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

Percentage Accurate: 99.9% → 100.0%

Time: 5.2s

Alternatives: 10

Speedup: 1.0×

• 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   4. associate-*l/ 99.9%

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

   5. associate-*r/ 99.9%

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

   6. fma-def 99.9%

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

   7. associate-*l/ 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-rgt-neg-in 100.0%

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

   10. associate-*r* 100.0%

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

   11. remove-double-neg 100.0%

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

   12. neg-mul-1 100.0%

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

   13. times-frac 100.0%

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

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

   15. metadata-eval 100.0%

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

   16. *-inverses 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ t_1 := -4 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+69}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -0.00026:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-235}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))) (t_1 (* -4.0 (/ y z))))
   (if (<= z -4.1e+69)
     -2.0
     (if (<= z -0.00026)
       t_1
       (if (<= z 6.2e-235)
         t_0
         (if (<= z 4.3e-160) t_1 (if (<= z 1.95e+92) t_0 -2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (z <= -4.1e+69) {
		tmp = -2.0;
	} else if (z <= -0.00026) {
		tmp = t_1;
	} else if (z <= 6.2e-235) {
		tmp = t_0;
	} else if (z <= 4.3e-160) {
		tmp = t_1;
	} else if (z <= 1.95e+92) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / z)
    t_1 = (-4.0d0) * (y / z)
    if (z <= (-4.1d+69)) then
        tmp = -2.0d0
    else if (z <= (-0.00026d0)) then
        tmp = t_1
    else if (z <= 6.2d-235) then
        tmp = t_0
    else if (z <= 4.3d-160) then
        tmp = t_1
    else if (z <= 1.95d+92) then
        tmp = t_0
    else
        tmp = -2.0d0
    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 * (y / z);
	double tmp;
	if (z <= -4.1e+69) {
		tmp = -2.0;
	} else if (z <= -0.00026) {
		tmp = t_1;
	} else if (z <= 6.2e-235) {
		tmp = t_0;
	} else if (z <= 4.3e-160) {
		tmp = t_1;
	} else if (z <= 1.95e+92) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	t_1 = -4.0 * (y / z)
	tmp = 0
	if z <= -4.1e+69:
		tmp = -2.0
	elif z <= -0.00026:
		tmp = t_1
	elif z <= 6.2e-235:
		tmp = t_0
	elif z <= 4.3e-160:
		tmp = t_1
	elif z <= 1.95e+92:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / z))
	t_1 = Float64(-4.0 * Float64(y / z))
	tmp = 0.0
	if (z <= -4.1e+69)
		tmp = -2.0;
	elseif (z <= -0.00026)
		tmp = t_1;
	elseif (z <= 6.2e-235)
		tmp = t_0;
	elseif (z <= 4.3e-160)
		tmp = t_1;
	elseif (z <= 1.95e+92)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / z);
	t_1 = -4.0 * (y / z);
	tmp = 0.0;
	if (z <= -4.1e+69)
		tmp = -2.0;
	elseif (z <= -0.00026)
		tmp = t_1;
	elseif (z <= 6.2e-235)
		tmp = t_0;
	elseif (z <= 4.3e-160)
		tmp = t_1;
	elseif (z <= 1.95e+92)
		tmp = t_0;
	else
		tmp = -2.0;
	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[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+69], -2.0, If[LessEqual[z, -0.00026], t$95$1, If[LessEqual[z, 6.2e-235], t$95$0, If[LessEqual[z, 4.3e-160], t$95$1, If[LessEqual[z, 1.95e+92], t$95$0, -2.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999999e69 or 1.95000000000000006e92 < 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/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 67.1%

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

   if -4.0999999999999999e69 < z < -2.59999999999999977e-4 or 6.2e-235 < z < 4.30000000000000014e-160

   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 72.8%

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

   if -2.59999999999999977e-4 < z < 6.2e-235 or 4.30000000000000014e-160 < z < 1.95000000000000006e92

   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 61.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+69}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -0.00026:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-235}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-160}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+92}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 3: 79.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+151}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+133} \lor \neg \left(z \leq -4.3 \cdot 10^{+91}\right) \land z \leq 10^{+180}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8e+151)
   -2.0
   (if (or (<= z -2.8e+133) (and (not (<= z -4.3e+91)) (<= z 1e+180)))
     (* (- x y) (/ 4.0 z))
     -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8e+151) {
		tmp = -2.0;
	} else if ((z <= -2.8e+133) || (!(z <= -4.3e+91) && (z <= 1e+180))) {
		tmp = (x - 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 <= (-8d+151)) then
        tmp = -2.0d0
    else if ((z <= (-2.8d+133)) .or. (.not. (z <= (-4.3d+91))) .and. (z <= 1d+180)) then
        tmp = (x - 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 <= -8e+151) {
		tmp = -2.0;
	} else if ((z <= -2.8e+133) || (!(z <= -4.3e+91) && (z <= 1e+180))) {
		tmp = (x - y) * (4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8e+151:
		tmp = -2.0
	elif (z <= -2.8e+133) or (not (z <= -4.3e+91) and (z <= 1e+180)):
		tmp = (x - y) * (4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8e+151)
		tmp = -2.0;
	elseif ((z <= -2.8e+133) || (!(z <= -4.3e+91) && (z <= 1e+180)))
		tmp = Float64(Float64(x - 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 <= -8e+151)
		tmp = -2.0;
	elseif ((z <= -2.8e+133) || (~((z <= -4.3e+91)) && (z <= 1e+180)))
		tmp = (x - y) * (4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8e+151], -2.0, If[Or[LessEqual[z, -2.8e+133], And[N[Not[LessEqual[z, -4.3e+91]], $MachinePrecision], LessEqual[z, 1e+180]]], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000014e151 or -2.80000000000000016e133 < z < -4.3000000000000001e91 or 1e180 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 78.9%

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

   if -8.00000000000000014e151 < z < -2.80000000000000016e133 or -4.3000000000000001e91 < z < 1e180

   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 z around 0 88.1%

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

      1. associate-/r/ 88.1%

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

   6. Applied egg-rr 88.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+151}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+133} \lor \neg \left(z \leq -4.3 \cdot 10^{+91}\right) \land z \leq 10^{+180}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+191}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{elif}\;z \leq -0.00096 \lor \neg \left(z \leq 8.2 \cdot 10^{+83}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e+191)
   (- (* 4.0 (/ x z)) 2.0)
   (if (or (<= z -0.00096) (not (<= z 8.2e+83)))
     (- (* -4.0 (/ y z)) 2.0)
     (* (- x y) (/ 4.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+191) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else if ((z <= -0.00096) || !(z <= 8.2e+83)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (x - y) * (4.0 / 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 <= (-3.6d+191)) then
        tmp = (4.0d0 * (x / z)) - 2.0d0
    else if ((z <= (-0.00096d0)) .or. (.not. (z <= 8.2d+83))) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    else
        tmp = (x - y) * (4.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+191) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else if ((z <= -0.00096) || !(z <= 8.2e+83)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (x - y) * (4.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.6e+191:
		tmp = (4.0 * (x / z)) - 2.0
	elif (z <= -0.00096) or not (z <= 8.2e+83):
		tmp = (-4.0 * (y / z)) - 2.0
	else:
		tmp = (x - y) * (4.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e+191)
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	elseif ((z <= -0.00096) || !(z <= 8.2e+83))
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	else
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.6e+191)
		tmp = (4.0 * (x / z)) - 2.0;
	elseif ((z <= -0.00096) || ~((z <= 8.2e+83)))
		tmp = (-4.0 * (y / z)) - 2.0;
	else
		tmp = (x - y) * (4.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.6e+191], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[z, -0.00096], N[Not[LessEqual[z, 8.2e+83]], $MachinePrecision]], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5999999999999999e191

   1. Initial program 99.9%

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

      1. associate-*l/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-lft-in 99.7%

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

      4. associate-*l/ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. fma-def 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. associate-*r* 100.0%

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

      11. remove-double-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

      15. metadata-eval 100.0%

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

      16. *-inverses 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.5%

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

   if -3.5999999999999999e191 < z < -9.60000000000000024e-4 or 8.2000000000000002e83 < 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/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-lft-in 99.6%

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

      4. associate-*l/ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. fma-def 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. associate-*r* 100.0%

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

      11. remove-double-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

      15. metadata-eval 100.0%

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

      16. *-inverses 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 88.5%

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

   if -9.60000000000000024e-4 < z < 8.2000000000000002e83

   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 z around 0 91.9%

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

      1. associate-/r/ 91.9%

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

   6. Applied egg-rr 91.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+191}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{elif}\;z \leq -0.00096 \lor \neg \left(z \leq 8.2 \cdot 10^{+83}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \]

Alternative 5: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+191}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{elif}\;z \leq -0.38 \lor \neg \left(z \leq 9.6 \cdot 10^{+83}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e+191)
   (- (* 4.0 (/ x z)) 2.0)
   (if (or (<= z -0.38) (not (<= z 9.6e+83)))
     (- (* -4.0 (/ y z)) 2.0)
     (/ 4.0 (/ z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+191) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else if ((z <= -0.38) || !(z <= 9.6e+83)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = 4.0 / (z / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.2d+191)) then
        tmp = (4.0d0 * (x / z)) - 2.0d0
    else if ((z <= (-0.38d0)) .or. (.not. (z <= 9.6d+83))) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    else
        tmp = 4.0d0 / (z / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+191) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else if ((z <= -0.38) || !(z <= 9.6e+83)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = 4.0 / (z / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e+191:
		tmp = (4.0 * (x / z)) - 2.0
	elif (z <= -0.38) or not (z <= 9.6e+83):
		tmp = (-4.0 * (y / z)) - 2.0
	else:
		tmp = 4.0 / (z / (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.2e+191)
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	elseif ((z <= -0.38) || !(z <= 9.6e+83))
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	else
		tmp = Float64(4.0 / Float64(z / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.2e+191)
		tmp = (4.0 * (x / z)) - 2.0;
	elseif ((z <= -0.38) || ~((z <= 9.6e+83)))
		tmp = (-4.0 * (y / z)) - 2.0;
	else
		tmp = 4.0 / (z / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.2e+191], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[z, -0.38], N[Not[LessEqual[z, 9.6e+83]], $MachinePrecision]], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(4.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2000000000000002e191

   1. Initial program 99.9%

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

      1. associate-*l/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-lft-in 99.7%

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

      4. associate-*l/ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. fma-def 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. associate-*r* 100.0%

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

      11. remove-double-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

      15. metadata-eval 100.0%

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

      16. *-inverses 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.5%

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

   if -3.2000000000000002e191 < z < -0.38 or 9.59999999999999965e83 < 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/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-lft-in 99.6%

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

      4. associate-*l/ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. fma-def 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. associate-*r* 100.0%

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

      11. remove-double-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

      15. metadata-eval 100.0%

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

      16. *-inverses 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 88.4%

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

   if -0.38 < z < 9.59999999999999965e83

   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 z around 0 91.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+191}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{elif}\;z \leq -0.38 \lor \neg \left(z \leq 9.6 \cdot 10^{+83}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 6: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0017 \lor \neg \left(z \leq 6 \cdot 10^{+84}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0017) (not (<= z 6e+84)))
   (- (* -4.0 (/ y z)) 2.0)
   (* (- x y) (/ 4.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0017) || !(z <= 6e+84)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (x - y) * (4.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.0017d0)) .or. (.not. (z <= 6d+84))) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    else
        tmp = (x - y) * (4.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0017) || !(z <= 6e+84)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (x - y) * (4.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0017) or not (z <= 6e+84):
		tmp = (-4.0 * (y / z)) - 2.0
	else:
		tmp = (x - y) * (4.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0017) || !(z <= 6e+84))
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	else
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.0017) || ~((z <= 6e+84)))
		tmp = (-4.0 * (y / z)) - 2.0;
	else
		tmp = (x - y) * (4.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0017], N[Not[LessEqual[z, 6e+84]], $MachinePrecision]], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00169999999999999991 or 5.99999999999999992e84 < 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/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-lft-in 99.6%

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

      4. associate-*l/ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. fma-def 99.8%

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

      7. associate-*l/ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. associate-*r* 100.0%

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

      11. remove-double-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

      15. metadata-eval 100.0%

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

      16. *-inverses 100.0%

          \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 86.2%

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

   if -0.00169999999999999991 < z < 5.99999999999999992e84

   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 z around 0 91.9%

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

      1. associate-/r/ 91.9%

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

   6. Applied egg-rr 91.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0017 \lor \neg \left(z \leq 6 \cdot 10^{+84}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \]

Alternative 7: 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]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 8: 53.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2050000000 \lor \neg \left(y \leq 6.1 \cdot 10^{+78}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2050000000.0) (not (<= y 6.1e+78))) (* -4.0 (/ y z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2050000000.0) || !(y <= 6.1e+78)) {
		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 <= (-2050000000.0d0)) .or. (.not. (y <= 6.1d+78))) 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 <= -2050000000.0) || !(y <= 6.1e+78)) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2050000000.0) or not (y <= 6.1e+78):
		tmp = -4.0 * (y / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2050000000.0) || !(y <= 6.1e+78))
		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 <= -2050000000.0) || ~((y <= 6.1e+78)))
		tmp = -4.0 * (y / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2050000000.0], N[Not[LessEqual[y, 6.1e+78]], $MachinePrecision]], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e9 or 6.10000000000000011e78 < y

   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/ 99.6%

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

      2. sub-neg 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 63.7%

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

   if -2.05e9 < y < 6.10000000000000011e78

   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 45.9%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2050000000 \lor \neg \left(y \leq 6.1 \cdot 10^{+78}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 9: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (-2.0d0) + ((x - y) * (4.0d0 / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   4. associate-*l/ 99.9%

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

   5. associate-*r/ 99.9%

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

   6. fma-def 99.9%

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

   7. associate-*l/ 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-rgt-neg-in 100.0%

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

   10. associate-*r* 100.0%

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

   11. remove-double-neg 100.0%

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

   12. neg-mul-1 100.0%

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

   13. times-frac 100.0%

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

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

   15. metadata-eval 100.0%

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

   16. *-inverses 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

   1. fma-udef 100.0%

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

   2. associate-*r/ 100.0%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(x - y\right)}{z}} + -2 \]

   3. associate-*l/ 99.8%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(x - y\right)} + -2 \]

5. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(x - y\right) + -2} \]

6. Final simplification 99.8%

   \[\leadsto -2 + \left(x - y\right) \cdot \frac{4}{z} \]

Alternative 10: 33.8% 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. 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 32.8%

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

5. Final simplification 32.8%

   \[\leadsto -2 \]

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 2023257 
(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))