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

Percentage Accurate: 99.8% → 100.0%

Time: 6.5s

Alternatives: 8

Speedup: 1.2×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 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: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{-4}{z}\\ t_1 := 4 \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+170}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -780000:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-207}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+83}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ -4.0 z))) (t_1 (* 4.0 (/ x z))))
   (if (<= z -6.5e+170)
     -2.0
     (if (<= z -5.2e+83)
       t_1
       (if (<= z -780000.0)
         -2.0
         (if (<= z -4.6e-76)
           t_1
           (if (<= z 2.7e-207)
             t_0
             (if (<= z 1.95e-80) t_1 (if (<= z 1.08e+83) t_0 -2.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (-4.0 / z);
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (z <= -6.5e+170) {
		tmp = -2.0;
	} else if (z <= -5.2e+83) {
		tmp = t_1;
	} else if (z <= -780000.0) {
		tmp = -2.0;
	} else if (z <= -4.6e-76) {
		tmp = t_1;
	} else if (z <= 2.7e-207) {
		tmp = t_0;
	} else if (z <= 1.95e-80) {
		tmp = t_1;
	} else if (z <= 1.08e+83) {
		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 = y * ((-4.0d0) / z)
    t_1 = 4.0d0 * (x / z)
    if (z <= (-6.5d+170)) then
        tmp = -2.0d0
    else if (z <= (-5.2d+83)) then
        tmp = t_1
    else if (z <= (-780000.0d0)) then
        tmp = -2.0d0
    else if (z <= (-4.6d-76)) then
        tmp = t_1
    else if (z <= 2.7d-207) then
        tmp = t_0
    else if (z <= 1.95d-80) then
        tmp = t_1
    else if (z <= 1.08d+83) 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 = y * (-4.0 / z);
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (z <= -6.5e+170) {
		tmp = -2.0;
	} else if (z <= -5.2e+83) {
		tmp = t_1;
	} else if (z <= -780000.0) {
		tmp = -2.0;
	} else if (z <= -4.6e-76) {
		tmp = t_1;
	} else if (z <= 2.7e-207) {
		tmp = t_0;
	} else if (z <= 1.95e-80) {
		tmp = t_1;
	} else if (z <= 1.08e+83) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (-4.0 / z)
	t_1 = 4.0 * (x / z)
	tmp = 0
	if z <= -6.5e+170:
		tmp = -2.0
	elif z <= -5.2e+83:
		tmp = t_1
	elif z <= -780000.0:
		tmp = -2.0
	elif z <= -4.6e-76:
		tmp = t_1
	elif z <= 2.7e-207:
		tmp = t_0
	elif z <= 1.95e-80:
		tmp = t_1
	elif z <= 1.08e+83:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-4.0 / z))
	t_1 = Float64(4.0 * Float64(x / z))
	tmp = 0.0
	if (z <= -6.5e+170)
		tmp = -2.0;
	elseif (z <= -5.2e+83)
		tmp = t_1;
	elseif (z <= -780000.0)
		tmp = -2.0;
	elseif (z <= -4.6e-76)
		tmp = t_1;
	elseif (z <= 2.7e-207)
		tmp = t_0;
	elseif (z <= 1.95e-80)
		tmp = t_1;
	elseif (z <= 1.08e+83)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (-4.0 / z);
	t_1 = 4.0 * (x / z);
	tmp = 0.0;
	if (z <= -6.5e+170)
		tmp = -2.0;
	elseif (z <= -5.2e+83)
		tmp = t_1;
	elseif (z <= -780000.0)
		tmp = -2.0;
	elseif (z <= -4.6e-76)
		tmp = t_1;
	elseif (z <= 2.7e-207)
		tmp = t_0;
	elseif (z <= 1.95e-80)
		tmp = t_1;
	elseif (z <= 1.08e+83)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+170], -2.0, If[LessEqual[z, -5.2e+83], t$95$1, If[LessEqual[z, -780000.0], -2.0, If[LessEqual[z, -4.6e-76], t$95$1, If[LessEqual[z, 2.7e-207], t$95$0, If[LessEqual[z, 1.95e-80], t$95$1, If[LessEqual[z, 1.08e+83], t$95$0, -2.0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e170 or -5.2000000000000002e83 < z < -7.8e5 or 1.08e83 < z

   1. Initial program 99.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 71.3%

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

   if -6.5e170 < z < -5.2000000000000002e83 or -7.8e5 < z < -4.60000000000000012e-76 or 2.7e-207 < z < 1.9499999999999999e-80

   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 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -4.60000000000000012e-76 < z < 2.7e-207 or 1.9499999999999999e-80 < z < 1.08e83

   1. Initial program 99.0%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 64.0%

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

      1. *-commutative 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in y around 0 64.0%

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

      1. associate-*r/ 64.0%

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

      2. associate-*l/ 64.0%

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

      3. *-commutative 64.0%

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

   9. Simplified 64.0%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+170}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -780000:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-76}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-80}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 3: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{z} \cdot -4\\ t_1 := 4 \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+170}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1300000:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-207}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ y z) -4.0)) (t_1 (* 4.0 (/ x z))))
   (if (<= z -4.2e+170)
     -2.0
     (if (<= z -8.2e+83)
       t_1
       (if (<= z -1300000.0)
         -2.0
         (if (<= z -6e-73)
           t_1
           (if (<= z 1.3e-207)
             t_0
             (if (<= z 1.75e-80) t_1 (if (<= z 1.1e+83) t_0 -2.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y / z) * -4.0;
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (z <= -4.2e+170) {
		tmp = -2.0;
	} else if (z <= -8.2e+83) {
		tmp = t_1;
	} else if (z <= -1300000.0) {
		tmp = -2.0;
	} else if (z <= -6e-73) {
		tmp = t_1;
	} else if (z <= 1.3e-207) {
		tmp = t_0;
	} else if (z <= 1.75e-80) {
		tmp = t_1;
	} else if (z <= 1.1e+83) {
		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 = (y / z) * (-4.0d0)
    t_1 = 4.0d0 * (x / z)
    if (z <= (-4.2d+170)) then
        tmp = -2.0d0
    else if (z <= (-8.2d+83)) then
        tmp = t_1
    else if (z <= (-1300000.0d0)) then
        tmp = -2.0d0
    else if (z <= (-6d-73)) then
        tmp = t_1
    else if (z <= 1.3d-207) then
        tmp = t_0
    else if (z <= 1.75d-80) then
        tmp = t_1
    else if (z <= 1.1d+83) 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 = (y / z) * -4.0;
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (z <= -4.2e+170) {
		tmp = -2.0;
	} else if (z <= -8.2e+83) {
		tmp = t_1;
	} else if (z <= -1300000.0) {
		tmp = -2.0;
	} else if (z <= -6e-73) {
		tmp = t_1;
	} else if (z <= 1.3e-207) {
		tmp = t_0;
	} else if (z <= 1.75e-80) {
		tmp = t_1;
	} else if (z <= 1.1e+83) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y / z) * -4.0
	t_1 = 4.0 * (x / z)
	tmp = 0
	if z <= -4.2e+170:
		tmp = -2.0
	elif z <= -8.2e+83:
		tmp = t_1
	elif z <= -1300000.0:
		tmp = -2.0
	elif z <= -6e-73:
		tmp = t_1
	elif z <= 1.3e-207:
		tmp = t_0
	elif z <= 1.75e-80:
		tmp = t_1
	elif z <= 1.1e+83:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y / z) * -4.0)
	t_1 = Float64(4.0 * Float64(x / z))
	tmp = 0.0
	if (z <= -4.2e+170)
		tmp = -2.0;
	elseif (z <= -8.2e+83)
		tmp = t_1;
	elseif (z <= -1300000.0)
		tmp = -2.0;
	elseif (z <= -6e-73)
		tmp = t_1;
	elseif (z <= 1.3e-207)
		tmp = t_0;
	elseif (z <= 1.75e-80)
		tmp = t_1;
	elseif (z <= 1.1e+83)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y / z) * -4.0;
	t_1 = 4.0 * (x / z);
	tmp = 0.0;
	if (z <= -4.2e+170)
		tmp = -2.0;
	elseif (z <= -8.2e+83)
		tmp = t_1;
	elseif (z <= -1300000.0)
		tmp = -2.0;
	elseif (z <= -6e-73)
		tmp = t_1;
	elseif (z <= 1.3e-207)
		tmp = t_0;
	elseif (z <= 1.75e-80)
		tmp = t_1;
	elseif (z <= 1.1e+83)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y / z), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+170], -2.0, If[LessEqual[z, -8.2e+83], t$95$1, If[LessEqual[z, -1300000.0], -2.0, If[LessEqual[z, -6e-73], t$95$1, If[LessEqual[z, 1.3e-207], t$95$0, If[LessEqual[z, 1.75e-80], t$95$1, If[LessEqual[z, 1.1e+83], t$95$0, -2.0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999996e170 or -8.2000000000000002e83 < z < -1.3e6 or 1.09999999999999999e83 < z

   1. Initial program 99.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 71.3%

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

   if -4.19999999999999996e170 < z < -8.2000000000000002e83 or -1.3e6 < z < -6e-73 or 1.3e-207 < z < 1.75000000000000007e-80

   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 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -6e-73 < z < 1.3e-207 or 1.75000000000000007e-80 < z < 1.09999999999999999e83

   1. Initial program 99.0%

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

      1. associate-*l/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 64.0%

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

      1. *-commutative 64.0%

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

   6. Simplified 64.0%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+170}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+83}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1300000:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-73}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-80}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 4: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+171}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+82} \lor \neg \left(z \leq -70000000\right) \land z \leq 8.5 \cdot 10^{+174}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4e+171)
   -2.0
   (if (or (<= z -3.5e+82) (and (not (<= z -70000000.0)) (<= z 8.5e+174)))
     (* 4.0 (/ (- x y) z))
     -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+171) {
		tmp = -2.0;
	} else if ((z <= -3.5e+82) || (!(z <= -70000000.0) && (z <= 8.5e+174))) {
		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 <= (-1.4d+171)) then
        tmp = -2.0d0
    else if ((z <= (-3.5d+82)) .or. (.not. (z <= (-70000000.0d0))) .and. (z <= 8.5d+174)) 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 <= -1.4e+171) {
		tmp = -2.0;
	} else if ((z <= -3.5e+82) || (!(z <= -70000000.0) && (z <= 8.5e+174))) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.4e+171:
		tmp = -2.0
	elif (z <= -3.5e+82) or (not (z <= -70000000.0) and (z <= 8.5e+174)):
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4e+171)
		tmp = -2.0;
	elseif ((z <= -3.5e+82) || (!(z <= -70000000.0) && (z <= 8.5e+174)))
		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 <= -1.4e+171)
		tmp = -2.0;
	elseif ((z <= -3.5e+82) || (~((z <= -70000000.0)) && (z <= 8.5e+174)))
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4e+171], -2.0, If[Or[LessEqual[z, -3.5e+82], And[N[Not[LessEqual[z, -70000000.0]], $MachinePrecision], LessEqual[z, 8.5e+174]]], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000002e171 or -3.5e82 < z < -7e7 or 8.5000000000000007e174 < z

   1. Initial program 98.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 77.6%

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

   if -1.40000000000000002e171 < z < -3.5e82 or -7e7 < z < 8.5000000000000007e174

   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 85.7%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+171}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+82} \lor \neg \left(z \leq -70000000\right) \land z \leq 8.5 \cdot 10^{+174}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 5: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-50} \lor \neg \left(z \leq 1.8 \cdot 10^{+63}\right):\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.9e-50) (not (<= z 1.8e+63)))
   (- (* 4.0 (/ x z)) 2.0)
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.9e-50) || !(z <= 1.8e+63)) {
		tmp = (4.0 * (x / 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 <= (-4.9d-50)) .or. (.not. (z <= 1.8d+63))) then
        tmp = (4.0d0 * (x / 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 <= -4.9e-50) || !(z <= 1.8e+63)) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.9e-50) or not (z <= 1.8e+63):
		tmp = (4.0 * (x / z)) - 2.0
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.9e-50) || !(z <= 1.8e+63))
		tmp = Float64(Float64(4.0 * Float64(x / 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 <= -4.9e-50) || ~((z <= 1.8e+63)))
		tmp = (4.0 * (x / z)) - 2.0;
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.9e-50], N[Not[LessEqual[z, 1.8e+63]], $MachinePrecision]], N[(N[(4.0 * N[(x / 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 < -4.8999999999999999e-50 or 1.79999999999999999e63 < 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. 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 0 100.0%

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

   5. Taylor expanded in x around inf 85.1%

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

   if -4.8999999999999999e-50 < z < 1.79999999999999999e63

   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-*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 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-50} \lor \neg \left(z \leq 1.8 \cdot 10^{+63}\right):\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 6: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+59} \lor \neg \left(y \leq 3.9 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{y}{z \cdot -0.25} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.72e+59) (not (<= y 3.9e+102)))
   (- (/ y (* z -0.25)) 2.0)
   (- (* 4.0 (/ x z)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.72e+59) || !(y <= 3.9e+102)) {
		tmp = (y / (z * -0.25)) - 2.0;
	} else {
		tmp = (4.0 * (x / z)) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.72d+59)) .or. (.not. (y <= 3.9d+102))) then
        tmp = (y / (z * (-0.25d0))) - 2.0d0
    else
        tmp = (4.0d0 * (x / z)) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.72e+59) || !(y <= 3.9e+102)) {
		tmp = (y / (z * -0.25)) - 2.0;
	} else {
		tmp = (4.0 * (x / z)) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.72e+59) or not (y <= 3.9e+102):
		tmp = (y / (z * -0.25)) - 2.0
	else:
		tmp = (4.0 * (x / z)) - 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.72e+59) || !(y <= 3.9e+102))
		tmp = Float64(Float64(y / Float64(z * -0.25)) - 2.0);
	else
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.72e+59) || ~((y <= 3.9e+102)))
		tmp = (y / (z * -0.25)) - 2.0;
	else
		tmp = (4.0 * (x / z)) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.72e+59], N[Not[LessEqual[y, 3.9e+102]], $MachinePrecision]], N[(N[(y / N[(z * -0.25), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.71999999999999996e59 or 3.8999999999999998e102 < y

   1. Initial program 99.0%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 91.9%

      \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot \frac{y}{z}\right)} - 2 \]
   6. Step-by-step derivation

      1. neg-mul-1 91.9%

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

      2. distribute-neg-frac 91.9%

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

   7. Simplified 91.9%

      \[\leadsto 4 \cdot \color{blue}{\frac{-y}{z}} - 2 \]
   8. Step-by-step derivation

      1. associate-*r/ 90.9%

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

      2. neg-mul-1 90.9%

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

      3. associate-*r* 90.9%

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

      4. metadata-eval 90.9%

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

      5. *-commutative 90.9%

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

      6. associate-/l* 91.9%

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

      7. div-inv 91.9%

         \[\leadsto \frac{y}{\color{blue}{z \cdot \frac{1}{-4}}} - 2 \]

      8. metadata-eval 91.9%

         \[\leadsto \frac{y}{z \cdot \color{blue}{-0.25}} - 2 \]

   9. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\frac{y}{z \cdot -0.25}} - 2 \]

   if -1.71999999999999996e59 < y < 3.8999999999999998e102

   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-*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. Taylor expanded in x around inf 89.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{+59} \lor \neg \left(y \leq 3.9 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{y}{z \cdot -0.25} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \end{array} \]

Alternative 7: 52.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-73}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7e-73) -2.0 (if (<= z 6.8e+79) (* y (/ -4.0 z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e-73) {
		tmp = -2.0;
	} else if (z <= 6.8e+79) {
		tmp = y * (-4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-7d-73)) then
        tmp = -2.0d0
    else if (z <= 6.8d+79) then
        tmp = y * ((-4.0d0) / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e-73) {
		tmp = -2.0;
	} else if (z <= 6.8e+79) {
		tmp = y * (-4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7e-73:
		tmp = -2.0
	elif z <= 6.8e+79:
		tmp = y * (-4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7e-73)
		tmp = -2.0;
	elseif (z <= 6.8e+79)
		tmp = Float64(y * Float64(-4.0 / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7e-73)
		tmp = -2.0;
	elseif (z <= 6.8e+79)
		tmp = y * (-4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7e-73], -2.0, If[LessEqual[z, 6.8e+79], N[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999995e-73 or 6.80000000000000063e79 < 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. 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 61.6%

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

   if -6.9999999999999995e-73 < z < 6.80000000000000063e79

   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/ 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 55.7%

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

      1. *-commutative 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in y around 0 55.7%

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

      1. associate-*r/ 55.7%

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

      2. associate-*l/ 55.7%

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

      3. *-commutative 55.7%

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

   9. Simplified 55.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-73}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 35.3% 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 99.2%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
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 z around inf 36.5%

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

5. Final simplification 36.5%

   \[\leadsto -2 \]

Developer target: 97.7% 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 2023274 
(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))