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

Percentage Accurate: 99.9% → 100.0%

Time: 5.7s

Alternatives: 9

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. remove-double-neg 100.0%

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

   2. neg-mul-1 100.0%

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

   3. times-frac 100.0%

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

   4. metadata-eval 100.0%

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

   5. div-sub 100.0%

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

   6. distribute-frac-neg2 100.0%

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

   7. distribute-frac-neg 100.0%

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

   8. sub-neg 100.0%

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

   9. +-commutative 100.0%

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

   10. distribute-neg-out 100.0%

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

   11. remove-double-neg 100.0%

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

   12. sub-neg 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. times-frac 100.0%

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

   16. metadata-eval 100.0%

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

   17. *-inverses 100.0%

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

   18. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{-4}{z}\\ t_1 := x \cdot \frac{4}{z}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-288}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-245}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-144}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ -4.0 z))) (t_1 (* x (/ 4.0 z))))
   (if (<= x -7.5e+43)
     t_1
     (if (<= x 4e-288)
       -2.0
       (if (<= x 5.7e-245)
         t_0
         (if (<= x 4.8e-144) -2.0 (if (<= x 5.8e+62) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (-4.0 / z);
	double t_1 = x * (4.0 / z);
	double tmp;
	if (x <= -7.5e+43) {
		tmp = t_1;
	} else if (x <= 4e-288) {
		tmp = -2.0;
	} else if (x <= 5.7e-245) {
		tmp = t_0;
	} else if (x <= 4.8e-144) {
		tmp = -2.0;
	} else if (x <= 5.8e+62) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * ((-4.0d0) / z)
    t_1 = x * (4.0d0 / z)
    if (x <= (-7.5d+43)) then
        tmp = t_1
    else if (x <= 4d-288) then
        tmp = -2.0d0
    else if (x <= 5.7d-245) then
        tmp = t_0
    else if (x <= 4.8d-144) then
        tmp = -2.0d0
    else if (x <= 5.8d+62) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (-4.0 / z);
	double t_1 = x * (4.0 / z);
	double tmp;
	if (x <= -7.5e+43) {
		tmp = t_1;
	} else if (x <= 4e-288) {
		tmp = -2.0;
	} else if (x <= 5.7e-245) {
		tmp = t_0;
	} else if (x <= 4.8e-144) {
		tmp = -2.0;
	} else if (x <= 5.8e+62) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (-4.0 / z)
	t_1 = x * (4.0 / z)
	tmp = 0
	if x <= -7.5e+43:
		tmp = t_1
	elif x <= 4e-288:
		tmp = -2.0
	elif x <= 5.7e-245:
		tmp = t_0
	elif x <= 4.8e-144:
		tmp = -2.0
	elif x <= 5.8e+62:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-4.0 / z))
	t_1 = Float64(x * Float64(4.0 / z))
	tmp = 0.0
	if (x <= -7.5e+43)
		tmp = t_1;
	elseif (x <= 4e-288)
		tmp = -2.0;
	elseif (x <= 5.7e-245)
		tmp = t_0;
	elseif (x <= 4.8e-144)
		tmp = -2.0;
	elseif (x <= 5.8e+62)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (-4.0 / z);
	t_1 = x * (4.0 / z);
	tmp = 0.0;
	if (x <= -7.5e+43)
		tmp = t_1;
	elseif (x <= 4e-288)
		tmp = -2.0;
	elseif (x <= 5.7e-245)
		tmp = t_0;
	elseif (x <= 4.8e-144)
		tmp = -2.0;
	elseif (x <= 5.8e+62)
		tmp = t_0;
	else
		tmp = t_1;
	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[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e+43], t$95$1, If[LessEqual[x, 4e-288], -2.0, If[LessEqual[x, 5.7e-245], t$95$0, If[LessEqual[x, 4.8e-144], -2.0, If[LessEqual[x, 5.8e+62], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999967e43 or 5.79999999999999968e62 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.6%

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

      3. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 68.7%

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

      1. associate-*r/ 68.7%

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

      2. associate-*l/ 68.5%

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

      3. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   if -7.49999999999999967e43 < x < 4.00000000000000023e-288 or 5.7000000000000001e-245 < x < 4.79999999999999988e-144

   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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 60.8%

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

   if 4.00000000000000023e-288 < x < 5.7000000000000001e-245 or 4.79999999999999988e-144 < x < 5.79999999999999968e62

   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. *-commutative 99.9%

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

      2. associate-/l* 99.8%

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

      3. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 66.7%

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

      1. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in y around 0 66.7%

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

      1. associate-*r/ 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-*r/ 66.6%

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

   10. Simplified 66.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-288}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-144}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{4}{z}\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.22 \cdot 10^{-287}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-151}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ 4.0 z))))
   (if (<= x -1.7e+42)
     t_0
     (if (<= x 2.22e-287)
       -2.0
       (if (<= x 6e-245)
         (* y (/ -4.0 z))
         (if (<= x 1.05e-151)
           -2.0
           (if (<= x 8.8e+63) (* -4.0 (/ y z)) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.0 / z);
	double tmp;
	if (x <= -1.7e+42) {
		tmp = t_0;
	} else if (x <= 2.22e-287) {
		tmp = -2.0;
	} else if (x <= 6e-245) {
		tmp = y * (-4.0 / z);
	} else if (x <= 1.05e-151) {
		tmp = -2.0;
	} else if (x <= 8.8e+63) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (4.0d0 / z)
    if (x <= (-1.7d+42)) then
        tmp = t_0
    else if (x <= 2.22d-287) then
        tmp = -2.0d0
    else if (x <= 6d-245) then
        tmp = y * ((-4.0d0) / z)
    else if (x <= 1.05d-151) then
        tmp = -2.0d0
    else if (x <= 8.8d+63) then
        tmp = (-4.0d0) * (y / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (4.0 / z);
	double tmp;
	if (x <= -1.7e+42) {
		tmp = t_0;
	} else if (x <= 2.22e-287) {
		tmp = -2.0;
	} else if (x <= 6e-245) {
		tmp = y * (-4.0 / z);
	} else if (x <= 1.05e-151) {
		tmp = -2.0;
	} else if (x <= 8.8e+63) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.0 / z)
	tmp = 0
	if x <= -1.7e+42:
		tmp = t_0
	elif x <= 2.22e-287:
		tmp = -2.0
	elif x <= 6e-245:
		tmp = y * (-4.0 / z)
	elif x <= 1.05e-151:
		tmp = -2.0
	elif x <= 8.8e+63:
		tmp = -4.0 * (y / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.0 / z))
	tmp = 0.0
	if (x <= -1.7e+42)
		tmp = t_0;
	elseif (x <= 2.22e-287)
		tmp = -2.0;
	elseif (x <= 6e-245)
		tmp = Float64(y * Float64(-4.0 / z));
	elseif (x <= 1.05e-151)
		tmp = -2.0;
	elseif (x <= 8.8e+63)
		tmp = Float64(-4.0 * Float64(y / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.0 / z);
	tmp = 0.0;
	if (x <= -1.7e+42)
		tmp = t_0;
	elseif (x <= 2.22e-287)
		tmp = -2.0;
	elseif (x <= 6e-245)
		tmp = y * (-4.0 / z);
	elseif (x <= 1.05e-151)
		tmp = -2.0;
	elseif (x <= 8.8e+63)
		tmp = -4.0 * (y / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+42], t$95$0, If[LessEqual[x, 2.22e-287], -2.0, If[LessEqual[x, 6e-245], N[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-151], -2.0, If[LessEqual[x, 8.8e+63], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.69999999999999988e42 or 8.7999999999999995e63 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.6%

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

      3. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 68.7%

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

      1. associate-*r/ 68.7%

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

      2. associate-*l/ 68.5%

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

      3. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   if -1.69999999999999988e42 < x < 2.21999999999999999e-287 or 6.0000000000000004e-245 < x < 1.04999999999999995e-151

   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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 60.8%

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

   if 2.21999999999999999e-287 < x < 6.0000000000000004e-245

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 89.2%

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

      1. *-commutative 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in y around 0 89.2%

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

      1. associate-*r/ 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*r/ 89.2%

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

   10. Simplified 89.2%

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

   if 1.04999999999999995e-151 < x < 8.7999999999999995e63

   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. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{elif}\;x \leq 2.22 \cdot 10^{-287}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-151}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot 4}{z}\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-288}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-158}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x 4.0) z)))
   (if (<= x -1.4e+44)
     t_0
     (if (<= x 7.5e-288)
       -2.0
       (if (<= x 4.6e-245)
         (* y (/ -4.0 z))
         (if (<= x 2.45e-158)
           -2.0
           (if (<= x 1.22e+63) (* -4.0 (/ y z)) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * 4.0) / z;
	double tmp;
	if (x <= -1.4e+44) {
		tmp = t_0;
	} else if (x <= 7.5e-288) {
		tmp = -2.0;
	} else if (x <= 4.6e-245) {
		tmp = y * (-4.0 / z);
	} else if (x <= 2.45e-158) {
		tmp = -2.0;
	} else if (x <= 1.22e+63) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * 4.0d0) / z
    if (x <= (-1.4d+44)) then
        tmp = t_0
    else if (x <= 7.5d-288) then
        tmp = -2.0d0
    else if (x <= 4.6d-245) then
        tmp = y * ((-4.0d0) / z)
    else if (x <= 2.45d-158) then
        tmp = -2.0d0
    else if (x <= 1.22d+63) then
        tmp = (-4.0d0) * (y / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * 4.0) / z;
	double tmp;
	if (x <= -1.4e+44) {
		tmp = t_0;
	} else if (x <= 7.5e-288) {
		tmp = -2.0;
	} else if (x <= 4.6e-245) {
		tmp = y * (-4.0 / z);
	} else if (x <= 2.45e-158) {
		tmp = -2.0;
	} else if (x <= 1.22e+63) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * 4.0) / z
	tmp = 0
	if x <= -1.4e+44:
		tmp = t_0
	elif x <= 7.5e-288:
		tmp = -2.0
	elif x <= 4.6e-245:
		tmp = y * (-4.0 / z)
	elif x <= 2.45e-158:
		tmp = -2.0
	elif x <= 1.22e+63:
		tmp = -4.0 * (y / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * 4.0) / z)
	tmp = 0.0
	if (x <= -1.4e+44)
		tmp = t_0;
	elseif (x <= 7.5e-288)
		tmp = -2.0;
	elseif (x <= 4.6e-245)
		tmp = Float64(y * Float64(-4.0 / z));
	elseif (x <= 2.45e-158)
		tmp = -2.0;
	elseif (x <= 1.22e+63)
		tmp = Float64(-4.0 * Float64(y / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * 4.0) / z;
	tmp = 0.0;
	if (x <= -1.4e+44)
		tmp = t_0;
	elseif (x <= 7.5e-288)
		tmp = -2.0;
	elseif (x <= 4.6e-245)
		tmp = y * (-4.0 / z);
	elseif (x <= 2.45e-158)
		tmp = -2.0;
	elseif (x <= 1.22e+63)
		tmp = -4.0 * (y / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * 4.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.4e+44], t$95$0, If[LessEqual[x, 7.5e-288], -2.0, If[LessEqual[x, 4.6e-245], N[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.45e-158], -2.0, If[LessEqual[x, 1.22e+63], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4e44 or 1.2199999999999999e63 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.6%

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

      3. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 68.7%

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

      1. associate-*r/ 68.7%

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

      2. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if -1.4e44 < x < 7.4999999999999998e-288 or 4.6000000000000003e-245 < x < 2.44999999999999997e-158

   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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 60.8%

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

   if 7.4999999999999998e-288 < x < 4.6000000000000003e-245

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. associate--l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 89.2%

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

      1. *-commutative 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in y around 0 89.2%

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

      1. associate-*r/ 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*r/ 89.2%

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

   10. Simplified 89.2%

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

   if 2.44999999999999997e-158 < x < 1.2199999999999999e63

   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. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-288}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-158}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+21} \lor \neg \left(y \leq 2.05 \cdot 10^{-37}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\frac{x}{-z} - -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+21) (not (<= y 2.05e-37)))
   (* 4.0 (- -0.5 (/ y z)))
   (* -4.0 (- (/ x (- z)) -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+21) || !(y <= 2.05e-37)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = -4.0 * ((x / -z) - -0.5);
	}
	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 <= (-7.2d+21)) .or. (.not. (y <= 2.05d-37))) then
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    else
        tmp = (-4.0d0) * ((x / -z) - (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+21) || !(y <= 2.05e-37)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = -4.0 * ((x / -z) - -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e+21) or not (y <= 2.05e-37):
		tmp = 4.0 * (-0.5 - (y / z))
	else:
		tmp = -4.0 * ((x / -z) - -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e+21) || !(y <= 2.05e-37))
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	else
		tmp = Float64(-4.0 * Float64(Float64(x / Float64(-z)) - -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e+21) || ~((y <= 2.05e-37)))
		tmp = 4.0 * (-0.5 - (y / z));
	else
		tmp = -4.0 * ((x / -z) - -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e+21], N[Not[LessEqual[y, 2.05e-37]], $MachinePrecision]], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(x / (-z)), $MachinePrecision] - -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e21 or 2.0499999999999999e-37 < 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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. metadata-eval 84.1%

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

      3. +-commutative 84.1%

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

      4. *-commutative 84.1%

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

      5. fma-undefine 84.1%

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

      6. associate-*r* 84.1%

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

      7. neg-mul-1 84.1%

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

      8. associate-/l* 84.1%

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

      9. fma-undefine 84.1%

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

      10. *-commutative 84.1%

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

      11. distribute-neg-in 84.1%

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

      12. sub-neg 84.1%

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

      13. div-sub 84.1%

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

      14. distribute-neg-frac 84.1%

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

      15. associate-/l* 84.1%

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

      16. *-inverses 84.1%

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

      17. metadata-eval 84.1%

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

      18. metadata-eval 84.1%

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

   7. Simplified 84.1%

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

   if -7.2e21 < y < 2.0499999999999999e-37

   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. remove-double-neg 99.9%

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

      2. neg-mul-1 99.9%

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

      3. times-frac 99.9%

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

      4. metadata-eval 99.9%

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

      5. div-sub 100.0%

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

      6. distribute-frac-neg2 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-out 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. times-frac 100.0%

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

      16. metadata-eval 100.0%

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

      17. *-inverses 100.0%

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.4%

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

      1. neg-mul-1 97.4%

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

      2. distribute-neg-frac 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+21} \lor \neg \left(y \leq 2.05 \cdot 10^{-37}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\frac{x}{-z} - -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+173} \lor \neg \left(x \leq 8.6 \cdot 10^{+161}\right):\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.22e+173) (not (<= x 8.6e+161)))
   (/ (* x 4.0) z)
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.22e+173) || !(x <= 8.6e+161)) {
		tmp = (x * 4.0) / z;
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.22d+173)) .or. (.not. (x <= 8.6d+161))) then
        tmp = (x * 4.0d0) / z
    else
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.22e+173) || !(x <= 8.6e+161)) {
		tmp = (x * 4.0) / z;
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.22e+173) or not (x <= 8.6e+161):
		tmp = (x * 4.0) / z
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.22e+173) || !(x <= 8.6e+161))
		tmp = Float64(Float64(x * 4.0) / z);
	else
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.22e+173) || ~((x <= 8.6e+161)))
		tmp = (x * 4.0) / z;
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.22e+173], N[Not[LessEqual[x, 8.6e+161]], $MachinePrecision]], N[(N[(x * 4.0), $MachinePrecision] / z), $MachinePrecision], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.22e173 or 8.6e161 < x

   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. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 88.6%

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

      1. associate-*r/ 88.6%

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

      2. *-commutative 88.6%

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

   7. Simplified 88.6%

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

   if -1.22e173 < x < 8.6e161

   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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 83.4%

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

      1. associate-*r/ 83.4%

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

      2. metadata-eval 83.4%

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

      3. +-commutative 83.4%

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

      4. *-commutative 83.4%

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

      5. fma-undefine 83.4%

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

      6. associate-*r* 83.4%

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

      7. neg-mul-1 83.4%

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

      8. associate-/l* 83.4%

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

      9. fma-undefine 83.4%

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

      10. *-commutative 83.4%

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

      11. distribute-neg-in 83.4%

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

      12. sub-neg 83.4%

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

      13. div-sub 83.4%

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

      14. distribute-neg-frac 83.4%

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

      15. associate-/l* 83.4%

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

      16. *-inverses 83.4%

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

      17. metadata-eval 83.4%

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

      18. metadata-eval 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+173} \lor \neg \left(x \leq 8.6 \cdot 10^{+161}\right):\\ \;\;\;\;\frac{x \cdot 4}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+41} \lor \neg \left(x \leq 5.3 \cdot 10^{-67}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e+41) (not (<= x 5.3e-67)))
   (* 4.0 (/ (- x y) z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+41) || !(x <= 5.3e-67)) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-4d+41)) .or. (.not. (x <= 5.3d-67))) then
        tmp = 4.0d0 * ((x - y) / z)
    else
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+41) || !(x <= 5.3e-67)) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e+41) or not (x <= 5.3e-67):
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e+41) || !(x <= 5.3e-67))
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e+41) || ~((x <= 5.3e-67)))
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e+41], N[Not[LessEqual[x, 5.3e-67]], $MachinePrecision]], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000002e41 or 5.29999999999999971e-67 < x

   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. *-commutative 99.9%

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

      2. associate-/l* 99.6%

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

      3. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 85.1%

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

   if -4.00000000000000002e41 < x < 5.29999999999999971e-67

   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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 92.7%

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

      1. associate-*r/ 92.7%

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

      2. metadata-eval 92.7%

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

      3. +-commutative 92.7%

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

      4. *-commutative 92.7%

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

      5. fma-undefine 92.7%

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

      6. associate-*r* 92.7%

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

      7. neg-mul-1 92.7%

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

      8. associate-/l* 92.7%

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

      9. fma-undefine 92.7%

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

      10. *-commutative 92.7%

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

      11. distribute-neg-in 92.7%

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

      12. sub-neg 92.7%

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

      13. div-sub 92.7%

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

      14. distribute-neg-frac 92.7%

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

      15. associate-/l* 92.7%

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

      16. *-inverses 92.7%

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

      17. metadata-eval 92.7%

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

      18. metadata-eval 92.7%

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

   7. Simplified 92.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+41} \lor \neg \left(x \leq 5.3 \cdot 10^{-67}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+40} \lor \neg \left(x \leq 5.3 \cdot 10^{-67}\right):\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+40) (not (<= x 5.3e-67))) (* x (/ 4.0 z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+40) || !(x <= 5.3e-67)) {
		tmp = x * (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 ((x <= (-5.5d+40)) .or. (.not. (x <= 5.3d-67))) then
        tmp = x * (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 ((x <= -5.5e+40) || !(x <= 5.3e-67)) {
		tmp = x * (4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+40) or not (x <= 5.3e-67):
		tmp = x * (4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+40) || !(x <= 5.3e-67))
		tmp = Float64(x * Float64(4.0 / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e+40) || ~((x <= 5.3e-67)))
		tmp = x * (4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+40], N[Not[LessEqual[x, 5.3e-67]], $MachinePrecision]], N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.49999999999999974e40 or 5.29999999999999971e-67 < x

   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. *-commutative 99.9%

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

      2. associate-/l* 99.6%

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

      3. associate--l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 61.3%

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

      1. associate-*r/ 61.3%

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

      2. associate-*l/ 61.2%

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

      3. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   if -5.49999999999999974e40 < x < 5.29999999999999971e-67

   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. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

      3. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.7%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+40} \lor \neg \left(x \leq 5.3 \cdot 10^{-67}\right):\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.3% 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 100.0%

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

   1. *-commutative 100.0%

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

   2. associate-/l* 99.7%

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

   3. associate--l- 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around inf 35.1%

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

6. Final simplification 35.1%

   \[\leadsto -2 \]
7. Add Preprocessing

Developer target: 97.6% 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 2024039 
(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))