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

Percentage Accurate: 99.7% → 100.0%

Time: 7.7s

Alternatives: 9

Speedup: 1.4×

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

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 + (4.0d0 * ((x - z) / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 100.0%

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

Alternative 2: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-79}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))))
   (if (<= x -1.15e+14)
     t_0
     (if (<= x 2.9e-79) 4.0 (if (<= x 3.6e+38) (* -4.0 (/ z y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double tmp;
	if (x <= -1.15e+14) {
		tmp = t_0;
	} else if (x <= 2.9e-79) {
		tmp = 4.0;
	} else if (x <= 3.6e+38) {
		tmp = -4.0 * (z / y);
	} 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 = 4.0d0 * (x / y)
    if (x <= (-1.15d+14)) then
        tmp = t_0
    else if (x <= 2.9d-79) then
        tmp = 4.0d0
    else if (x <= 3.6d+38) then
        tmp = (-4.0d0) * (z / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double tmp;
	if (x <= -1.15e+14) {
		tmp = t_0;
	} else if (x <= 2.9e-79) {
		tmp = 4.0;
	} else if (x <= 3.6e+38) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	tmp = 0
	if x <= -1.15e+14:
		tmp = t_0
	elif x <= 2.9e-79:
		tmp = 4.0
	elif x <= 3.6e+38:
		tmp = -4.0 * (z / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (x <= -1.15e+14)
		tmp = t_0;
	elseif (x <= 2.9e-79)
		tmp = 4.0;
	elseif (x <= 3.6e+38)
		tmp = Float64(-4.0 * Float64(z / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / y);
	tmp = 0.0;
	if (x <= -1.15e+14)
		tmp = t_0;
	elseif (x <= 2.9e-79)
		tmp = 4.0;
	elseif (x <= 3.6e+38)
		tmp = -4.0 * (z / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+14], t$95$0, If[LessEqual[x, 2.9e-79], 4.0, If[LessEqual[x, 3.6e+38], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e14 or 3.59999999999999969e38 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-*r/ 96.6%

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

      3. associate-*l/ 96.4%

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

      4. metadata-eval 96.4%

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

      5. distribute-lft-neg-in 96.4%

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

      6. associate-/l* 96.4%

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

      7. associate-*l/ 96.4%

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

      8. distribute-rgt-neg-in 96.4%

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

      9. distribute-lft-in 99.8%

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

      10. sub-neg 99.8%

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

      11. *-commutative 99.8%

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

      12. +-commutative 99.8%

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

      13. fma-define 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around inf 65.7%

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

   if -1.15e14 < x < 2.9000000000000001e-79

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 56.5%

      \[\leadsto \color{blue}{4} \]

   if 2.9000000000000001e-79 < x < 3.59999999999999969e38

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-lft-neg-in 100.0%

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

      6. associate-/l* 100.0%

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

      7. associate-*l/ 99.8%

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

      8. distribute-rgt-neg-in 99.8%

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

      9. distribute-lft-in 99.8%

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

      10. sub-neg 99.8%

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

      11. *-commutative 99.8%

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

      12. +-commutative 99.8%

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

      13. fma-define 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 60.3%

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

Alternative 3: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+29} \lor \neg \left(y \leq 360000000\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e+29) (not (<= y 360000000.0)))
   (+ 4.0 (* 4.0 (/ x y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+29) || !(y <= 360000000.0)) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.2d+29)) .or. (.not. (y <= 360000000.0d0))) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+29) || !(y <= 360000000.0)) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e+29) or not (y <= 360000000.0):
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e+29) || !(y <= 360000000.0))
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e+29) || ~((y <= 360000000.0)))
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e+29], N[Not[LessEqual[y, 360000000.0]], $MachinePrecision]], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999998e29 or 3.6e8 < y

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 84.1%

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

   if -6.1999999999999998e29 < y < 3.6e8

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 95.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+29} \lor \neg \left(y \leq 360000000\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+48}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 60000000000:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+48)
   (+ 4.0 (/ (* z -4.0) y))
   (if (<= y 60000000000.0) (* 4.0 (/ (- x z) y)) (+ 4.0 (* 4.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+48) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (y <= 60000000000.0) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.7d+48)) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    else if (y <= 60000000000.0d0) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+48) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else if (y <= 60000000000.0) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+48:
		tmp = 4.0 + ((z * -4.0) / y)
	elif y <= 60000000000.0:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+48)
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	elseif (y <= 60000000000.0)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+48)
		tmp = 4.0 + ((z * -4.0) / y);
	elseif (y <= 60000000000.0)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+48], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 60000000000.0], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000004e48

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} + 1} \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} + 1 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{\left(x + y \cdot 0.75\right) - z}{y}, 1\right)} \]

      4. associate--l+ 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y}, 1\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) + x}}{y}, 1\right) \]

      6. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\left(y \cdot 0.75 - z\right) + \color{blue}{\left(-\left(-x\right)\right)}}{y}, 1\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) - \left(-x\right)}}{y}, 1\right) \]

      8. associate--r+ 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{y \cdot 0.75 - \left(z + \left(-x\right)\right)}}{y}, 1\right) \]

      9. div-sub 99.8%

         \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} - \frac{z + \left(-x\right)}{y}}, 1\right) \]

      10. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} + \left(-\frac{z + \left(-x\right)}{y}\right)}, 1\right) \]

      11. associate-*l/ 99.9%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y}{y} \cdot 0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      12. *-inverses 99.9%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{1} \cdot 0.75 + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      13. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      14. distribute-frac-neg2 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{z + \left(-x\right)}{-y}}, 1\right) \]

      15. remove-double-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{\left(-\left(-z\right)\right)} + \left(-x\right)}{-y}, 1\right) \]

      16. distribute-neg-out 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{-\left(\left(-z\right) + x\right)}}{-y}, 1\right) \]

      17. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x + \left(-z\right)\right)}}{-y}, 1\right) \]

      18. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x - z\right)}}{-y}, 1\right) \]

      19. distribute-frac-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\left(-\frac{x - z}{-y}\right)}, 1\right) \]

      20. distribute-frac-neg2 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{x - z}{-\left(-y\right)}}, 1\right) \]

      21. remove-double-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{x - z}{\color{blue}{y}}, 1\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.7%

      \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 - \frac{z}{y}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 86.7%

         \[\leadsto 1 + 4 \cdot \color{blue}{\left(0.75 + \left(-\frac{z}{y}\right)\right)} \]

      2. distribute-lft-in 86.7%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot 0.75 + 4 \cdot \left(-\frac{z}{y}\right)\right)} \]

      3. metadata-eval 86.7%

         \[\leadsto 1 + \left(\color{blue}{3} + 4 \cdot \left(-\frac{z}{y}\right)\right) \]

      4. associate-+r+ 86.8%

         \[\leadsto \color{blue}{\left(1 + 3\right) + 4 \cdot \left(-\frac{z}{y}\right)} \]

      5. metadata-eval 86.8%

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

      6. neg-mul-1 86.8%

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

      7. associate-*r* 86.8%

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

      8. metadata-eval 86.8%

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

      9. *-commutative 86.8%

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

      10. associate-*l/ 86.8%

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

      11. associate-/l* 86.7%

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

   7. Simplified 86.7%

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

      1. associate-*r/ 86.8%

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

   9. Applied egg-rr 86.8%

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

   if -2.70000000000000004e48 < y < 6e10

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 94.4%

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

   if 6e10 < y

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 85.3%

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

Alternative 5: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+51}:\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq 105000000:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.36e+51)
   (+ 4.0 (* z (/ -4.0 y)))
   (if (<= y 105000000.0) (* 4.0 (/ (- x z) y)) (+ 4.0 (* 4.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.36e+51) {
		tmp = 4.0 + (z * (-4.0 / y));
	} else if (y <= 105000000.0) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.36d+51)) then
        tmp = 4.0d0 + (z * ((-4.0d0) / y))
    else if (y <= 105000000.0d0) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.36e+51) {
		tmp = 4.0 + (z * (-4.0 / y));
	} else if (y <= 105000000.0) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.36e+51:
		tmp = 4.0 + (z * (-4.0 / y))
	elif y <= 105000000.0:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.36e+51)
		tmp = Float64(4.0 + Float64(z * Float64(-4.0 / y)));
	elseif (y <= 105000000.0)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.36e+51)
		tmp = 4.0 + (z * (-4.0 / y));
	elseif (y <= 105000000.0)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.36e+51], N[(4.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 105000000.0], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3599999999999999e51

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} + 1} \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{4 \cdot \frac{\left(x + y \cdot 0.75\right) - z}{y}} + 1 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{\left(x + y \cdot 0.75\right) - z}{y}, 1\right)} \]

      4. associate--l+ 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{x + \left(y \cdot 0.75 - z\right)}}{y}, 1\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) + x}}{y}, 1\right) \]

      6. remove-double-neg 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\left(y \cdot 0.75 - z\right) + \color{blue}{\left(-\left(-x\right)\right)}}{y}, 1\right) \]

      7. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{\left(y \cdot 0.75 - z\right) - \left(-x\right)}}{y}, 1\right) \]

      8. associate--r+ 99.8%

         \[\leadsto \mathsf{fma}\left(4, \frac{\color{blue}{y \cdot 0.75 - \left(z + \left(-x\right)\right)}}{y}, 1\right) \]

      9. div-sub 99.8%

         \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} - \frac{z + \left(-x\right)}{y}}, 1\right) \]

      10. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y \cdot 0.75}{y} + \left(-\frac{z + \left(-x\right)}{y}\right)}, 1\right) \]

      11. associate-*l/ 99.9%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{\frac{y}{y} \cdot 0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      12. *-inverses 99.9%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{1} \cdot 0.75 + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      13. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(4, \color{blue}{0.75} + \left(-\frac{z + \left(-x\right)}{y}\right), 1\right) \]

      14. distribute-frac-neg2 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{z + \left(-x\right)}{-y}}, 1\right) \]

      15. remove-double-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{\left(-\left(-z\right)\right)} + \left(-x\right)}{-y}, 1\right) \]

      16. distribute-neg-out 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{\color{blue}{-\left(\left(-z\right) + x\right)}}{-y}, 1\right) \]

      17. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x + \left(-z\right)\right)}}{-y}, 1\right) \]

      18. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{-\color{blue}{\left(x - z\right)}}{-y}, 1\right) \]

      19. distribute-frac-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\left(-\frac{x - z}{-y}\right)}, 1\right) \]

      20. distribute-frac-neg2 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \color{blue}{\frac{x - z}{-\left(-y\right)}}, 1\right) \]

      21. remove-double-neg 99.9%

          \[\leadsto \mathsf{fma}\left(4, 0.75 + \frac{x - z}{\color{blue}{y}}, 1\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.7%

      \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 - \frac{z}{y}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 86.7%

         \[\leadsto 1 + 4 \cdot \color{blue}{\left(0.75 + \left(-\frac{z}{y}\right)\right)} \]

      2. distribute-lft-in 86.7%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot 0.75 + 4 \cdot \left(-\frac{z}{y}\right)\right)} \]

      3. metadata-eval 86.7%

         \[\leadsto 1 + \left(\color{blue}{3} + 4 \cdot \left(-\frac{z}{y}\right)\right) \]

      4. associate-+r+ 86.8%

         \[\leadsto \color{blue}{\left(1 + 3\right) + 4 \cdot \left(-\frac{z}{y}\right)} \]

      5. metadata-eval 86.8%

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

      6. neg-mul-1 86.8%

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

      7. associate-*r* 86.8%

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

      8. metadata-eval 86.8%

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

      9. *-commutative 86.8%

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

      10. associate-*l/ 86.8%

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

      11. associate-/l* 86.7%

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

   7. Simplified 86.7%

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

   if -1.3599999999999999e51 < y < 1.05e8

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 94.4%

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

   if 1.05e8 < y

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 85.3%

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

Alternative 6: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+52}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+175}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.2e+52) 4.0 (if (<= y 8.5e+175) (* 4.0 (/ (- x z) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e+52) {
		tmp = 4.0;
	} else if (y <= 8.5e+175) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9.2d+52)) then
        tmp = 4.0d0
    else if (y <= 8.5d+175) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.2e+52) {
		tmp = 4.0;
	} else if (y <= 8.5e+175) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.2e+52:
		tmp = 4.0
	elif y <= 8.5e+175:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.2e+52)
		tmp = 4.0;
	elseif (y <= 8.5e+175)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.2e+52)
		tmp = 4.0;
	elseif (y <= 8.5e+175)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.2e+52], 4.0, If[LessEqual[y, 8.5e+175], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999999e52 or 8.50000000000000034e175 < y

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.9%

      \[\leadsto \color{blue}{4} \]

   if -9.1999999999999999e52 < y < 8.50000000000000034e175

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 84.2%

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

Alternative 7: 55.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+34}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 36000000000:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e+34) 4.0 (if (<= y 36000000000.0) (* -4.0 (/ z y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+34) {
		tmp = 4.0;
	} else if (y <= 36000000000.0) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.3d+34)) then
        tmp = 4.0d0
    else if (y <= 36000000000.0d0) then
        tmp = (-4.0d0) * (z / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+34) {
		tmp = 4.0;
	} else if (y <= 36000000000.0) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+34:
		tmp = 4.0
	elif y <= 36000000000.0:
		tmp = -4.0 * (z / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+34)
		tmp = 4.0;
	elseif (y <= 36000000000.0)
		tmp = Float64(-4.0 * Float64(z / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e+34)
		tmp = 4.0;
	elseif (y <= 36000000000.0)
		tmp = -4.0 * (z / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+34], 4.0, If[LessEqual[y, 36000000000.0], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999999e34 or 3.6e10 < y

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.2%

      \[\leadsto \color{blue}{4} \]

   if -1.29999999999999999e34 < y < 3.6e10

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-*r/ 96.9%

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

      3. associate-*l/ 96.8%

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

      4. metadata-eval 96.8%

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

      5. distribute-lft-neg-in 96.8%

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

      6. associate-/l* 96.8%

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

      7. associate-*l/ 96.6%

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

      8. distribute-rgt-neg-in 96.6%

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

      9. distribute-lft-in 99.8%

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

      10. sub-neg 99.8%

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

      11. *-commutative 99.8%

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

      12. +-commutative 99.8%

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

      13. fma-define 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 50.6%

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

Alternative 8: 35.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 4.0)

C

double code(double x, double y, double z) {
	return 4.0;
}

Fortran

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

Java

public static double code(double x, double y, double z) {
	return 4.0;
}

Python

def code(x, y, z):
	return 4.0

Julia

function code(x, y, z)
	return 4.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0;
end

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 35.4%

   \[\leadsto \color{blue}{4} \]
4. Add Preprocessing

Alternative 9: 7.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 38.4%

   \[\leadsto 1 + \color{blue}{-4 \cdot \frac{z}{y}} \]
4. Step-by-step derivation

   1. associate-*r/ 38.4%

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

   2. *-commutative 38.4%

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

5. Simplified 38.4%

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

6. Taylor expanded in z around 0 8.0%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024114 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))