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

Percentage Accurate: 99.8% → 100.0%

Time: 5.5s

Alternatives: 6

Speedup: 1.2×

• 21.6% 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

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

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: 53.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ t_1 := -4 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -0.62:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))) (t_1 (* -4.0 (/ y z))))
   (if (<= z -8.5e+46)
     -2.0
     (if (<= z -0.62)
       t_1
       (if (<= z -1.5e-17)
         -2.0
         (if (<= z 3.9e-142)
           t_0
           (if (<= z 1.3e-112) t_1 (if (<= z 1.08e+43) t_0 -2.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (z <= -8.5e+46) {
		tmp = -2.0;
	} else if (z <= -0.62) {
		tmp = t_1;
	} else if (z <= -1.5e-17) {
		tmp = -2.0;
	} else if (z <= 3.9e-142) {
		tmp = t_0;
	} else if (z <= 1.3e-112) {
		tmp = t_1;
	} else if (z <= 1.08e+43) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / z)
    t_1 = (-4.0d0) * (y / z)
    if (z <= (-8.5d+46)) then
        tmp = -2.0d0
    else if (z <= (-0.62d0)) then
        tmp = t_1
    else if (z <= (-1.5d-17)) then
        tmp = -2.0d0
    else if (z <= 3.9d-142) then
        tmp = t_0
    else if (z <= 1.3d-112) then
        tmp = t_1
    else if (z <= 1.08d+43) then
        tmp = t_0
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (z <= -8.5e+46) {
		tmp = -2.0;
	} else if (z <= -0.62) {
		tmp = t_1;
	} else if (z <= -1.5e-17) {
		tmp = -2.0;
	} else if (z <= 3.9e-142) {
		tmp = t_0;
	} else if (z <= 1.3e-112) {
		tmp = t_1;
	} else if (z <= 1.08e+43) {
		tmp = t_0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	t_1 = -4.0 * (y / z)
	tmp = 0
	if z <= -8.5e+46:
		tmp = -2.0
	elif z <= -0.62:
		tmp = t_1
	elif z <= -1.5e-17:
		tmp = -2.0
	elif z <= 3.9e-142:
		tmp = t_0
	elif z <= 1.3e-112:
		tmp = t_1
	elif z <= 1.08e+43:
		tmp = t_0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / z))
	t_1 = Float64(-4.0 * Float64(y / z))
	tmp = 0.0
	if (z <= -8.5e+46)
		tmp = -2.0;
	elseif (z <= -0.62)
		tmp = t_1;
	elseif (z <= -1.5e-17)
		tmp = -2.0;
	elseif (z <= 3.9e-142)
		tmp = t_0;
	elseif (z <= 1.3e-112)
		tmp = t_1;
	elseif (z <= 1.08e+43)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / z);
	t_1 = -4.0 * (y / z);
	tmp = 0.0;
	if (z <= -8.5e+46)
		tmp = -2.0;
	elseif (z <= -0.62)
		tmp = t_1;
	elseif (z <= -1.5e-17)
		tmp = -2.0;
	elseif (z <= 3.9e-142)
		tmp = t_0;
	elseif (z <= 1.3e-112)
		tmp = t_1;
	elseif (z <= 1.08e+43)
		tmp = t_0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+46], -2.0, If[LessEqual[z, -0.62], t$95$1, If[LessEqual[z, -1.5e-17], -2.0, If[LessEqual[z, 3.9e-142], t$95$0, If[LessEqual[z, 1.3e-112], t$95$1, If[LessEqual[z, 1.08e+43], t$95$0, -2.0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999996e46 or -0.619999999999999996 < z < -1.50000000000000003e-17 or 1.08e43 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      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 z around inf 69.3%

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

   if -8.4999999999999996e46 < z < -0.619999999999999996 or 3.9000000000000003e-142 < z < 1.29999999999999996e-112

   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* 99.5%

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

      3. associate--l- 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 77.5%

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

      1. *-commutative 77.5%

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

   7. Simplified 77.5%

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

   if -1.50000000000000003e-17 < z < 3.9000000000000003e-142 or 1.29999999999999996e-112 < z < 1.08e43

   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* 99.8%

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

      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 x around inf 61.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -0.62:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+43}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+99} \lor \neg \left(y \leq -8 \cdot 10^{+72} \lor \neg \left(y \leq -1.8 \cdot 10^{+27}\right) \land y \leq 1.1 \cdot 10^{+140}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(0.5 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+99)
         (not (or (<= y -8e+72) (and (not (<= y -1.8e+27)) (<= y 1.1e+140)))))
   (* 4.0 (- -0.5 (/ y z)))
   (* -4.0 (- 0.5 (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+99) || !((y <= -8e+72) || (!(y <= -1.8e+27) && (y <= 1.1e+140)))) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = -4.0 * (0.5 - (x / 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 ((y <= (-1.4d+99)) .or. (.not. (y <= (-8d+72)) .or. (.not. (y <= (-1.8d+27))) .and. (y <= 1.1d+140))) then
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    else
        tmp = (-4.0d0) * (0.5d0 - (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+99) || !((y <= -8e+72) || (!(y <= -1.8e+27) && (y <= 1.1e+140)))) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = -4.0 * (0.5 - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e+99) or not ((y <= -8e+72) or (not (y <= -1.8e+27) and (y <= 1.1e+140))):
		tmp = 4.0 * (-0.5 - (y / z))
	else:
		tmp = -4.0 * (0.5 - (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+99) || !((y <= -8e+72) || (!(y <= -1.8e+27) && (y <= 1.1e+140))))
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	else
		tmp = Float64(-4.0 * Float64(0.5 - Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e+99) || ~(((y <= -8e+72) || (~((y <= -1.8e+27)) && (y <= 1.1e+140)))))
		tmp = 4.0 * (-0.5 - (y / z));
	else
		tmp = -4.0 * (0.5 - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+99], N[Not[Or[LessEqual[y, -8e+72], And[N[Not[LessEqual[y, -1.8e+27]], $MachinePrecision], LessEqual[y, 1.1e+140]]]], $MachinePrecision]], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(0.5 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e99 or -7.99999999999999955e72 < y < -1.79999999999999991e27 or 1.0999999999999999e140 < 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* 99.9%

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

      3. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 95.8%

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

      1. associate-*r/ 95.8%

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

      2. metadata-eval 95.8%

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

      3. +-commutative 95.8%

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

      4. *-commutative 95.8%

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

      5. fma-undefine 95.8%

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

      6. associate-*r* 95.8%

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

      7. neg-mul-1 95.8%

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

      8. associate-/l* 95.8%

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

      9. fma-undefine 95.8%

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

      10. *-commutative 95.8%

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

      11. distribute-neg-in 95.8%

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

      12. sub-neg 95.8%

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

      13. div-sub 95.8%

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

      14. distribute-neg-frac 95.8%

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

      15. associate-/l* 95.8%

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

      16. *-inverses 95.8%

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

      17. metadata-eval 95.8%

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

      18. metadata-eval 95.8%

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

   7. Simplified 95.8%

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

   if -1.4e99 < y < -7.99999999999999955e72 or -1.79999999999999991e27 < y < 1.0999999999999999e140

   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. Taylor expanded in y around 0 94.4%

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

      1. neg-mul-1 94.4%

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

      2. distribute-neg-frac 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in x around 0 94.4%

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

      1. mul-1-neg 94.4%

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

      2. unsub-neg 94.4%

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

   10. Simplified 94.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+99} \lor \neg \left(y \leq -8 \cdot 10^{+72} \lor \neg \left(y \leq -1.8 \cdot 10^{+27}\right) \land y \leq 1.1 \cdot 10^{+140}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(0.5 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+122} \lor \neg \left(y \leq 2.9 \cdot 10^{+140}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(0.5 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e+122) (not (<= y 2.9e+140)))
   (* -4.0 (/ y z))
   (* -4.0 (- 0.5 (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e+122) || !(y <= 2.9e+140)) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = -4.0 * (0.5 - (x / 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 ((y <= (-6.8d+122)) .or. (.not. (y <= 2.9d+140))) then
        tmp = (-4.0d0) * (y / z)
    else
        tmp = (-4.0d0) * (0.5d0 - (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e+122) || !(y <= 2.9e+140)) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = -4.0 * (0.5 - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.8e+122) or not (y <= 2.9e+140):
		tmp = -4.0 * (y / z)
	else:
		tmp = -4.0 * (0.5 - (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e+122) || !(y <= 2.9e+140))
		tmp = Float64(-4.0 * Float64(y / z));
	else
		tmp = Float64(-4.0 * Float64(0.5 - Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.8e+122) || ~((y <= 2.9e+140)))
		tmp = -4.0 * (y / z);
	else
		tmp = -4.0 * (0.5 - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.8e+122], N[Not[LessEqual[y, 2.9e+140]], $MachinePrecision]], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(0.5 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e122 or 2.8999999999999999e140 < 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* 99.9%

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

      3. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 86.8%

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

      1. *-commutative 86.8%

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

   7. Simplified 86.8%

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

   if -6.8e122 < y < 2.8999999999999999e140

   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. Taylor expanded in y around 0 90.5%

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

      1. neg-mul-1 90.5%

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

      2. distribute-neg-frac 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in x around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

   10. Simplified 90.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+122} \lor \neg \left(y \leq 2.9 \cdot 10^{+140}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(0.5 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-17}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+43}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.5e-17) -2.0 (if (<= z 1.1e+43) (* 4.0 (/ x z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e-17) {
		tmp = -2.0;
	} else if (z <= 1.1e+43) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.5d-17)) then
        tmp = -2.0d0
    else if (z <= 1.1d+43) then
        tmp = 4.0d0 * (x / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e-17) {
		tmp = -2.0;
	} else if (z <= 1.1e+43) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.5e-17:
		tmp = -2.0
	elif z <= 1.1e+43:
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.5e-17)
		tmp = -2.0;
	elseif (z <= 1.1e+43)
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.5e-17)
		tmp = -2.0;
	elseif (z <= 1.1e+43)
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.5e-17], -2.0, If[LessEqual[z, 1.1e+43], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e-17 or 1.1e43 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      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 z around inf 65.9%

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

   if -3.5000000000000002e-17 < z < 1.1e43

   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* 99.8%

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

      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 x around inf 58.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-17}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+43}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 33.9% 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* 99.8%

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

   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 z around inf 39.3%

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

6. Final simplification 39.3%

   \[\leadsto -2 \]
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 2024071 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

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

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