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

Percentage Accurate: 99.8% → 100.0%

Time: 8.0s

Alternatives: 8

Speedup: 1.2×

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

Specification

Math

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

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: 99.8% 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

\[\begin{array}{l} \\ 4 \cdot \frac{x - y}{z} - 2 \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - 2.0), $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/ 99.7%

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

   2. sub-neg 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around 0 100.0%

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

5. Final simplification 100.0%

   \[\leadsto 4 \cdot \frac{x - y}{z} - 2 \]

Alternative 2: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ t_1 := \frac{-4}{\frac{z}{y}}\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{+119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.95 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-150}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1200000:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))) (t_1 (/ -4.0 (/ z y))))
   (if (<= x -1.18e+119)
     t_0
     (if (<= x -3.95e-41)
       t_1
       (if (<= x -3e-150)
         -2.0
         (if (<= x 7.2e-118)
           t_1
           (if (<= x 1200000.0) -2.0 (if (<= x 2.5e+71) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = -4.0 / (z / y);
	double tmp;
	if (x <= -1.18e+119) {
		tmp = t_0;
	} else if (x <= -3.95e-41) {
		tmp = t_1;
	} else if (x <= -3e-150) {
		tmp = -2.0;
	} else if (x <= 7.2e-118) {
		tmp = t_1;
	} else if (x <= 1200000.0) {
		tmp = -2.0;
	} else if (x <= 2.5e+71) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / z)
    t_1 = (-4.0d0) / (z / y)
    if (x <= (-1.18d+119)) then
        tmp = t_0
    else if (x <= (-3.95d-41)) then
        tmp = t_1
    else if (x <= (-3d-150)) then
        tmp = -2.0d0
    else if (x <= 7.2d-118) then
        tmp = t_1
    else if (x <= 1200000.0d0) then
        tmp = -2.0d0
    else if (x <= 2.5d+71) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = -4.0 / (z / y);
	double tmp;
	if (x <= -1.18e+119) {
		tmp = t_0;
	} else if (x <= -3.95e-41) {
		tmp = t_1;
	} else if (x <= -3e-150) {
		tmp = -2.0;
	} else if (x <= 7.2e-118) {
		tmp = t_1;
	} else if (x <= 1200000.0) {
		tmp = -2.0;
	} else if (x <= 2.5e+71) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	t_1 = -4.0 / (z / y)
	tmp = 0
	if x <= -1.18e+119:
		tmp = t_0
	elif x <= -3.95e-41:
		tmp = t_1
	elif x <= -3e-150:
		tmp = -2.0
	elif x <= 7.2e-118:
		tmp = t_1
	elif x <= 1200000.0:
		tmp = -2.0
	elif x <= 2.5e+71:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / z))
	t_1 = Float64(-4.0 / Float64(z / y))
	tmp = 0.0
	if (x <= -1.18e+119)
		tmp = t_0;
	elseif (x <= -3.95e-41)
		tmp = t_1;
	elseif (x <= -3e-150)
		tmp = -2.0;
	elseif (x <= 7.2e-118)
		tmp = t_1;
	elseif (x <= 1200000.0)
		tmp = -2.0;
	elseif (x <= 2.5e+71)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / z);
	t_1 = -4.0 / (z / y);
	tmp = 0.0;
	if (x <= -1.18e+119)
		tmp = t_0;
	elseif (x <= -3.95e-41)
		tmp = t_1;
	elseif (x <= -3e-150)
		tmp = -2.0;
	elseif (x <= 7.2e-118)
		tmp = t_1;
	elseif (x <= 1200000.0)
		tmp = -2.0;
	elseif (x <= 2.5e+71)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.18e+119], t$95$0, If[LessEqual[x, -3.95e-41], t$95$1, If[LessEqual[x, -3e-150], -2.0, If[LessEqual[x, 7.2e-118], t$95$1, If[LessEqual[x, 1200000.0], -2.0, If[LessEqual[x, 2.5e+71], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1799999999999999e119 or 2.49999999999999986e71 < x

   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/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.0%

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

   if -1.1799999999999999e119 < x < -3.95e-41 or -3.0000000000000002e-150 < x < 7.2000000000000004e-118 or 1.2e6 < x < 2.49999999999999986e71

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 58.2%

      \[\leadsto \frac{4}{\color{blue}{-1 \cdot \frac{z}{y}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 58.2%

         \[\leadsto \frac{4}{\color{blue}{\frac{-1 \cdot z}{y}}} \]

      2. neg-mul-1 58.2%

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

   6. Simplified 58.2%

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

      1. clear-num 58.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{-z}{y}}{4}}} \]

      2. associate-/r/ 58.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{-z}{y}} \cdot 4} \]

      3. clear-num 58.3%

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

      4. add-sqr-sqrt 25.5%

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

      5. sqrt-unprod 22.0%

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

      6. sqr-neg 22.0%

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

      7. sqrt-unprod 1.1%

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

      8. add-sqr-sqrt 2.0%

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

   8. Applied egg-rr 2.0%

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

      1. add-sqr-sqrt 0.8%

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

      2. sqrt-unprod 21.6%

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

      3. swap-sqr 21.6%

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

      4. metadata-eval 21.6%

         \[\leadsto \sqrt{\left(\frac{y}{z} \cdot \frac{y}{z}\right) \cdot \color{blue}{16}} \]

      5. metadata-eval 21.6%

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

      6. swap-sqr 21.6%

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

      7. *-commutative 21.6%

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

      8. *-commutative 21.6%

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

      9. sqrt-unprod 26.5%

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

      10. add-sqr-sqrt 58.3%

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

      11. clear-num 58.2%

          \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{z}{y}}} \]

      12. un-div-inv 58.2%

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

   10. Applied egg-rr 58.2%

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

   if -3.95e-41 < x < -3.0000000000000002e-150 or 7.2000000000000004e-118 < x < 1.2e6

   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/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 60.4%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+119}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -3.95 \cdot 10^{-41}:\\ \;\;\;\;\frac{-4}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-150}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-118}:\\ \;\;\;\;\frac{-4}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq 1200000:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;\frac{-4}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ t_1 := \frac{y \cdot -4}{z}\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-150}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 7.7 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 260000000000:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+71}:\\ \;\;\;\;\frac{-4}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))) (t_1 (/ (* y -4.0) z)))
   (if (<= x -4.1e+116)
     t_0
     (if (<= x -2.7e-39)
       t_1
       (if (<= x -3.7e-150)
         -2.0
         (if (<= x 7.7e-118)
           t_1
           (if (<= x 260000000000.0)
             -2.0
             (if (<= x 1.42e+71) (/ -4.0 (/ z y)) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = (y * -4.0) / z;
	double tmp;
	if (x <= -4.1e+116) {
		tmp = t_0;
	} else if (x <= -2.7e-39) {
		tmp = t_1;
	} else if (x <= -3.7e-150) {
		tmp = -2.0;
	} else if (x <= 7.7e-118) {
		tmp = t_1;
	} else if (x <= 260000000000.0) {
		tmp = -2.0;
	} else if (x <= 1.42e+71) {
		tmp = -4.0 / (z / y);
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / z)
    t_1 = (y * (-4.0d0)) / z
    if (x <= (-4.1d+116)) then
        tmp = t_0
    else if (x <= (-2.7d-39)) then
        tmp = t_1
    else if (x <= (-3.7d-150)) then
        tmp = -2.0d0
    else if (x <= 7.7d-118) then
        tmp = t_1
    else if (x <= 260000000000.0d0) then
        tmp = -2.0d0
    else if (x <= 1.42d+71) then
        tmp = (-4.0d0) / (z / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = (y * -4.0) / z;
	double tmp;
	if (x <= -4.1e+116) {
		tmp = t_0;
	} else if (x <= -2.7e-39) {
		tmp = t_1;
	} else if (x <= -3.7e-150) {
		tmp = -2.0;
	} else if (x <= 7.7e-118) {
		tmp = t_1;
	} else if (x <= 260000000000.0) {
		tmp = -2.0;
	} else if (x <= 1.42e+71) {
		tmp = -4.0 / (z / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	t_1 = (y * -4.0) / z
	tmp = 0
	if x <= -4.1e+116:
		tmp = t_0
	elif x <= -2.7e-39:
		tmp = t_1
	elif x <= -3.7e-150:
		tmp = -2.0
	elif x <= 7.7e-118:
		tmp = t_1
	elif x <= 260000000000.0:
		tmp = -2.0
	elif x <= 1.42e+71:
		tmp = -4.0 / (z / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / z))
	t_1 = Float64(Float64(y * -4.0) / z)
	tmp = 0.0
	if (x <= -4.1e+116)
		tmp = t_0;
	elseif (x <= -2.7e-39)
		tmp = t_1;
	elseif (x <= -3.7e-150)
		tmp = -2.0;
	elseif (x <= 7.7e-118)
		tmp = t_1;
	elseif (x <= 260000000000.0)
		tmp = -2.0;
	elseif (x <= 1.42e+71)
		tmp = Float64(-4.0 / Float64(z / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / z);
	t_1 = (y * -4.0) / z;
	tmp = 0.0;
	if (x <= -4.1e+116)
		tmp = t_0;
	elseif (x <= -2.7e-39)
		tmp = t_1;
	elseif (x <= -3.7e-150)
		tmp = -2.0;
	elseif (x <= 7.7e-118)
		tmp = t_1;
	elseif (x <= 260000000000.0)
		tmp = -2.0;
	elseif (x <= 1.42e+71)
		tmp = -4.0 / (z / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y * -4.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -4.1e+116], t$95$0, If[LessEqual[x, -2.7e-39], t$95$1, If[LessEqual[x, -3.7e-150], -2.0, If[LessEqual[x, 7.7e-118], t$95$1, If[LessEqual[x, 260000000000.0], -2.0, If[LessEqual[x, 1.42e+71], N[(-4.0 / N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.0999999999999998e116 or 1.42000000000000012e71 < x

   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/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 76.0%

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

   if -4.0999999999999998e116 < x < -2.7000000000000001e-39 or -3.70000000000000001e-150 < x < 7.6999999999999996e-118

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-*l/ 59.6%

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

   6. Simplified 59.6%

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

   if -2.7000000000000001e-39 < x < -3.70000000000000001e-150 or 7.6999999999999996e-118 < x < 2.6e11

   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/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 60.4%

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

   if 2.6e11 < x < 1.42000000000000012e71

   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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 51.7%

      \[\leadsto \frac{4}{\color{blue}{-1 \cdot \frac{z}{y}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 51.7%

         \[\leadsto \frac{4}{\color{blue}{\frac{-1 \cdot z}{y}}} \]

      2. neg-mul-1 51.7%

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

   6. Simplified 51.7%

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

      1. clear-num 51.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{-z}{y}}{4}}} \]

      2. associate-/r/ 51.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{-z}{y}} \cdot 4} \]

      3. clear-num 51.7%

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

      4. add-sqr-sqrt 22.5%

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

      5. sqrt-unprod 24.0%

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

      6. sqr-neg 24.0%

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

      7. sqrt-unprod 1.2%

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

      8. add-sqr-sqrt 1.5%

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

   8. Applied egg-rr 1.5%

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

      1. add-sqr-sqrt 0.8%

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

      2. sqrt-unprod 29.8%

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

      3. swap-sqr 29.8%

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

      4. metadata-eval 29.8%

         \[\leadsto \sqrt{\left(\frac{y}{z} \cdot \frac{y}{z}\right) \cdot \color{blue}{16}} \]

      5. metadata-eval 29.8%

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

      6. swap-sqr 29.8%

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

      7. *-commutative 29.8%

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

      8. *-commutative 29.8%

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

      9. sqrt-unprod 34.5%

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

      10. add-sqr-sqrt 51.7%

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

      11. clear-num 51.7%

          \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{z}{y}}} \]

      12. un-div-inv 51.7%

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

   10. Applied egg-rr 51.7%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+116}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-150}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 7.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;x \leq 260000000000:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+71}:\\ \;\;\;\;\frac{-4}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+123} \lor \neg \left(x \leq 6.2 \cdot 10^{+72} \lor \neg \left(x \leq 1.5 \cdot 10^{+138}\right) \land x \leq 1.55 \cdot 10^{+164}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+123)
         (not
          (or (<= x 6.2e+72) (and (not (<= x 1.5e+138)) (<= x 1.55e+164)))))
   (* 4.0 (/ x z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+123) || !((x <= 6.2e+72) || (!(x <= 1.5e+138) && (x <= 1.55e+164)))) {
		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 <= (-9.5d+123)) .or. (.not. (x <= 6.2d+72) .or. (.not. (x <= 1.5d+138)) .and. (x <= 1.55d+164))) 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 <= -9.5e+123) || !((x <= 6.2e+72) || (!(x <= 1.5e+138) && (x <= 1.55e+164)))) {
		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 <= -9.5e+123) or not ((x <= 6.2e+72) or (not (x <= 1.5e+138) and (x <= 1.55e+164))):
		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 <= -9.5e+123) || !((x <= 6.2e+72) || (!(x <= 1.5e+138) && (x <= 1.55e+164))))
		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 <= -9.5e+123) || ~(((x <= 6.2e+72) || (~((x <= 1.5e+138)) && (x <= 1.55e+164)))))
		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, -9.5e+123], N[Not[Or[LessEqual[x, 6.2e+72], And[N[Not[LessEqual[x, 1.5e+138]], $MachinePrecision], LessEqual[x, 1.55e+164]]]], $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 < -9.4999999999999996e123 or 6.19999999999999977e72 < x < 1.50000000000000005e138 or 1.5500000000000001e164 < x

   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/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 81.3%

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

   if -9.4999999999999996e123 < x < 6.19999999999999977e72 or 1.50000000000000005e138 < x < 1.5500000000000001e164

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 89.4%

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

      1. div-sub 89.4%

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

      2. associate-/l* 89.4%

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

      3. *-lft-identity 89.4%

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

      4. associate-*l/ 89.3%

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

      5. lft-mult-inverse 89.4%

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

      6. metadata-eval 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+123} \lor \neg \left(x \leq 6.2 \cdot 10^{+72} \lor \neg \left(x \leq 1.5 \cdot 10^{+138}\right) \land x \leq 1.55 \cdot 10^{+164}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 5: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+79} \lor \neg \left(x \leq 1.2 \cdot 10^{+31}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e+79) (not (<= x 1.2e+31)))
   (* 4.0 (/ (- x y) z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+79) || !(x <= 1.2e+31)) {
		tmp = 4.0 * ((x - y) / 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 <= (-5.2d+79)) .or. (.not. (x <= 1.2d+31))) then
        tmp = 4.0d0 * ((x - y) / 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 <= -5.2e+79) || !(x <= 1.2e+31)) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e+79) or not (x <= 1.2e+31):
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e+79) || !(x <= 1.2e+31))
		tmp = Float64(4.0 * Float64(Float64(x - y) / 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 <= -5.2e+79) || ~((x <= 1.2e+31)))
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e+79], N[Not[LessEqual[x, 1.2e+31]], $MachinePrecision]], N[(4.0 * N[(N[(x - y), $MachinePrecision] / 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 < -5.20000000000000029e79 or 1.19999999999999991e31 < x

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 85.6%

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

   if -5.20000000000000029e79 < x < 1.19999999999999991e31

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 92.3%

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

      1. div-sub 92.3%

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

      2. associate-/l* 92.3%

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

      3. *-lft-identity 92.3%

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

      4. associate-*l/ 92.2%

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

      5. lft-mult-inverse 92.3%

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

      6. metadata-eval 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+79} \lor \neg \left(x \leq 1.2 \cdot 10^{+31}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 6: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+82}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+71}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e+82)
   (* 4.0 (/ (- x y) z))
   (if (<= x 3.3e+71) (* 4.0 (- -0.5 (/ y z))) (+ (* 4.0 (/ x z)) -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e+82) {
		tmp = 4.0 * ((x - y) / z);
	} else if (x <= 3.3e+71) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = (4.0 * (x / z)) + -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 (x <= (-1.2d+82)) then
        tmp = 4.0d0 * ((x - y) / z)
    else if (x <= 3.3d+71) then
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    else
        tmp = (4.0d0 * (x / z)) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e+82) {
		tmp = 4.0 * ((x - y) / z);
	} else if (x <= 3.3e+71) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = (4.0 * (x / z)) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e+82:
		tmp = 4.0 * ((x - y) / z)
	elif x <= 3.3e+71:
		tmp = 4.0 * (-0.5 - (y / z))
	else:
		tmp = (4.0 * (x / z)) + -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e+82)
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	elseif (x <= 3.3e+71)
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	else
		tmp = Float64(Float64(4.0 * Float64(x / z)) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.2e+82)
		tmp = 4.0 * ((x - y) / z);
	elseif (x <= 3.3e+71)
		tmp = 4.0 * (-0.5 - (y / z));
	else
		tmp = (4.0 * (x / z)) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e+82], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+71], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999999e82

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 88.9%

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

   if -1.19999999999999999e82 < x < 3.2999999999999998e71

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 90.3%

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

      1. div-sub 90.3%

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

      2. associate-/l* 90.3%

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

      3. *-lft-identity 90.3%

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

      4. associate-*l/ 90.2%

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

      5. lft-mult-inverse 90.3%

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

      6. metadata-eval 90.3%

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

   6. Simplified 90.3%

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

   if 3.2999999999999998e71 < x

   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/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. metadata-eval 90.2%

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

      3. cancel-sign-sub-inv 90.2%

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

      4. div-sub 90.2%

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

      5. associate-/l* 90.2%

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

      6. *-lft-identity 90.2%

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

      7. associate-*l/ 90.2%

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

      8. lft-mult-inverse 90.2%

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

      9. metadata-eval 90.2%

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

      10. sub-neg 90.2%

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

      11. metadata-eval 90.2%

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

      12. distribute-lft-in 90.2%

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

      13. metadata-eval 90.2%

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

   6. Simplified 90.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+82}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+71}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \end{array} \]

Alternative 7: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+77} \lor \neg \left(x \leq 4.4 \cdot 10^{+33}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.6e+77) (not (<= x 4.4e+33))) (* 4.0 (/ x z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.6e+77) || !(x <= 4.4e+33)) {
		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 ((x <= (-9.6d+77)) .or. (.not. (x <= 4.4d+33))) 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 ((x <= -9.6e+77) || !(x <= 4.4e+33)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.6e+77) or not (x <= 4.4e+33):
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.6e+77) || !(x <= 4.4e+33))
		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 ((x <= -9.6e+77) || ~((x <= 4.4e+33)))
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.6e+77], N[Not[LessEqual[x, 4.4e+33]], $MachinePrecision]], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if x < -9.5999999999999994e77 or 4.39999999999999988e33 < x

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 69.8%

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

   if -9.5999999999999994e77 < x < 4.39999999999999988e33

   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/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 43.4%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+77} \lor \neg \left(x \leq 4.4 \cdot 10^{+33}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 33.6% 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. Step-by-step derivation

   1. associate-*l/ 99.7%

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

   2. sub-neg 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 31.1%

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

5. Final simplification 31.1%

   \[\leadsto -2 \]

Developer target: 97.9% 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 2023199 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

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

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