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

Percentage Accurate: 99.9% → 100.0%

Time: 5.3s

Alternatives: 7

Speedup: 1.2×

• 21.5% 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

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

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 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
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: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4}{\frac{z}{x}}\\ t_1 := -4 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-209}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-149}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+39}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ 4.0 (/ z x))) (t_1 (* -4.0 (/ y z))))
   (if (<= y -8.2e+26)
     t_1
     (if (<= y 1.3e-209)
       -2.0
       (if (<= y 7e-189)
         t_0
         (if (<= y 9e-149)
           -2.0
           (if (<= y 3.55e-84)
             t_0
             (if (<= y 5.6e+39) -2.0 (if (<= y 1.9e+85) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 / (z / x);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -8.2e+26) {
		tmp = t_1;
	} else if (y <= 1.3e-209) {
		tmp = -2.0;
	} else if (y <= 7e-189) {
		tmp = t_0;
	} else if (y <= 9e-149) {
		tmp = -2.0;
	} else if (y <= 3.55e-84) {
		tmp = t_0;
	} else if (y <= 5.6e+39) {
		tmp = -2.0;
	} else if (y <= 1.9e+85) {
		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 = 4.0d0 / (z / x)
    t_1 = (-4.0d0) * (y / z)
    if (y <= (-8.2d+26)) then
        tmp = t_1
    else if (y <= 1.3d-209) then
        tmp = -2.0d0
    else if (y <= 7d-189) then
        tmp = t_0
    else if (y <= 9d-149) then
        tmp = -2.0d0
    else if (y <= 3.55d-84) then
        tmp = t_0
    else if (y <= 5.6d+39) then
        tmp = -2.0d0
    else if (y <= 1.9d+85) 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 = 4.0 / (z / x);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -8.2e+26) {
		tmp = t_1;
	} else if (y <= 1.3e-209) {
		tmp = -2.0;
	} else if (y <= 7e-189) {
		tmp = t_0;
	} else if (y <= 9e-149) {
		tmp = -2.0;
	} else if (y <= 3.55e-84) {
		tmp = t_0;
	} else if (y <= 5.6e+39) {
		tmp = -2.0;
	} else if (y <= 1.9e+85) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 / (z / x)
	t_1 = -4.0 * (y / z)
	tmp = 0
	if y <= -8.2e+26:
		tmp = t_1
	elif y <= 1.3e-209:
		tmp = -2.0
	elif y <= 7e-189:
		tmp = t_0
	elif y <= 9e-149:
		tmp = -2.0
	elif y <= 3.55e-84:
		tmp = t_0
	elif y <= 5.6e+39:
		tmp = -2.0
	elif y <= 1.9e+85:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 / Float64(z / x))
	t_1 = Float64(-4.0 * Float64(y / z))
	tmp = 0.0
	if (y <= -8.2e+26)
		tmp = t_1;
	elseif (y <= 1.3e-209)
		tmp = -2.0;
	elseif (y <= 7e-189)
		tmp = t_0;
	elseif (y <= 9e-149)
		tmp = -2.0;
	elseif (y <= 3.55e-84)
		tmp = t_0;
	elseif (y <= 5.6e+39)
		tmp = -2.0;
	elseif (y <= 1.9e+85)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 / (z / x);
	t_1 = -4.0 * (y / z);
	tmp = 0.0;
	if (y <= -8.2e+26)
		tmp = t_1;
	elseif (y <= 1.3e-209)
		tmp = -2.0;
	elseif (y <= 7e-189)
		tmp = t_0;
	elseif (y <= 9e-149)
		tmp = -2.0;
	elseif (y <= 3.55e-84)
		tmp = t_0;
	elseif (y <= 5.6e+39)
		tmp = -2.0;
	elseif (y <= 1.9e+85)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+26], t$95$1, If[LessEqual[y, 1.3e-209], -2.0, If[LessEqual[y, 7e-189], t$95$0, If[LessEqual[y, 9e-149], -2.0, If[LessEqual[y, 3.55e-84], t$95$0, If[LessEqual[y, 5.6e+39], -2.0, If[LessEqual[y, 1.9e+85], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.19999999999999967e26 or 1.89999999999999996e85 < y

   1. Initial program 99.1%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 76.7%

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

      1. *-commutative 76.7%

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

   6. Simplified 76.7%

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

   if -8.19999999999999967e26 < y < 1.29999999999999992e-209 or 7.0000000000000003e-189 < y < 8.9999999999999996e-149 or 3.5499999999999998e-84 < y < 5.60000000000000003e39

   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 61.4%

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

   if 1.29999999999999992e-209 < y < 7.0000000000000003e-189 or 8.9999999999999996e-149 < y < 3.5499999999999998e-84 or 5.60000000000000003e39 < y < 1.89999999999999996e85

   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-*r/ 100.0%

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

      2. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 93.1%

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

      1. clear-num 92.8%

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

      2. un-div-inv 92.8%

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

   6. Applied egg-rr 92.8%

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

   7. Taylor expanded in x around inf 78.3%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+26}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-209}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-189}:\\ \;\;\;\;\frac{4}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-149}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-84}:\\ \;\;\;\;\frac{4}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+39}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{4}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 53.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{z}{4}}\\ t_1 := -4 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-209}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-148}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (/ z 4.0))) (t_1 (* -4.0 (/ y z))))
   (if (<= y -2.2e+26)
     t_1
     (if (<= y 5.2e-209)
       -2.0
       (if (<= y 8.5e-187)
         t_0
         (if (<= y 3.6e-148) -2.0 (if (<= y 1.9e+85) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z / 4.0);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -2.2e+26) {
		tmp = t_1;
	} else if (y <= 5.2e-209) {
		tmp = -2.0;
	} else if (y <= 8.5e-187) {
		tmp = t_0;
	} else if (y <= 3.6e-148) {
		tmp = -2.0;
	} else if (y <= 1.9e+85) {
		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 = x / (z / 4.0d0)
    t_1 = (-4.0d0) * (y / z)
    if (y <= (-2.2d+26)) then
        tmp = t_1
    else if (y <= 5.2d-209) then
        tmp = -2.0d0
    else if (y <= 8.5d-187) then
        tmp = t_0
    else if (y <= 3.6d-148) then
        tmp = -2.0d0
    else if (y <= 1.9d+85) 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 = x / (z / 4.0);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -2.2e+26) {
		tmp = t_1;
	} else if (y <= 5.2e-209) {
		tmp = -2.0;
	} else if (y <= 8.5e-187) {
		tmp = t_0;
	} else if (y <= 3.6e-148) {
		tmp = -2.0;
	} else if (y <= 1.9e+85) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z / 4.0)
	t_1 = -4.0 * (y / z)
	tmp = 0
	if y <= -2.2e+26:
		tmp = t_1
	elif y <= 5.2e-209:
		tmp = -2.0
	elif y <= 8.5e-187:
		tmp = t_0
	elif y <= 3.6e-148:
		tmp = -2.0
	elif y <= 1.9e+85:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z / 4.0))
	t_1 = Float64(-4.0 * Float64(y / z))
	tmp = 0.0
	if (y <= -2.2e+26)
		tmp = t_1;
	elseif (y <= 5.2e-209)
		tmp = -2.0;
	elseif (y <= 8.5e-187)
		tmp = t_0;
	elseif (y <= 3.6e-148)
		tmp = -2.0;
	elseif (y <= 1.9e+85)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z / 4.0);
	t_1 = -4.0 * (y / z);
	tmp = 0.0;
	if (y <= -2.2e+26)
		tmp = t_1;
	elseif (y <= 5.2e-209)
		tmp = -2.0;
	elseif (y <= 8.5e-187)
		tmp = t_0;
	elseif (y <= 3.6e-148)
		tmp = -2.0;
	elseif (y <= 1.9e+85)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z / 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+26], t$95$1, If[LessEqual[y, 5.2e-209], -2.0, If[LessEqual[y, 8.5e-187], t$95$0, If[LessEqual[y, 3.6e-148], -2.0, If[LessEqual[y, 1.9e+85], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000007e26 or 1.89999999999999996e85 < y

   1. Initial program 99.1%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 76.7%

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

      1. *-commutative 76.7%

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

   6. Simplified 76.7%

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

   if -2.20000000000000007e26 < y < 5.19999999999999969e-209 or 8.4999999999999999e-187 < y < 3.5999999999999998e-148

   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 63.8%

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

   if 5.19999999999999969e-209 < y < 8.4999999999999999e-187 or 3.5999999999999998e-148 < y < 1.89999999999999996e85

   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 59.9%

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

      1. *-commutative 59.9%

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

      2. associate-/r/ 59.9%

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

   6. Simplified 59.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-209}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{\frac{z}{4}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-148}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{\frac{z}{4}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 4: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+93}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2050000000000:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+127}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e+93)
   -2.0
   (if (<= z -3.8e+70)
     (* -4.0 (/ y z))
     (if (<= z -2050000000000.0)
       -2.0
       (if (<= z 1.2e+127) (* 4.0 (/ (- x y) z)) -2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+93) {
		tmp = -2.0;
	} else if (z <= -3.8e+70) {
		tmp = -4.0 * (y / z);
	} else if (z <= -2050000000000.0) {
		tmp = -2.0;
	} else if (z <= 1.2e+127) {
		tmp = 4.0 * ((x - y) / 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 <= (-4.1d+93)) then
        tmp = -2.0d0
    else if (z <= (-3.8d+70)) then
        tmp = (-4.0d0) * (y / z)
    else if (z <= (-2050000000000.0d0)) then
        tmp = -2.0d0
    else if (z <= 1.2d+127) then
        tmp = 4.0d0 * ((x - y) / 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 <= -4.1e+93) {
		tmp = -2.0;
	} else if (z <= -3.8e+70) {
		tmp = -4.0 * (y / z);
	} else if (z <= -2050000000000.0) {
		tmp = -2.0;
	} else if (z <= 1.2e+127) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e+93:
		tmp = -2.0
	elif z <= -3.8e+70:
		tmp = -4.0 * (y / z)
	elif z <= -2050000000000.0:
		tmp = -2.0
	elif z <= 1.2e+127:
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e+93)
		tmp = -2.0;
	elseif (z <= -3.8e+70)
		tmp = Float64(-4.0 * Float64(y / z));
	elseif (z <= -2050000000000.0)
		tmp = -2.0;
	elseif (z <= 1.2e+127)
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e+93)
		tmp = -2.0;
	elseif (z <= -3.8e+70)
		tmp = -4.0 * (y / z);
	elseif (z <= -2050000000000.0)
		tmp = -2.0;
	elseif (z <= 1.2e+127)
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e+93], -2.0, If[LessEqual[z, -3.8e+70], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2050000000000.0], -2.0, If[LessEqual[z, 1.2e+127], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], -2.0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1000000000000001e93 or -3.7999999999999998e70 < z < -2.05e12 or 1.2000000000000001e127 < 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/ 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 77.5%

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

   if -4.1000000000000001e93 < z < -3.7999999999999998e70

   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 90.0%

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

      1. *-commutative 90.0%

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

   6. Simplified 90.0%

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

   if -2.05e12 < z < 1.2000000000000001e127

   1. Initial program 99.4%

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

      1. associate-*r/ 100.0%

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

      2. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 89.2%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+93}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2050000000000:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+127}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 5: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -900000000000 \lor \neg \left(z \leq 0.00025\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -900000000000.0) (not (<= z 0.00025)))
   (- (* -4.0 (/ y z)) 2.0)
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -900000000000.0) || !(z <= 0.00025)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} 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 <= (-900000000000.0d0)) .or. (.not. (z <= 0.00025d0))) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    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 <= -900000000000.0) || !(z <= 0.00025)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -900000000000.0) or not (z <= 0.00025):
		tmp = (-4.0 * (y / z)) - 2.0
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -900000000000.0) || !(z <= 0.00025))
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	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 <= -900000000000.0) || ~((z <= 0.00025)))
		tmp = (-4.0 * (y / z)) - 2.0;
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -900000000000.0], N[Not[LessEqual[z, 0.00025]], $MachinePrecision]], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e11 or 2.5000000000000001e-4 < z

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. *-lft-identity 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 99.9%

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

      7. associate-/r/ 99.8%

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

      8. fma-neg 99.8%

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

      9. metadata-eval 99.8%

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

      10. /-rgt-identity 99.8%

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

      11. associate-/r/ 99.8%

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

      12. distribute-rgt-neg-in 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{4}{z}, -2\right)} \]

   4. Taylor expanded in x around 0 90.8%

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

   if -9e11 < z < 2.5000000000000001e-4

   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-*r/ 100.0%

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

      2. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 92.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -900000000000 \lor \neg \left(z \leq 0.00025\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 6: 54.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+26} \lor \neg \left(y \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e+26) (not (<= y 2.8e+18))) (* -4.0 (/ y z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e+26) || !(y <= 2.8e+18)) {
		tmp = -4.0 * (y / 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 ((y <= (-2.5d+26)) .or. (.not. (y <= 2.8d+18))) then
        tmp = (-4.0d0) * (y / 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 ((y <= -2.5e+26) || !(y <= 2.8e+18)) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e+26) or not (y <= 2.8e+18):
		tmp = -4.0 * (y / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e+26) || !(y <= 2.8e+18))
		tmp = Float64(-4.0 * Float64(y / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.5e+26) || ~((y <= 2.8e+18)))
		tmp = -4.0 * (y / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e+26], N[Not[LessEqual[y, 2.8e+18]], $MachinePrecision]], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e26 or 2.8e18 < y

   1. Initial program 99.2%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 72.8%

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

      1. *-commutative 72.8%

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

   6. Simplified 72.8%

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

   if -2.5e26 < y < 2.8e18

   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 53.2%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+26} \lor \neg \left(y \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 7: 34.6% 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 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
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 35.7%

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

5. Final simplification 35.7%

   \[\leadsto -2 \]

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 2023290 
(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))