(\mathsf{neg}\left(z\right)\right) \cdot x} \]

      3. *-lft-identity N/A

         \[\leadsto \color{blue}{x} + \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot x + x} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), x, x\right)} \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

      7. --lowering--.f64 99.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

   7. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0 - z, x, x\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, x, x\right) \]

      2. neg-lowering-neg.f64 99.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]

   9. Applied egg-rr 99.4%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0 - x \cdot z\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 27500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 0.0 (* x z))))
   (if (<= z -1.0) t_0 (if (<= z 27500000.0) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 0.0 - (x * z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 27500000.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.0d0 - (x * z)
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 27500000.0d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.0 - (x * z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 27500000.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.0 - (x * z)
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 27500000.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.0 - Float64(x * z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 27500000.0)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.0 - (x * z);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 27500000.0)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.0 - N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 27500000.0], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2.75e7 < z

   1. Initial program 90.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 53.2

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

   5. Simplified 53.2%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto x \cdot \color{blue}{\left(0 - z\right)} \]

      3. --lowering--.f64 52.6

         \[\leadsto x \cdot \color{blue}{\left(0 - z\right)} \]

   8. Simplified 52.6%

      \[\leadsto x \cdot \color{blue}{\left(0 - z\right)} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 52.6

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

   10. Applied egg-rr 52.6%

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

   if -1 < z < 2.75e7

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 70.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;0 - x \cdot z\\ \mathbf{elif}\;z \leq 27500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(y + -1\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, x \cdot z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5e-55) (fma (* x (+ y -1.0)) z x) (fma (+ y -1.0) (* x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e-55) {
		tmp = fma((x * (y + -1.0)), z, x);
	} else {
		tmp = fma((y + -1.0), (x * z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5e-55)
		tmp = fma(Float64(x * Float64(y + -1.0)), z, x);
	else
		tmp = fma(Float64(y + -1.0), Float64(x * z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5e-55], N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.0000000000000002e-55

   1. Initial program 93.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 96.0%

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

   if 5.0000000000000002e-55 < x

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y + -1, z \cdot x, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(y + -1\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, x \cdot z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(y + -1\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y + -1\right) \cdot z, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5e-55) (fma (* x (+ y -1.0)) z x) (fma (* (+ y -1.0) z) x x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e-55) {
		tmp = fma((x * (y + -1.0)), z, x);
	} else {
		tmp = fma(((y + -1.0) * z), x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5e-55)
		tmp = fma(Float64(x * Float64(y + -1.0)), z, x);
	else
		tmp = fma(Float64(Float64(y + -1.0) * z), x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5e-55], N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.0000000000000002e-55

   1. Initial program 93.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 96.0%

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

   if 5.0000000000000002e-55 < x

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(y + -1\right), x, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(y + -1\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y + -1\right) \cdot z, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0 - z, x, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- 0.0 z) x x))

C

double code(double x, double y, double z) {
	return fma((0.0 - z), x, x);
}

Julia

function code(x, y, z)
	return fma(Float64(0.0 - z), x, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(0.0 - z), $MachinePrecision] * x + x), $MachinePrecision]

Derivation

1. Initial program 95.5%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. --lowering--.f64 63.3

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

5. Simplified 63.3%

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

   1. sub-neg N/A

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

   2. distribute-rgt-in N/A

      \[\leadsto \color{blue}{1 \cdot x + \left(\mathsf{neg}\left(z\right)\right) \cdot x} \]

   3. *-lft-identity N/A

      \[\leadsto \color{blue}{x} + \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot x + x} \]

   5. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), x, x\right)} \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

   7. --lowering--.f64 63.4

      \[\leadsto \mathsf{fma}\left(\color{blue}{0 - z}, x, x\right) \]

7. Applied egg-rr 63.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0 - z, x, x\right)} \]
8. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(z\right)}, x, x\right) \]

   2. neg-lowering-neg.f64 63.4

      \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]

9. Applied egg-rr 63.4%

   \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, x, x\right) \]

10. Final simplification 63.4%

    \[\leadsto \mathsf{fma}\left(0 - z, x, x\right) \]
11. Add Preprocessing

Alternative 10: 66.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 z)))

C

double code(double x, double y, double z) {
	return x * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - z);
}

Python

def code(x, y, z):
	return x * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.5%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. --lowering--.f64 63.3

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

5. Simplified 63.3%

   \[\leadsto x \cdot \color{blue}{\left(1 - z\right)} \]
6. Add Preprocessing

Alternative 11: 39.0% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.5%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 39.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024195 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

  (* x (- 1.0 (* (- 1.0 y) z))))