Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.8%

Time: 9.9s

Alternatives: 14

Speedup: 1.2×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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 + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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 + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fma (- y x) (* 6.0 (- 0.6666666666666666 z)) x))

C

double code(double x, double y, double z) {
	return fma((y - x), (6.0 * (0.6666666666666666 - z)), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(6.0 * Float64(0.6666666666666666 - z)), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.3%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.3%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.5%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\color{blue}{0.6666666666666666} - z\right), x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right) \]

Alternative 2: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ t_1 := z \cdot \left(y \cdot -6\right)\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-217}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+189}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))) (t_1 (* z (* y -6.0))))
   (if (<= z -4.7e+72)
     t_0
     (if (<= z -115000000.0)
       t_1
       (if (<= z 8.6e-296)
         (* y 4.0)
         (if (<= z 3.8e-217)
           (* x -3.0)
           (if (<= z 0.65)
             (* y 4.0)
             (if (<= z 1.4e+149)
               (* -6.0 (* y z))
               (if (<= z 3.5e+189) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double t_1 = z * (y * -6.0);
	double tmp;
	if (z <= -4.7e+72) {
		tmp = t_0;
	} else if (z <= -115000000.0) {
		tmp = t_1;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 3.8e-217) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 1.4e+149) {
		tmp = -6.0 * (y * z);
	} else if (z <= 3.5e+189) {
		tmp = t_0;
	} 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 * 6.0d0)
    t_1 = z * (y * (-6.0d0))
    if (z <= (-4.7d+72)) then
        tmp = t_0
    else if (z <= (-115000000.0d0)) then
        tmp = t_1
    else if (z <= 8.6d-296) then
        tmp = y * 4.0d0
    else if (z <= 3.8d-217) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if (z <= 1.4d+149) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= 3.5d+189) then
        tmp = t_0
    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 * 6.0);
	double t_1 = z * (y * -6.0);
	double tmp;
	if (z <= -4.7e+72) {
		tmp = t_0;
	} else if (z <= -115000000.0) {
		tmp = t_1;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 3.8e-217) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 1.4e+149) {
		tmp = -6.0 * (y * z);
	} else if (z <= 3.5e+189) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	t_1 = z * (y * -6.0)
	tmp = 0
	if z <= -4.7e+72:
		tmp = t_0
	elif z <= -115000000.0:
		tmp = t_1
	elif z <= 8.6e-296:
		tmp = y * 4.0
	elif z <= 3.8e-217:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif z <= 1.4e+149:
		tmp = -6.0 * (y * z)
	elif z <= 3.5e+189:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	t_1 = Float64(z * Float64(y * -6.0))
	tmp = 0.0
	if (z <= -4.7e+72)
		tmp = t_0;
	elseif (z <= -115000000.0)
		tmp = t_1;
	elseif (z <= 8.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.8e-217)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.4e+149)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= 3.5e+189)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	t_1 = z * (y * -6.0);
	tmp = 0.0;
	if (z <= -4.7e+72)
		tmp = t_0;
	elseif (z <= -115000000.0)
		tmp = t_1;
	elseif (z <= 8.6e-296)
		tmp = y * 4.0;
	elseif (z <= 3.8e-217)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif (z <= 1.4e+149)
		tmp = -6.0 * (y * z);
	elseif (z <= 3.5e+189)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e+72], t$95$0, If[LessEqual[z, -115000000.0], t$95$1, If[LessEqual[z, 8.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.8e-217], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.4e+149], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+189], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.70000000000000034e72 or 1.4e149 < z < 3.49999999999999996e189

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around 0 64.0%

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

      1. *-commutative 64.0%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot 6} \]

      2. associate-*l* 64.1%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot 6\right)} \]

   5. Simplified 64.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot 6\right)} \]

   if -4.70000000000000034e72 < z < -1.15e8 or 3.49999999999999996e189 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 98.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around inf 68.1%

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

      1. associate-*r* 68.2%

         \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]

      2. *-commutative 68.2%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   5. Simplified 68.2%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   if -1.15e8 < z < 8.59999999999999956e-296 or 3.79999999999999987e-217 < z < 0.650000000000000022

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 96.1%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 8.59999999999999956e-296 < z < 3.79999999999999987e-217

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.650000000000000022 < z < 1.4e149

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.6%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around inf 68.0%

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

      1. *-commutative 68.0%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-217}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+149}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+189}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]

Alternative 3: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ t_1 := z \cdot \left(y \cdot -6\right)\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+188}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))) (t_1 (* z (* y -6.0))))
   (if (<= z -1.56e+71)
     t_0
     (if (<= z -115000000.0)
       t_1
       (if (<= z 8.6e-296)
         (* y 4.0)
         (if (<= z 2.5e-217)
           (* x -3.0)
           (if (<= z 0.65)
             (* y 4.0)
             (if (<= z 3.3e+131)
               (* y (* z -6.0))
               (if (<= z 1.8e+188) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double t_1 = z * (y * -6.0);
	double tmp;
	if (z <= -1.56e+71) {
		tmp = t_0;
	} else if (z <= -115000000.0) {
		tmp = t_1;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-217) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 3.3e+131) {
		tmp = y * (z * -6.0);
	} else if (z <= 1.8e+188) {
		tmp = t_0;
	} 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 * 6.0d0)
    t_1 = z * (y * (-6.0d0))
    if (z <= (-1.56d+71)) then
        tmp = t_0
    else if (z <= (-115000000.0d0)) then
        tmp = t_1
    else if (z <= 8.6d-296) then
        tmp = y * 4.0d0
    else if (z <= 2.5d-217) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if (z <= 3.3d+131) then
        tmp = y * (z * (-6.0d0))
    else if (z <= 1.8d+188) then
        tmp = t_0
    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 * 6.0);
	double t_1 = z * (y * -6.0);
	double tmp;
	if (z <= -1.56e+71) {
		tmp = t_0;
	} else if (z <= -115000000.0) {
		tmp = t_1;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-217) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 3.3e+131) {
		tmp = y * (z * -6.0);
	} else if (z <= 1.8e+188) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	t_1 = z * (y * -6.0)
	tmp = 0
	if z <= -1.56e+71:
		tmp = t_0
	elif z <= -115000000.0:
		tmp = t_1
	elif z <= 8.6e-296:
		tmp = y * 4.0
	elif z <= 2.5e-217:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif z <= 3.3e+131:
		tmp = y * (z * -6.0)
	elif z <= 1.8e+188:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	t_1 = Float64(z * Float64(y * -6.0))
	tmp = 0.0
	if (z <= -1.56e+71)
		tmp = t_0;
	elseif (z <= -115000000.0)
		tmp = t_1;
	elseif (z <= 8.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.5e-217)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.3e+131)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= 1.8e+188)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	t_1 = z * (y * -6.0);
	tmp = 0.0;
	if (z <= -1.56e+71)
		tmp = t_0;
	elseif (z <= -115000000.0)
		tmp = t_1;
	elseif (z <= 8.6e-296)
		tmp = y * 4.0;
	elseif (z <= 2.5e-217)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif (z <= 3.3e+131)
		tmp = y * (z * -6.0);
	elseif (z <= 1.8e+188)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.56e+71], t$95$0, If[LessEqual[z, -115000000.0], t$95$1, If[LessEqual[z, 8.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.5e-217], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.3e+131], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+188], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5599999999999999e71 or 3.2999999999999998e131 < z < 1.8000000000000001e188

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around 0 64.0%

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

      1. *-commutative 64.0%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot 6} \]

      2. associate-*l* 64.1%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot 6\right)} \]

   5. Simplified 64.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot 6\right)} \]

   if -1.5599999999999999e71 < z < -1.15e8 or 1.8000000000000001e188 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 98.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around inf 68.1%

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

      1. associate-*r* 68.2%

         \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]

      2. *-commutative 68.2%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   5. Simplified 68.2%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   if -1.15e8 < z < 8.59999999999999956e-296 or 2.5000000000000001e-217 < z < 0.650000000000000022

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 96.1%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 8.59999999999999956e-296 < z < 2.5000000000000001e-217

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.650000000000000022 < z < 3.2999999999999998e131

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\left(-z\right) + \frac{2}{3}\right)}, x\right) \]

      6. distribute-lft-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{6 \cdot \left(-z\right) + 6 \cdot \frac{2}{3}}, x\right) \]

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, \color{blue}{-6}, 6 \cdot \frac{2}{3}\right), x\right) \]

      12. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 6 \cdot \color{blue}{0.6666666666666666}\right), x\right) \]

      13. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, \color{blue}{4}\right), x\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 4\right), x\right)} \]

   4. Taylor expanded in y around inf 68.1%

      \[\leadsto \color{blue}{\left(4 + -6 \cdot z\right) \cdot y} \]

   5. Taylor expanded in z around inf 68.1%

      \[\leadsto \color{blue}{\left(-6 \cdot z\right)} \cdot y \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+188}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0285:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0285)
     t_0
     (if (<= z 8.6e-296)
       (* y 4.0)
       (if (<= z 1.6e-215) (* x -3.0) (if (<= z 0.55) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0285) {
		tmp = t_0;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-215) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} 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 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0285d0)) then
        tmp = t_0
    else if (z <= 8.6d-296) then
        tmp = y * 4.0d0
    else if (z <= 1.6d-215) then
        tmp = x * (-3.0d0)
    else if (z <= 0.55d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0285) {
		tmp = t_0;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-215) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0285:
		tmp = t_0
	elif z <= 8.6e-296:
		tmp = y * 4.0
	elif z <= 1.6e-215:
		tmp = x * -3.0
	elif z <= 0.55:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0285)
		tmp = t_0;
	elseif (z <= 8.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.6e-215)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.55)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0285)
		tmp = t_0;
	elseif (z <= 8.6e-296)
		tmp = y * 4.0;
	elseif (z <= 1.6e-215)
		tmp = x * -3.0;
	elseif (z <= 0.55)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0285], t$95$0, If[LessEqual[z, 8.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.6e-215], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.028500000000000001 or 0.55000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.028500000000000001 < z < 8.59999999999999956e-296 or 1.6000000000000001e-215 < z < 0.55000000000000004

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 96.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 58.4%

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

      1. *-commutative 58.4%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 8.59999999999999956e-296 < z < 1.6000000000000001e-215

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0285:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.018:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.018)
   (* z (* (- y x) -6.0))
   (if (<= z 8.6e-296)
     (* y 4.0)
     (if (<= z 8e-215)
       (* x -3.0)
       (if (<= z 0.56) (* y 4.0) (* -6.0 (* (- y x) z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.018) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 8e-215) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	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 <= (-0.018d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 8.6d-296) then
        tmp = y * 4.0d0
    else if (z <= 8d-215) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) then
        tmp = y * 4.0d0
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.018) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 8e-215) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.018:
		tmp = z * ((y - x) * -6.0)
	elif z <= 8.6e-296:
		tmp = y * 4.0
	elif z <= 8e-215:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.018)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 8.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 8e-215)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.018)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 8.6e-296)
		tmp = y * 4.0;
	elseif (z <= 8e-215)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		tmp = y * 4.0;
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.018], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8e-215], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0179999999999999986

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.8%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.8%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. associate-*l* 98.9%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   4. Simplified 98.9%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   if -0.0179999999999999986 < z < 8.59999999999999956e-296 or 8.00000000000000033e-215 < z < 0.56000000000000005

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 96.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 58.4%

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

      1. *-commutative 58.4%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 8.59999999999999956e-296 < z < 8.00000000000000033e-215

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.56000000000000005 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.018:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0132:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0132)
   (* z (* (- y x) -6.0))
   (if (<= z 8.6e-296)
     (* y 4.0)
     (if (<= z 1.2e-216)
       (* x -3.0)
       (if (<= z 0.65) (* y 4.0) (* (- y x) (* z -6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0132) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-216) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	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) :: tmp
    if (z <= (-0.0132d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 8.6d-296) then
        tmp = y * 4.0d0
    else if (z <= 1.2d-216) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = (y - x) * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0132) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-216) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0132:
		tmp = z * ((y - x) * -6.0)
	elif z <= 8.6e-296:
		tmp = y * 4.0
	elif z <= 1.2e-216:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = (y - x) * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0132)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 8.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.2e-216)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0132)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 8.6e-296)
		tmp = y * 4.0;
	elseif (z <= 1.2e-216)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = (y - x) * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0132], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.2e-216], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0132

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.8%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.8%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. associate-*l* 98.9%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   4. Simplified 98.9%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   if -0.0132 < z < 8.59999999999999956e-296 or 1.20000000000000002e-216 < z < 0.650000000000000022

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 96.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 58.4%

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

      1. *-commutative 58.4%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 8.59999999999999956e-296 < z < 1.20000000000000002e-216

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.650000000000000022 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(y - x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0132:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 7: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;z \leq -490:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 300000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))))
   (if (<= z -490.0)
     (* z (* (- y x) -6.0))
     (if (<= z 8.6e-296)
       t_0
       (if (<= z 2.05e-215)
         (* x -3.0)
         (if (<= z 300000.0) t_0 (* (- y x) (* z -6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (z <= -490.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = t_0;
	} else if (z <= 2.05e-215) {
		tmp = x * -3.0;
	} else if (z <= 300000.0) {
		tmp = t_0;
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	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 = y * (4.0d0 + (z * (-6.0d0)))
    if (z <= (-490.0d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 8.6d-296) then
        tmp = t_0
    else if (z <= 2.05d-215) then
        tmp = x * (-3.0d0)
    else if (z <= 300000.0d0) then
        tmp = t_0
    else
        tmp = (y - x) * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (z <= -490.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = t_0;
	} else if (z <= 2.05e-215) {
		tmp = x * -3.0;
	} else if (z <= 300000.0) {
		tmp = t_0;
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	tmp = 0
	if z <= -490.0:
		tmp = z * ((y - x) * -6.0)
	elif z <= 8.6e-296:
		tmp = t_0
	elif z <= 2.05e-215:
		tmp = x * -3.0
	elif z <= 300000.0:
		tmp = t_0
	else:
		tmp = (y - x) * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (z <= -490.0)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 8.6e-296)
		tmp = t_0;
	elseif (z <= 2.05e-215)
		tmp = Float64(x * -3.0);
	elseif (z <= 300000.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (z <= -490.0)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 8.6e-296)
		tmp = t_0;
	elseif (z <= 2.05e-215)
		tmp = x * -3.0;
	elseif (z <= 300000.0)
		tmp = t_0;
	else
		tmp = (y - x) * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -490.0], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-296], t$95$0, If[LessEqual[z, 2.05e-215], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 300000.0], t$95$0, N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -490

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.8%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.8%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. associate-*l* 98.9%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   4. Simplified 98.9%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   if -490 < z < 8.59999999999999956e-296 or 2.04999999999999992e-215 < z < 3e5

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 98.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\left(-z\right) + \frac{2}{3}\right)}, x\right) \]

      6. distribute-lft-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{6 \cdot \left(-z\right) + 6 \cdot \frac{2}{3}}, x\right) \]

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, \color{blue}{-6}, 6 \cdot \frac{2}{3}\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 6 \cdot \color{blue}{0.6666666666666666}\right), x\right) \]

      13. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, \color{blue}{4}\right), x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 4\right), x\right)} \]

   4. Taylor expanded in y around inf 59.7%

      \[\leadsto \color{blue}{\left(4 + -6 \cdot z\right) \cdot y} \]

   if 8.59999999999999956e-296 < z < 2.04999999999999992e-215

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 3e5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(y - x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -490:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 300000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 8: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -115000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -115000000.0)
     t_0
     (if (<= z 8.6e-296)
       (* y 4.0)
       (if (<= z 2.3e-215) (* x -3.0) (if (<= z 0.65) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -115000000.0) {
		tmp = t_0;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 2.3e-215) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} 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 = (-6.0d0) * (y * z)
    if (z <= (-115000000.0d0)) then
        tmp = t_0
    else if (z <= 8.6d-296) then
        tmp = y * 4.0d0
    else if (z <= 2.3d-215) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -115000000.0) {
		tmp = t_0;
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 2.3e-215) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -115000000.0:
		tmp = t_0
	elif z <= 8.6e-296:
		tmp = y * 4.0
	elif z <= 2.3e-215:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -115000000.0)
		tmp = t_0;
	elseif (z <= 8.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.3e-215)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -115000000.0)
		tmp = t_0;
	elseif (z <= 8.6e-296)
		tmp = y * 4.0;
	elseif (z <= 2.3e-215)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -115000000.0], t$95$0, If[LessEqual[z, 8.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.3e-215], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e8 or 0.650000000000000022 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.5%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around inf 55.7%

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

      1. *-commutative 55.7%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -1.15e8 < z < 8.59999999999999956e-296 or 2.2999999999999999e-215 < z < 0.650000000000000022

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 96.1%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 8.59999999999999956e-296 < z < 2.2999999999999999e-215

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 9: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -115000000:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -115000000.0)
   (* z (* y -6.0))
   (if (<= z 8.6e-296)
     (* y 4.0)
     (if (<= z 2.4e-216)
       (* x -3.0)
       (if (<= z 0.65) (* y 4.0) (* -6.0 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -115000000.0) {
		tmp = z * (y * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 2.4e-216) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	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 <= (-115000000.0d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= 8.6d-296) then
        tmp = y * 4.0d0
    else if (z <= 2.4d-216) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -115000000.0) {
		tmp = z * (y * -6.0);
	} else if (z <= 8.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 2.4e-216) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -115000000.0:
		tmp = z * (y * -6.0)
	elif z <= 8.6e-296:
		tmp = y * 4.0
	elif z <= 2.4e-216:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -115000000.0)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= 8.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.4e-216)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -115000000.0)
		tmp = z * (y * -6.0);
	elseif (z <= 8.6e-296)
		tmp = y * 4.0;
	elseif (z <= 2.4e-216)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -115000000.0], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.4e-216], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15e8

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.3%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around inf 52.8%

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

      1. associate-*r* 52.8%

         \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]

      2. *-commutative 52.8%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   5. Simplified 52.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   if -1.15e8 < z < 8.59999999999999956e-296 or 2.40000000000000004e-216 < z < 0.650000000000000022

   1. Initial program 98.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 96.1%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 8.59999999999999956e-296 < z < 2.40000000000000004e-216

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 66.8%

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

      1. distribute-lft1-in 66.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 66.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.650000000000000022 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   3. Taylor expanded in y around inf 60.2%

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

      1. *-commutative 60.2%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   5. Simplified 60.2%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115000000:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-14} \lor \neg \left(x \leq 3.9 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(6 \cdot z - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.05e-14) (not (<= x 3.9e-20)))
   (* x (- (* 6.0 z) 3.0))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.05e-14) || !(x <= 3.9e-20)) {
		tmp = x * ((6.0 * z) - 3.0);
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	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) :: tmp
    if ((x <= (-2.05d-14)) .or. (.not. (x <= 3.9d-20))) then
        tmp = x * ((6.0d0 * z) - 3.0d0)
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.05e-14) || !(x <= 3.9e-20)) {
		tmp = x * ((6.0 * z) - 3.0);
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.05e-14) or not (x <= 3.9e-20):
		tmp = x * ((6.0 * z) - 3.0)
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.05e-14) || !(x <= 3.9e-20))
		tmp = Float64(x * Float64(Float64(6.0 * z) - 3.0));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.05e-14) || ~((x <= 3.9e-20)))
		tmp = x * ((6.0 * z) - 3.0);
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.05e-14], N[Not[LessEqual[x, 3.9e-20]], $MachinePrecision]], N[(x * N[(N[(6.0 * z), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0500000000000001e-14 or 3.90000000000000007e-20 < x

   1. Initial program 99.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 99.2%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)} \]

   3. Taylor expanded in x around inf 80.3%

      \[\leadsto \color{blue}{\left(6 \cdot z - 3\right) \cdot x} \]

   if -2.0500000000000001e-14 < x < 3.90000000000000007e-20

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\left(-z\right) + \frac{2}{3}\right)}, x\right) \]

      6. distribute-lft-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{6 \cdot \left(-z\right) + 6 \cdot \frac{2}{3}}, x\right) \]

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, \color{blue}{-6}, 6 \cdot \frac{2}{3}\right), x\right) \]

      12. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 6 \cdot \color{blue}{0.6666666666666666}\right), x\right) \]

      13. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, \color{blue}{4}\right), x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 4\right), x\right)} \]

   4. Taylor expanded in y around inf 85.4%

      \[\leadsto \color{blue}{\left(4 + -6 \cdot z\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-14} \lor \neg \left(x \leq 3.9 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(6 \cdot z - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 11: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* z (* (- y x) -6.0))
   (if (<= z 0.64) (+ (* x -3.0) (* y 4.0)) (* (- y x) (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.64) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	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) :: tmp
    if (z <= (-0.6d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.64d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = (y - x) * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.64) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.64:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = (y - x) * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.64)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.6)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.64)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = (y - x) * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.64], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.8%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.8%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. associate-*l* 98.9%

         \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   4. Simplified 98.9%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   if -0.599999999999999978 < z < 0.640000000000000013

   1. Initial program 98.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 97.3%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 0.640000000000000013 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

   4. Simplified 99.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 12: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (- y x) (* 6.0 (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * (0.6666666666666666 - 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 + ((y - x) * (6.0d0 * (0.6666666666666666d0 - z)))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * (0.6666666666666666 - z)));
}

Python

def code(x, y, z):
	return x + ((y - x) * (6.0 * (0.6666666666666666 - z)))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(6.0 * Float64(0.6666666666666666 - z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (6.0 * (0.6666666666666666 - z)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. associate-*l* 99.5%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \]

   2. metadata-eval 99.5%

      \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot \left(\color{blue}{0.6666666666666666} - z\right)\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

4. Final simplification 99.5%

   \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) \]

Alternative 13: 37.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.8e-52) (* x -3.0) (if (<= x 4.4e+67) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e-52) {
		tmp = x * -3.0;
	} else if (x <= 4.4e+67) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	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) :: tmp
    if (x <= (-5.8d-52)) then
        tmp = x * (-3.0d0)
    else if (x <= 4.4d+67) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e-52) {
		tmp = x * -3.0;
	} else if (x <= 4.4e+67) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.8e-52:
		tmp = x * -3.0
	elif x <= 4.4e+67:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.8e-52)
		tmp = Float64(x * -3.0);
	elseif (x <= 4.4e+67)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.8e-52)
		tmp = x * -3.0;
	elseif (x <= 4.4e+67)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.8e-52], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 4.4e+67], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000003e-52 or 4.4e67 < x

   1. Initial program 99.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 49.9%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around 0 40.2%

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

      1. distribute-lft1-in 40.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

      2. metadata-eval 40.8%

         \[\leadsto \color{blue}{-3} \cdot x \]

      3. *-commutative 40.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   5. Simplified 40.8%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if -5.8000000000000003e-52 < x < 4.4e67

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0 53.7%

      \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

   3. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

         \[\leadsto \color{blue}{y \cdot 4} \]

   5. Simplified 44.7%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 14: 25.9% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

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 * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.3%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

2. Taylor expanded in z around 0 52.0%

   \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + x} \]

3. Taylor expanded in y around 0 24.0%

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

   1. distribute-lft1-in 24.3%

      \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} \]

   2. metadata-eval 24.3%

      \[\leadsto \color{blue}{-3} \cdot x \]

   3. *-commutative 24.3%

      \[\leadsto \color{blue}{x \cdot -3} \]

5. Simplified 24.3%

   \[\leadsto \color{blue}{x \cdot -3} \]

6. Final simplification 24.3%

   \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))