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

Percentage Accurate: 96.1% → 97.8%

Time: 6.6s

Alternatives: 9

Speedup: 0.8×

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: 96.1% 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: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, z \cdot x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 8.2e-101)
   (* x (+ 1.0 (* z (+ y -1.0))))
   (fma (+ y -1.0) (* z x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 8.2e-101) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = fma((y + -1.0), (z * x), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 8.2e-101)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = fma(Float64(y + -1.0), Float64(z * x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 8.2e-101], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.20000000000000052e-101

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 8.20000000000000052e-101 < z

   1. Initial program 94.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.2%

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

      2. *-lft-identity 94.2%

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

      3. cancel-sign-sub-inv 94.2%

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

      4. +-commutative 94.2%

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

      5. distribute-lft-neg-in 94.2%

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

      6. associate-*l* 99.9%

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

      7. fma-def 99.9%

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

      8. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(1 - y\right)}, z \cdot x, x\right) \]

      9. associate--r- 99.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - 1\right) + y}, z \cdot x, x\right) \]

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

      12. *-commutative 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, z \cdot x, x\right)\\ \end{array} \]

Alternative 2: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* z y))))
   (if (<= y -1.85e+121)
     t_1
     (if (<= y -2.9e-110)
       x
       (if (<= y -2.5e-189)
         t_0
         (if (<= y -9e-250)
           x
           (if (<= y 1.55e-6) t_0 (if (<= y 7.8e+34) x t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (z * y);
	double tmp;
	if (y <= -1.85e+121) {
		tmp = t_1;
	} else if (y <= -2.9e-110) {
		tmp = x;
	} else if (y <= -2.5e-189) {
		tmp = t_0;
	} else if (y <= -9e-250) {
		tmp = x;
	} else if (y <= 1.55e-6) {
		tmp = t_0;
	} else if (y <= 7.8e+34) {
		tmp = 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 = z * -x
    t_1 = x * (z * y)
    if (y <= (-1.85d+121)) then
        tmp = t_1
    else if (y <= (-2.9d-110)) then
        tmp = x
    else if (y <= (-2.5d-189)) then
        tmp = t_0
    else if (y <= (-9d-250)) then
        tmp = x
    else if (y <= 1.55d-6) then
        tmp = t_0
    else if (y <= 7.8d+34) then
        tmp = 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 = z * -x;
	double t_1 = x * (z * y);
	double tmp;
	if (y <= -1.85e+121) {
		tmp = t_1;
	} else if (y <= -2.9e-110) {
		tmp = x;
	} else if (y <= -2.5e-189) {
		tmp = t_0;
	} else if (y <= -9e-250) {
		tmp = x;
	} else if (y <= 1.55e-6) {
		tmp = t_0;
	} else if (y <= 7.8e+34) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (z * y)
	tmp = 0
	if y <= -1.85e+121:
		tmp = t_1
	elif y <= -2.9e-110:
		tmp = x
	elif y <= -2.5e-189:
		tmp = t_0
	elif y <= -9e-250:
		tmp = x
	elif y <= 1.55e-6:
		tmp = t_0
	elif y <= 7.8e+34:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(z * y))
	tmp = 0.0
	if (y <= -1.85e+121)
		tmp = t_1;
	elseif (y <= -2.9e-110)
		tmp = x;
	elseif (y <= -2.5e-189)
		tmp = t_0;
	elseif (y <= -9e-250)
		tmp = x;
	elseif (y <= 1.55e-6)
		tmp = t_0;
	elseif (y <= 7.8e+34)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (z * y);
	tmp = 0.0;
	if (y <= -1.85e+121)
		tmp = t_1;
	elseif (y <= -2.9e-110)
		tmp = x;
	elseif (y <= -2.5e-189)
		tmp = t_0;
	elseif (y <= -9e-250)
		tmp = x;
	elseif (y <= 1.55e-6)
		tmp = t_0;
	elseif (y <= 7.8e+34)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+121], t$95$1, If[LessEqual[y, -2.9e-110], x, If[LessEqual[y, -2.5e-189], t$95$0, If[LessEqual[y, -9e-250], x, If[LessEqual[y, 1.55e-6], t$95$0, If[LessEqual[y, 7.8e+34], x, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85000000000000006e121 or 7.80000000000000038e34 < y

   1. Initial program 93.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   if -1.85000000000000006e121 < y < -2.9000000000000002e-110 or -2.4999999999999999e-189 < y < -8.99999999999999987e-250 or 1.55e-6 < y < 7.80000000000000038e34

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 72.3%

      \[\leadsto \color{blue}{x} \]

   if -2.9000000000000002e-110 < y < -2.4999999999999999e-189 or -8.99999999999999987e-250 < y < 1.55e-6

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. distribute-rgt1-in 99.3%

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

      4. cancel-sign-sub-inv 99.3%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 99.3%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-out 66.7%

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

   7. Simplified 66.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-189}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 3: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= y -8.2e+121)
     (* x (* z y))
     (if (<= y -6.5e-110)
       x
       (if (<= y -5.8e-191)
         t_0
         (if (<= y -1.15e-247)
           x
           (if (<= y 1.3e-7) t_0 (if (<= y 9.8e+33) x (* y (* z x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (y <= -8.2e+121) {
		tmp = x * (z * y);
	} else if (y <= -6.5e-110) {
		tmp = x;
	} else if (y <= -5.8e-191) {
		tmp = t_0;
	} else if (y <= -1.15e-247) {
		tmp = x;
	} else if (y <= 1.3e-7) {
		tmp = t_0;
	} else if (y <= 9.8e+33) {
		tmp = x;
	} else {
		tmp = y * (z * x);
	}
	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 = z * -x
    if (y <= (-8.2d+121)) then
        tmp = x * (z * y)
    else if (y <= (-6.5d-110)) then
        tmp = x
    else if (y <= (-5.8d-191)) then
        tmp = t_0
    else if (y <= (-1.15d-247)) then
        tmp = x
    else if (y <= 1.3d-7) then
        tmp = t_0
    else if (y <= 9.8d+33) then
        tmp = x
    else
        tmp = y * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (y <= -8.2e+121) {
		tmp = x * (z * y);
	} else if (y <= -6.5e-110) {
		tmp = x;
	} else if (y <= -5.8e-191) {
		tmp = t_0;
	} else if (y <= -1.15e-247) {
		tmp = x;
	} else if (y <= 1.3e-7) {
		tmp = t_0;
	} else if (y <= 9.8e+33) {
		tmp = x;
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if y <= -8.2e+121:
		tmp = x * (z * y)
	elif y <= -6.5e-110:
		tmp = x
	elif y <= -5.8e-191:
		tmp = t_0
	elif y <= -1.15e-247:
		tmp = x
	elif y <= 1.3e-7:
		tmp = t_0
	elif y <= 9.8e+33:
		tmp = x
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (y <= -8.2e+121)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= -6.5e-110)
		tmp = x;
	elseif (y <= -5.8e-191)
		tmp = t_0;
	elseif (y <= -1.15e-247)
		tmp = x;
	elseif (y <= 1.3e-7)
		tmp = t_0;
	elseif (y <= 9.8e+33)
		tmp = x;
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (y <= -8.2e+121)
		tmp = x * (z * y);
	elseif (y <= -6.5e-110)
		tmp = x;
	elseif (y <= -5.8e-191)
		tmp = t_0;
	elseif (y <= -1.15e-247)
		tmp = x;
	elseif (y <= 1.3e-7)
		tmp = t_0;
	elseif (y <= 9.8e+33)
		tmp = x;
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[y, -8.2e+121], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-110], x, If[LessEqual[y, -5.8e-191], t$95$0, If[LessEqual[y, -1.15e-247], x, If[LessEqual[y, 1.3e-7], t$95$0, If[LessEqual[y, 9.8e+33], x, N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.2e121

   1. Initial program 97.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 89.8%

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

      1. *-commutative 89.8%

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

   4. Simplified 89.8%

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

   if -8.2e121 < y < -6.4999999999999996e-110 or -5.7999999999999999e-191 < y < -1.15e-247 or 1.29999999999999999e-7 < y < 9.80000000000000027e33

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 72.3%

      \[\leadsto \color{blue}{x} \]

   if -6.4999999999999996e-110 < y < -5.7999999999999999e-191 or -1.15e-247 < y < 1.29999999999999999e-7

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. distribute-rgt1-in 99.3%

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

      4. cancel-sign-sub-inv 99.3%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 99.3%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-out 66.7%

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

   7. Simplified 66.7%

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

   if 9.80000000000000027e33 < y

   1. Initial program 91.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 77.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 4: 57.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= y -1.7e+121)
     (* x (* z y))
     (if (<= y -2.9e-110)
       x
       (if (<= y -2.8e-192)
         t_0
         (if (<= y -1.02e-250)
           x
           (if (<= y 1.8e-8) t_0 (if (<= y 8.8e+33) x (* z (* x y))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (y <= -1.7e+121) {
		tmp = x * (z * y);
	} else if (y <= -2.9e-110) {
		tmp = x;
	} else if (y <= -2.8e-192) {
		tmp = t_0;
	} else if (y <= -1.02e-250) {
		tmp = x;
	} else if (y <= 1.8e-8) {
		tmp = t_0;
	} else if (y <= 8.8e+33) {
		tmp = x;
	} else {
		tmp = z * (x * y);
	}
	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 = z * -x
    if (y <= (-1.7d+121)) then
        tmp = x * (z * y)
    else if (y <= (-2.9d-110)) then
        tmp = x
    else if (y <= (-2.8d-192)) then
        tmp = t_0
    else if (y <= (-1.02d-250)) then
        tmp = x
    else if (y <= 1.8d-8) then
        tmp = t_0
    else if (y <= 8.8d+33) then
        tmp = x
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (y <= -1.7e+121) {
		tmp = x * (z * y);
	} else if (y <= -2.9e-110) {
		tmp = x;
	} else if (y <= -2.8e-192) {
		tmp = t_0;
	} else if (y <= -1.02e-250) {
		tmp = x;
	} else if (y <= 1.8e-8) {
		tmp = t_0;
	} else if (y <= 8.8e+33) {
		tmp = x;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if y <= -1.7e+121:
		tmp = x * (z * y)
	elif y <= -2.9e-110:
		tmp = x
	elif y <= -2.8e-192:
		tmp = t_0
	elif y <= -1.02e-250:
		tmp = x
	elif y <= 1.8e-8:
		tmp = t_0
	elif y <= 8.8e+33:
		tmp = x
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (y <= -1.7e+121)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= -2.9e-110)
		tmp = x;
	elseif (y <= -2.8e-192)
		tmp = t_0;
	elseif (y <= -1.02e-250)
		tmp = x;
	elseif (y <= 1.8e-8)
		tmp = t_0;
	elseif (y <= 8.8e+33)
		tmp = x;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (y <= -1.7e+121)
		tmp = x * (z * y);
	elseif (y <= -2.9e-110)
		tmp = x;
	elseif (y <= -2.8e-192)
		tmp = t_0;
	elseif (y <= -1.02e-250)
		tmp = x;
	elseif (y <= 1.8e-8)
		tmp = t_0;
	elseif (y <= 8.8e+33)
		tmp = x;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.7e+121], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e-110], x, If[LessEqual[y, -2.8e-192], t$95$0, If[LessEqual[y, -1.02e-250], x, If[LessEqual[y, 1.8e-8], t$95$0, If[LessEqual[y, 8.8e+33], x, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.70000000000000005e121

   1. Initial program 97.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 89.8%

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

      1. *-commutative 89.8%

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

   4. Simplified 89.8%

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

   if -1.70000000000000005e121 < y < -2.9000000000000002e-110 or -2.80000000000000004e-192 < y < -1.02000000000000001e-250 or 1.79999999999999991e-8 < y < 8.79999999999999975e33

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 72.3%

      \[\leadsto \color{blue}{x} \]

   if -2.9000000000000002e-110 < y < -2.80000000000000004e-192 or -1.02000000000000001e-250 < y < 1.79999999999999991e-8

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. distribute-rgt1-in 99.3%

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

      4. cancel-sign-sub-inv 99.3%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 99.3%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-out 66.7%

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

   7. Simplified 66.7%

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

   if 8.79999999999999975e33 < y

   1. Initial program 91.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 77.6%

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

      1. associate-*r* 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*l* 79.2%

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

   4. Simplified 79.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 5: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -380 \lor \neg \left(z \leq 2.9 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -380.0) (not (<= z 2.9e-16)))
   (* z (- (* x y) x))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -380.0) || !(z <= 2.9e-16)) {
		tmp = z * ((x * y) - x);
	} else {
		tmp = x + (x * (z * y));
	}
	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) :: tmp
    if ((z <= (-380.0d0)) .or. (.not. (z <= 2.9d-16))) then
        tmp = z * ((x * y) - x)
    else
        tmp = x + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -380.0) || !(z <= 2.9e-16)) {
		tmp = z * ((x * y) - x);
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -380.0) or not (z <= 2.9e-16):
		tmp = z * ((x * y) - x)
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -380.0) || !(z <= 2.9e-16))
		tmp = Float64(z * Float64(Float64(x * y) - x));
	else
		tmp = Float64(x + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -380.0) || ~((z <= 2.9e-16)))
		tmp = z * ((x * y) - x);
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -380.0], N[Not[LessEqual[z, 2.9e-16]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -380 or 2.8999999999999998e-16 < z

   1. Initial program 95.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 98.9%

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

      1. *-commutative 98.9%

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

      2. sub-neg 98.9%

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

      3. metadata-eval 98.9%

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

      4. distribute-rgt-in 98.9%

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

      5. neg-mul-1 98.9%

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

      6. unsub-neg 98.9%

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

   4. Simplified 98.9%

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

   if -380 < z < 2.8999999999999998e-16

   1. Initial program 99.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-lft-neg-out 99.3%

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

      3. *-commutative 99.3%

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

   4. Simplified 99.3%

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

      1. *-commutative 99.3%

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

      2. cancel-sign-sub 99.3%

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

      3. *-commutative 99.3%

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

      4. distribute-rgt-in 99.3%

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

      5. *-un-lft-identity 99.3%

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

   6. Applied egg-rr 99.3%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -380 \lor \neg \left(z \leq 2.9 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 6: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 5e+14) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (- (* x y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+14) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * ((x * y) - x);
	}
	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) :: tmp
    if (z <= 5d+14) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * ((x * y) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+14) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5e+14:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * ((x * y) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5e+14)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(Float64(x * y) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 5e+14)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * ((x * y) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5e+14], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5e14

   1. Initial program 99.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 5e14 < z

   1. Initial program 92.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 7: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+34}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e+120)
   (* x (* z y))
   (if (<= y 4.6e+34) (- x (* z x)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+120) {
		tmp = x * (z * y);
	} else if (y <= 4.6e+34) {
		tmp = x - (z * x);
	} else {
		tmp = z * (x * y);
	}
	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) :: tmp
    if (y <= (-3.6d+120)) then
        tmp = x * (z * y)
    else if (y <= 4.6d+34) then
        tmp = x - (z * x)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+120) {
		tmp = x * (z * y);
	} else if (y <= 4.6e+34) {
		tmp = x - (z * x);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e+120:
		tmp = x * (z * y)
	elif y <= 4.6e+34:
		tmp = x - (z * x)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e+120)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 4.6e+34)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e+120)
		tmp = x * (z * y);
	elseif (y <= 4.6e+34)
		tmp = x - (z * x);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e+120], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+34], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000016e120

   1. Initial program 97.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 89.8%

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

      1. *-commutative 89.8%

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

   4. Simplified 89.8%

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

   if -3.60000000000000016e120 < y < 4.5999999999999996e34

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 95.2%

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

      1. sub-neg 95.2%

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

      2. +-commutative 95.2%

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

      3. distribute-rgt1-in 95.2%

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

      4. cancel-sign-sub-inv 95.2%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 95.2%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   if 4.5999999999999996e34 < y

   1. Initial program 91.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 77.6%

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

      1. associate-*r* 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*l* 79.2%

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

   4. Simplified 79.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+34}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 8: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.12 \cdot 10^{-26}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.12e-26))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.12e-26)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	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) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.12d-26))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.12e-26)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.12e-26):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.12e-26))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.12e-26)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.12e-26]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.12e-26 < z

   1. Initial program 95.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 58.7%

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

      1. sub-neg 58.7%

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

      2. +-commutative 58.7%

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

      3. distribute-rgt1-in 58.7%

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

      4. cancel-sign-sub-inv 58.7%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 58.7%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 57.8%

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

      1. mul-1-neg 57.8%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-out 57.8%

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

   7. Simplified 57.8%

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

   if -1 < z < 1.12e-26

   1. Initial program 99.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 76.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.12 \cdot 10^{-26}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 40.0% accurate, 9.0× 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 97.7%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in z around 0 37.8%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 37.8%

   \[\leadsto x \]

Developer target: 99.7% 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 2023252 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

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