Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B

Percentage Accurate: 99.9% → 100.0%

Time: 7.5s

Alternatives: 8

Speedup: 1.2×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \left(\frac{x - y}{z} + -0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 4.0 (+ (/ (- x y) z) -0.5)))

C

double code(double x, double y, double z) {
	return 4.0 * (((x - y) / z) + -0.5);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 4.0d0 * (((x - y) / z) + (-0.5d0))
end function

Java

public static double code(double x, double y, double z) {
	return 4.0 * (((x - y) / z) + -0.5);
}

Python

def code(x, y, z):
	return 4.0 * (((x - y) / z) + -0.5)

Julia

function code(x, y, z)
	return Float64(4.0 * Float64(Float64(Float64(x - y) / z) + -0.5))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0 * (((x - y) / z) + -0.5);
end

Wolfram

code[x_, y_, z_] := N[(4.0 * N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + -0.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

      \[\leadsto \color{blue}{4 \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z}} \]

   2. div-sub 100.0%

      \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} - \frac{z \cdot 0.5}{z}\right)} \]

   3. associate-*l/ 100.0%

      \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\frac{z}{z} \cdot 0.5}\right) \]

   4. *-inverses 100.0%

      \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{1} \cdot 0.5\right) \]

   5. metadata-eval 100.0%

      \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{0.5}\right) \]

   6. sub-neg 100.0%

      \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} + \left(-0.5\right)\right)} \]

   7. metadata-eval 100.0%

      \[\leadsto 4 \cdot \left(\frac{x - y}{z} + \color{blue}{-0.5}\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} + -0.5\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+159}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-69}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+88}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+159)
   -2.0
   (if (<= z -2.25e-69)
     (* 4.0 (/ x z))
     (if (<= z 1.8e+88) (/ (* y -4.0) z) -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+159) {
		tmp = -2.0;
	} else if (z <= -2.25e-69) {
		tmp = 4.0 * (x / z);
	} else if (z <= 1.8e+88) {
		tmp = (y * -4.0) / z;
	} else {
		tmp = -2.0;
	}
	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 <= (-9d+159)) then
        tmp = -2.0d0
    else if (z <= (-2.25d-69)) then
        tmp = 4.0d0 * (x / z)
    else if (z <= 1.8d+88) then
        tmp = (y * (-4.0d0)) / z
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+159) {
		tmp = -2.0;
	} else if (z <= -2.25e-69) {
		tmp = 4.0 * (x / z);
	} else if (z <= 1.8e+88) {
		tmp = (y * -4.0) / z;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+159:
		tmp = -2.0
	elif z <= -2.25e-69:
		tmp = 4.0 * (x / z)
	elif z <= 1.8e+88:
		tmp = (y * -4.0) / z
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+159)
		tmp = -2.0;
	elseif (z <= -2.25e-69)
		tmp = Float64(4.0 * Float64(x / z));
	elseif (z <= 1.8e+88)
		tmp = Float64(Float64(y * -4.0) / z);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+159)
		tmp = -2.0;
	elseif (z <= -2.25e-69)
		tmp = 4.0 * (x / z);
	elseif (z <= 1.8e+88)
		tmp = (y * -4.0) / z;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+159], -2.0, If[LessEqual[z, -2.25e-69], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+88], N[(N[(y * -4.0), $MachinePrecision] / z), $MachinePrecision], -2.0]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000053e159 or 1.8000000000000001e88 < z

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.9%

      \[\leadsto \color{blue}{-2} \]

   if -9.00000000000000053e159 < z < -2.25000000000000005e-69

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 47.8%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{z}} \]

   if -2.25000000000000005e-69 < z < 1.8000000000000001e88

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.4%

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

      1. *-commutative 61.4%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot -4} \]

      2. associate-*l/ 61.4%

         \[\leadsto \color{blue}{\frac{y \cdot -4}{z}} \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{y \cdot -4}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 52.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+159}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-70}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+159)
   -2.0
   (if (<= z -5.6e-70)
     (* 4.0 (/ x z))
     (if (<= z 8e+86) (* y (/ -4.0 z)) -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+159) {
		tmp = -2.0;
	} else if (z <= -5.6e-70) {
		tmp = 4.0 * (x / z);
	} else if (z <= 8e+86) {
		tmp = y * (-4.0 / z);
	} else {
		tmp = -2.0;
	}
	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 <= (-9d+159)) then
        tmp = -2.0d0
    else if (z <= (-5.6d-70)) then
        tmp = 4.0d0 * (x / z)
    else if (z <= 8d+86) then
        tmp = y * ((-4.0d0) / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+159) {
		tmp = -2.0;
	} else if (z <= -5.6e-70) {
		tmp = 4.0 * (x / z);
	} else if (z <= 8e+86) {
		tmp = y * (-4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+159:
		tmp = -2.0
	elif z <= -5.6e-70:
		tmp = 4.0 * (x / z)
	elif z <= 8e+86:
		tmp = y * (-4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+159)
		tmp = -2.0;
	elseif (z <= -5.6e-70)
		tmp = Float64(4.0 * Float64(x / z));
	elseif (z <= 8e+86)
		tmp = Float64(y * Float64(-4.0 / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+159)
		tmp = -2.0;
	elseif (z <= -5.6e-70)
		tmp = 4.0 * (x / z);
	elseif (z <= 8e+86)
		tmp = y * (-4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+159], -2.0, If[LessEqual[z, -5.6e-70], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+86], N[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000053e159 or 8.0000000000000001e86 < z

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.9%

      \[\leadsto \color{blue}{-2} \]

   if -9.00000000000000053e159 < z < -5.5999999999999998e-70

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 47.8%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{z}} \]

   if -5.5999999999999998e-70 < z < 8.0000000000000001e86

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.0%

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

      1. *-commutative 92.0%

         \[\leadsto \color{blue}{\frac{x - y}{z} \cdot 4} \]

      2. associate-*l/ 92.0%

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

      3. associate-/l* 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in x around 0 61.4%

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

      1. associate-*r/ 61.4%

         \[\leadsto \color{blue}{\frac{-4 \cdot y}{z}} \]

      2. metadata-eval 61.4%

         \[\leadsto \frac{\color{blue}{\left(4 \cdot -1\right)} \cdot y}{z} \]

      3. associate-*r* 61.4%

         \[\leadsto \frac{\color{blue}{4 \cdot \left(-1 \cdot y\right)}}{z} \]

      4. neg-mul-1 61.4%

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

      5. associate-*l/ 61.4%

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

      6. *-commutative 61.4%

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

      7. distribute-lft-neg-out 61.4%

         \[\leadsto \color{blue}{-y \cdot \frac{4}{z}} \]

      8. distribute-rgt-neg-in 61.4%

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

      9. distribute-neg-frac 61.4%

         \[\leadsto y \cdot \color{blue}{\frac{-4}{z}} \]

      10. metadata-eval 61.4%

          \[\leadsto y \cdot \frac{\color{blue}{-4}}{z} \]

   8. Simplified 61.4%

      \[\leadsto \color{blue}{y \cdot \frac{-4}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+61} \lor \neg \left(x \leq 4.4 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \frac{4}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e+61) (not (<= x 4.4e+26)))
   (+ (* x (/ 4.0 z)) -2.0)
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e+61) || !(x <= 4.4e+26)) {
		tmp = (x * (4.0 / z)) + -2.0;
	} else {
		tmp = 4.0 * (-0.5 - (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 ((x <= (-3.3d+61)) .or. (.not. (x <= 4.4d+26))) then
        tmp = (x * (4.0d0 / z)) + (-2.0d0)
    else
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e+61) || !(x <= 4.4e+26)) {
		tmp = (x * (4.0 / z)) + -2.0;
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e+61) or not (x <= 4.4e+26):
		tmp = (x * (4.0 / z)) + -2.0
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e+61) || !(x <= 4.4e+26))
		tmp = Float64(Float64(x * Float64(4.0 / z)) + -2.0);
	else
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.3e+61) || ~((x <= 4.4e+26)))
		tmp = (x * (4.0 / z)) + -2.0;
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e+61], N[Not[LessEqual[x, 4.4e+26]], $MachinePrecision]], N[(N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2999999999999998e61 or 4.40000000000000014e26 < x

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.8%

      \[\leadsto \color{blue}{4 \cdot \frac{x - 0.5 \cdot z}{z}} \]
   4. Step-by-step derivation

      1. div-sub 85.7%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \frac{0.5 \cdot z}{z}\right)} \]

      2. associate-/l* 85.7%

         \[\leadsto 4 \cdot \left(\frac{x}{z} - \color{blue}{0.5 \cdot \frac{z}{z}}\right) \]

      3. *-inverses 85.7%

         \[\leadsto 4 \cdot \left(\frac{x}{z} - 0.5 \cdot \color{blue}{1}\right) \]

      4. cancel-sign-sub-inv 85.7%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} + \left(-0.5\right) \cdot 1\right)} \]

      5. metadata-eval 85.7%

         \[\leadsto 4 \cdot \left(\frac{x}{z} + \color{blue}{-0.5} \cdot 1\right) \]

      6. metadata-eval 85.7%

         \[\leadsto 4 \cdot \left(\frac{x}{z} + \color{blue}{-0.5}\right) \]

      7. distribute-rgt-in 85.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot 4 + -0.5 \cdot 4} \]

      8. associate-*l/ 85.7%

         \[\leadsto \color{blue}{\frac{x \cdot 4}{z}} + -0.5 \cdot 4 \]

      9. associate-*r/ 85.6%

         \[\leadsto \color{blue}{x \cdot \frac{4}{z}} + -0.5 \cdot 4 \]

      10. metadata-eval 85.6%

          \[\leadsto x \cdot \frac{4}{z} + \color{blue}{-2} \]

   5. Simplified 85.6%

      \[\leadsto \color{blue}{x \cdot \frac{4}{z} + -2} \]

   if -3.2999999999999998e61 < x < 4.40000000000000014e26

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{4 \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z}} \]

      2. div-sub 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} - \frac{z \cdot 0.5}{z}\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\frac{z}{z} \cdot 0.5}\right) \]

      4. *-inverses 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{1} \cdot 0.5\right) \]

      5. metadata-eval 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{0.5}\right) \]

      6. sub-neg 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} + \left(-0.5\right)\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} + \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} + -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 91.6%

      \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot \left(0.5 + \frac{y}{z}\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-in 91.6%

         \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot 0.5 + -1 \cdot \frac{y}{z}\right)} \]

      2. metadata-eval 91.6%

         \[\leadsto 4 \cdot \left(\color{blue}{-0.5} + -1 \cdot \frac{y}{z}\right) \]

      3. neg-mul-1 91.6%

         \[\leadsto 4 \cdot \left(-0.5 + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      4. unsub-neg 91.6%

         \[\leadsto 4 \cdot \color{blue}{\left(-0.5 - \frac{y}{z}\right)} \]

   7. Simplified 91.6%

      \[\leadsto 4 \cdot \color{blue}{\left(-0.5 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+61} \lor \neg \left(x \leq 4.4 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \frac{4}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+161} \lor \neg \left(z \leq 4.6 \cdot 10^{+20}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e+161) (not (<= z 4.6e+20)))
   (* 4.0 (- -0.5 (/ y z)))
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+161) || !(z <= 4.6e+20)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = 4.0 * ((x - 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 <= (-1.4d+161)) .or. (.not. (z <= 4.6d+20))) then
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    else
        tmp = 4.0d0 * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+161) || !(z <= 4.6e+20)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.4e+161) or not (z <= 4.6e+20):
		tmp = 4.0 * (-0.5 - (y / z))
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e+161) || !(z <= 4.6e+20))
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.4e+161) || ~((z <= 4.6e+20)))
		tmp = 4.0 * (-0.5 - (y / z));
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e+161], N[Not[LessEqual[z, 4.6e+20]], $MachinePrecision]], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e161 or 4.6e20 < z

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{4 \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z}} \]

      2. div-sub 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} - \frac{z \cdot 0.5}{z}\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\frac{z}{z} \cdot 0.5}\right) \]

      4. *-inverses 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{1} \cdot 0.5\right) \]

      5. metadata-eval 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{0.5}\right) \]

      6. sub-neg 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} + \left(-0.5\right)\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} + \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} + -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.9%

      \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot \left(0.5 + \frac{y}{z}\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-in 86.9%

         \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot 0.5 + -1 \cdot \frac{y}{z}\right)} \]

      2. metadata-eval 86.9%

         \[\leadsto 4 \cdot \left(\color{blue}{-0.5} + -1 \cdot \frac{y}{z}\right) \]

      3. neg-mul-1 86.9%

         \[\leadsto 4 \cdot \left(-0.5 + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      4. unsub-neg 86.9%

         \[\leadsto 4 \cdot \color{blue}{\left(-0.5 - \frac{y}{z}\right)} \]

   7. Simplified 86.9%

      \[\leadsto 4 \cdot \color{blue}{\left(-0.5 - \frac{y}{z}\right)} \]

   if -1.4000000000000001e161 < z < 4.6e20

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+161} \lor \neg \left(z \leq 4.6 \cdot 10^{+20}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+167} \lor \neg \left(x \leq 4.2 \cdot 10^{+77}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.25e+167) (not (<= x 4.2e+77)))
   (* 4.0 (/ x z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.25e+167) || !(x <= 4.2e+77)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = 4.0 * (-0.5 - (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 ((x <= (-2.25d+167)) .or. (.not. (x <= 4.2d+77))) then
        tmp = 4.0d0 * (x / z)
    else
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.25e+167) || !(x <= 4.2e+77)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.25e+167) or not (x <= 4.2e+77):
		tmp = 4.0 * (x / z)
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.25e+167) || !(x <= 4.2e+77))
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.25e+167) || ~((x <= 4.2e+77)))
		tmp = 4.0 * (x / z);
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.25e+167], N[Not[LessEqual[x, 4.2e+77]], $MachinePrecision]], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e167 or 4.1999999999999997e77 < x

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.1%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{z}} \]

   if -2.25e167 < x < 4.1999999999999997e77

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{4 \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z}} \]

      2. div-sub 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} - \frac{z \cdot 0.5}{z}\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\frac{z}{z} \cdot 0.5}\right) \]

      4. *-inverses 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{1} \cdot 0.5\right) \]

      5. metadata-eval 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{0.5}\right) \]

      6. sub-neg 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} + \left(-0.5\right)\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} + \color{blue}{-0.5}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} + -0.5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 85.8%

      \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot \left(0.5 + \frac{y}{z}\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-in 85.8%

         \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot 0.5 + -1 \cdot \frac{y}{z}\right)} \]

      2. metadata-eval 85.8%

         \[\leadsto 4 \cdot \left(\color{blue}{-0.5} + -1 \cdot \frac{y}{z}\right) \]

      3. neg-mul-1 85.8%

         \[\leadsto 4 \cdot \left(-0.5 + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      4. unsub-neg 85.8%

         \[\leadsto 4 \cdot \color{blue}{\left(-0.5 - \frac{y}{z}\right)} \]

   7. Simplified 85.8%

      \[\leadsto 4 \cdot \color{blue}{\left(-0.5 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+167} \lor \neg \left(x \leq 4.2 \cdot 10^{+77}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+159}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+39}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+159) -2.0 (if (<= z 1.35e+39) (* 4.0 (/ x z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+159) {
		tmp = -2.0;
	} else if (z <= 1.35e+39) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	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 <= (-9d+159)) then
        tmp = -2.0d0
    else if (z <= 1.35d+39) then
        tmp = 4.0d0 * (x / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+159) {
		tmp = -2.0;
	} else if (z <= 1.35e+39) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+159:
		tmp = -2.0
	elif z <= 1.35e+39:
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+159)
		tmp = -2.0;
	elseif (z <= 1.35e+39)
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+159)
		tmp = -2.0;
	elseif (z <= 1.35e+39)
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+159], -2.0, If[LessEqual[z, 1.35e+39], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000053e159 or 1.35000000000000002e39 < z

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{-2} \]

   if -9.00000000000000053e159 < z < 1.35000000000000002e39

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.7%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 34.8% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 -2.0)

C

double code(double x, double y, double z) {
	return -2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return -2.0;
}

Python

def code(x, y, z):
	return -2.0

Julia

function code(x, y, z)
	return -2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = -2.0;
end

Wolfram

code[x_, y_, z_] := -2.0

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 30.2%

   \[\leadsto \color{blue}{-2} \]
4. Add Preprocessing

Developer target: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z)))))

C

double code(double x, double y, double z) {
	return (4.0 * (x / z)) - (2.0 + (4.0 * (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 = (4.0d0 * (x / z)) - (2.0d0 + (4.0d0 * (y / z)))
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * (x / z)) - (2.0 + (4.0 * (y / z)));
}

Python

def code(x, y, z):
	return (4.0 * (x / z)) - (2.0 + (4.0 * (y / z)))

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(x / z)) - Float64(2.0 + Float64(4.0 * Float64(y / z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * (x / z)) - (2.0 + (4.0 * (y / z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - N[(2.0 + N[(4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :alt
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))