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

Percentage Accurate: 99.8% → 100.0%

Time: 5.8s

Alternatives: 7

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: 99.8% 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

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

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(Float64(4.0 * 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[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. associate-*l/ 99.6%

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

   2. +-commutative 99.6%

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

   3. fma-def 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around 0 100.0%

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

   1. associate-*r/ 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+177}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+81}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1050000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-223}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+70}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))))
   (if (<= x -3.5e+177)
     t_0
     (if (<= x -2.45e+81)
       4.0
       (if (<= x -1050000000000.0)
         t_0
         (if (<= x -5.3e-223)
           4.0
           (if (<= x 3.8e-203)
             (/ (* z -4.0) y)
             (if (<= x 1.2e+70) 4.0 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double tmp;
	if (x <= -3.5e+177) {
		tmp = t_0;
	} else if (x <= -2.45e+81) {
		tmp = 4.0;
	} else if (x <= -1050000000000.0) {
		tmp = t_0;
	} else if (x <= -5.3e-223) {
		tmp = 4.0;
	} else if (x <= 3.8e-203) {
		tmp = (z * -4.0) / y;
	} else if (x <= 1.2e+70) {
		tmp = 4.0;
	} 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 <= (-3.5d+177)) then
        tmp = t_0
    else if (x <= (-2.45d+81)) then
        tmp = 4.0d0
    else if (x <= (-1050000000000.0d0)) then
        tmp = t_0
    else if (x <= (-5.3d-223)) then
        tmp = 4.0d0
    else if (x <= 3.8d-203) then
        tmp = (z * (-4.0d0)) / y
    else if (x <= 1.2d+70) then
        tmp = 4.0d0
    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 <= -3.5e+177) {
		tmp = t_0;
	} else if (x <= -2.45e+81) {
		tmp = 4.0;
	} else if (x <= -1050000000000.0) {
		tmp = t_0;
	} else if (x <= -5.3e-223) {
		tmp = 4.0;
	} else if (x <= 3.8e-203) {
		tmp = (z * -4.0) / y;
	} else if (x <= 1.2e+70) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	tmp = 0
	if x <= -3.5e+177:
		tmp = t_0
	elif x <= -2.45e+81:
		tmp = 4.0
	elif x <= -1050000000000.0:
		tmp = t_0
	elif x <= -5.3e-223:
		tmp = 4.0
	elif x <= 3.8e-203:
		tmp = (z * -4.0) / y
	elif x <= 1.2e+70:
		tmp = 4.0
	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 <= -3.5e+177)
		tmp = t_0;
	elseif (x <= -2.45e+81)
		tmp = 4.0;
	elseif (x <= -1050000000000.0)
		tmp = t_0;
	elseif (x <= -5.3e-223)
		tmp = 4.0;
	elseif (x <= 3.8e-203)
		tmp = Float64(Float64(z * -4.0) / y);
	elseif (x <= 1.2e+70)
		tmp = 4.0;
	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 <= -3.5e+177)
		tmp = t_0;
	elseif (x <= -2.45e+81)
		tmp = 4.0;
	elseif (x <= -1050000000000.0)
		tmp = t_0;
	elseif (x <= -5.3e-223)
		tmp = 4.0;
	elseif (x <= 3.8e-203)
		tmp = (z * -4.0) / y;
	elseif (x <= 1.2e+70)
		tmp = 4.0;
	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, -3.5e+177], t$95$0, If[LessEqual[x, -2.45e+81], 4.0, If[LessEqual[x, -1050000000000.0], t$95$0, If[LessEqual[x, -5.3e-223], 4.0, If[LessEqual[x, 3.8e-203], N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 1.2e+70], 4.0, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999991e177 or -2.45000000000000011e81 < x < -1.05e12 or 1.19999999999999993e70 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 71.7%

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

   if -3.49999999999999991e177 < x < -2.45000000000000011e81 or -1.05e12 < x < -5.30000000000000027e-223 or 3.80000000000000025e-203 < x < 1.19999999999999993e70

   1. Initial program 99.1%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 58.0%

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

   if -5.30000000000000027e-223 < x < 3.80000000000000025e-203

   1. Initial program 100.0%

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

      1. associate-*l/ 99.4%

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

      2. +-commutative 99.4%

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

      3. fma-def 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around inf 58.6%

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

      1. associate-*r/ 58.6%

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

   10. Simplified 58.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+177}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+81}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1050000000000:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-223}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+70}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+177} \lor \neg \left(x \leq -3.2 \cdot 10^{+81}\right) \land \left(x \leq -120000000000 \lor \neg \left(x \leq 2.2 \cdot 10^{+72}\right)\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e+177)
         (and (not (<= x -3.2e+81))
              (or (<= x -120000000000.0) (not (<= x 2.2e+72)))))
   (* 4.0 (/ x y))
   4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+177) || (!(x <= -3.2e+81) && ((x <= -120000000000.0) || !(x <= 2.2e+72)))) {
		tmp = 4.0 * (x / 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 ((x <= (-6.5d+177)) .or. (.not. (x <= (-3.2d+81))) .and. (x <= (-120000000000.0d0)) .or. (.not. (x <= 2.2d+72))) then
        tmp = 4.0d0 * (x / 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 ((x <= -6.5e+177) || (!(x <= -3.2e+81) && ((x <= -120000000000.0) || !(x <= 2.2e+72)))) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e+177) or (not (x <= -3.2e+81) and ((x <= -120000000000.0) or not (x <= 2.2e+72))):
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e+177) || (!(x <= -3.2e+81) && ((x <= -120000000000.0) || !(x <= 2.2e+72))))
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e+177) || (~((x <= -3.2e+81)) && ((x <= -120000000000.0) || ~((x <= 2.2e+72)))))
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e+177], And[N[Not[LessEqual[x, -3.2e+81]], $MachinePrecision], Or[LessEqual[x, -120000000000.0], N[Not[LessEqual[x, 2.2e+72]], $MachinePrecision]]]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000002e177 or -3.2e81 < x < -1.2e11 or 2.2e72 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 71.7%

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

   if -6.5000000000000002e177 < x < -3.2e81 or -1.2e11 < x < 2.2e72

   1. Initial program 99.3%

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

      1. associate-*l/ 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 53.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+177} \lor \neg \left(x \leq -3.2 \cdot 10^{+81}\right) \land \left(x \leq -120000000000 \lor \neg \left(x \leq 2.2 \cdot 10^{+72}\right)\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+69} \lor \neg \left(y \leq 1.4 \cdot 10^{+61}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e+69) (not (<= y 1.4e+61)))
   (+ 4.0 (* -4.0 (/ z y)))
   (* (- x z) (/ 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+69) || !(y <= 1.4e+61)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = (x - z) * (4.0 / 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 <= (-1.5d+69)) .or. (.not. (y <= 1.4d+61))) then
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = (x - z) * (4.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+69) || !(y <= 1.4e+61)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = (x - z) * (4.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e+69) or not (y <= 1.4e+61):
		tmp = 4.0 + (-4.0 * (z / y))
	else:
		tmp = (x - z) * (4.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e+69) || !(y <= 1.4e+61))
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(Float64(x - z) * Float64(4.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.5e+69) || ~((y <= 1.4e+61)))
		tmp = 4.0 + (-4.0 * (z / y));
	else
		tmp = (x - z) * (4.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e+69], N[Not[LessEqual[y, 1.4e+61]], $MachinePrecision]], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.49999999999999992e69 or 1.4000000000000001e61 < y

   1. Initial program 99.0%

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

      1. associate-*l/ 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 89.6%

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

   if -1.49999999999999992e69 < y < 1.4000000000000001e61

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 86.4%

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

      1. div-sub 83.1%

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

      2. sub-neg 83.1%

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

      3. distribute-lft-in 83.1%

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

      4. associate-*r/ 83.1%

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

      5. associate-*l/ 82.9%

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

      6. distribute-rgt-neg-in 82.9%

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

      7. associate-*r/ 82.9%

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

      8. associate-*l/ 82.8%

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

      9. distribute-rgt-neg-in 82.8%

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

      10. distribute-lft-out 86.2%

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

      11. sub-neg 86.2%

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

   10. Simplified 86.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+69} \lor \neg \left(y \leq 1.4 \cdot 10^{+61}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+109}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+149) 4.0 (if (<= y 7e+109) (* (- x z) (/ 4.0 y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+149) {
		tmp = 4.0;
	} else if (y <= 7e+109) {
		tmp = (x - z) * (4.0 / 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 <= (-3.5d+149)) then
        tmp = 4.0d0
    else if (y <= 7d+109) then
        tmp = (x - z) * (4.0d0 / 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 <= -3.5e+149) {
		tmp = 4.0;
	} else if (y <= 7e+109) {
		tmp = (x - z) * (4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e+149:
		tmp = 4.0
	elif y <= 7e+109:
		tmp = (x - z) * (4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+149)
		tmp = 4.0;
	elseif (y <= 7e+109)
		tmp = Float64(Float64(x - z) * Float64(4.0 / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.5e+149)
		tmp = 4.0;
	elseif (y <= 7e+109)
		tmp = (x - z) * (4.0 / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+149], 4.0, If[LessEqual[y, 7e+109], N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000011e149 or 6.99999999999999966e109 < y

   1. Initial program 98.8%

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

      1. associate-*l/ 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 82.5%

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

   if -3.50000000000000011e149 < y < 6.99999999999999966e109

   1. Initial program 100.0%

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

      1. associate-*l/ 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 84.2%

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

      1. div-sub 81.3%

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

      2. sub-neg 81.3%

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

      3. distribute-lft-in 81.3%

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

      4. associate-*r/ 81.3%

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

      5. associate-*l/ 81.2%

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

      6. distribute-rgt-neg-in 81.2%

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

      7. associate-*r/ 81.2%

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

      8. associate-*l/ 81.1%

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

      9. distribute-rgt-neg-in 81.1%

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

      10. distribute-lft-out 84.0%

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

      11. sub-neg 84.0%

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

   10. Simplified 84.0%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+109}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+87}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.8e-61)
   (* (- x z) (/ 4.0 y))
   (if (<= z 6.2e+87) (+ 4.0 (* 4.0 (/ x y))) (+ 4.0 (* -4.0 (/ z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e-61) {
		tmp = (x - z) * (4.0 / y);
	} else if (z <= 6.2e+87) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + (-4.0 * (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 (z <= (-2.8d-61)) then
        tmp = (x - z) * (4.0d0 / y)
    else if (z <= 6.2d+87) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e-61) {
		tmp = (x - z) * (4.0 / y);
	} else if (z <= 6.2e+87) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.8e-61:
		tmp = (x - z) * (4.0 / y)
	elif z <= 6.2e+87:
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.8e-61)
		tmp = Float64(Float64(x - z) * Float64(4.0 / y));
	elseif (z <= 6.2e+87)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.8e-61)
		tmp = (x - z) * (4.0 / y);
	elseif (z <= 6.2e+87)
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = 4.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.8e-61], N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+87], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000001e-61

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 83.3%

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

      1. div-sub 78.4%

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

      2. sub-neg 78.4%

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

      3. distribute-lft-in 78.4%

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

      4. associate-*r/ 78.4%

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

      5. associate-*l/ 78.3%

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

      6. distribute-rgt-neg-in 78.3%

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

      7. associate-*r/ 78.3%

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

      8. associate-*l/ 78.2%

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

      9. distribute-rgt-neg-in 78.2%

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

      10. distribute-lft-out 83.0%

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

      11. sub-neg 83.0%

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

   10. Simplified 83.0%

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

   if -2.8000000000000001e-61 < z < 6.1999999999999999e87

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 96.2%

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

   if 6.1999999999999999e87 < z

   1. Initial program 97.9%

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

      1. associate-*l/ 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 87.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+87}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.7% 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 99.6%

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

   1. associate-*l/ 99.6%

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

   2. +-commutative 99.6%

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

   3. fma-def 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around inf 37.9%

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

6. Final simplification 37.9%

   \[\leadsto 4 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(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)))