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

Percentage Accurate: 99.8% → 100.0%

Time: 7.6s

Alternatives: 10

Speedup: 1.2×

• 20.8% 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, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 + (4.0 * (0.75 + ((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 = 1.0d0 + (4.0d0 * (0.75d0 + ((x - z) / y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. associate-/l* 99.9%

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

   2. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around 0 97.7%

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

   1. +-commutative 97.7%

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

   2. associate--l+ 97.7%

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

   3. +-commutative 97.7%

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

   4. associate-+l- 97.7%

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

   5. div-sub 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -250 \lor \neg \left(x \leq 1.36 \cdot 10^{-31} \lor \neg \left(x \leq 4.8 \cdot 10^{+30}\right) \land x \leq 2.8 \cdot 10^{+63}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -250.0)
         (not (or (<= x 1.36e-31) (and (not (<= x 4.8e+30)) (<= x 2.8e+63)))))
   (+ 4.0 (* 4.0 (/ x y)))
   (+ 4.0 (* (/ z y) -4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -250.0) || !((x <= 1.36e-31) || (!(x <= 4.8e+30) && (x <= 2.8e+63)))) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + ((z / y) * -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 <= (-250.0d0)) .or. (.not. (x <= 1.36d-31) .or. (.not. (x <= 4.8d+30)) .and. (x <= 2.8d+63))) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 + ((z / y) * (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -250.0) || !((x <= 1.36e-31) || (!(x <= 4.8e+30) && (x <= 2.8e+63)))) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -250.0) or not ((x <= 1.36e-31) or (not (x <= 4.8e+30) and (x <= 2.8e+63))):
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 + ((z / y) * -4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -250.0) || !((x <= 1.36e-31) || (!(x <= 4.8e+30) && (x <= 2.8e+63))))
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 + Float64(Float64(z / y) * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -250.0) || ~(((x <= 1.36e-31) || (~((x <= 4.8e+30)) && (x <= 2.8e+63)))))
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = 4.0 + ((z / y) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -250.0], N[Not[Or[LessEqual[x, 1.36e-31], And[N[Not[LessEqual[x, 4.8e+30]], $MachinePrecision], LessEqual[x, 2.8e+63]]]], $MachinePrecision]], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -250 or 1.35999999999999991e-31 < x < 4.7999999999999999e30 or 2.79999999999999987e63 < x

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 95.0%

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

      1. +-commutative 95.0%

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

      2. associate--l+ 95.0%

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

      3. +-commutative 95.0%

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

      4. associate-+l- 95.0%

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

      5. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 91.1%

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

      1. associate-*r/ 91.1%

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

      2. neg-mul-1 91.1%

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

   10. Simplified 91.1%

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

   11. Taylor expanded in x around 0 91.1%

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

   if -250 < x < 1.35999999999999991e-31 or 4.7999999999999999e30 < x < 2.79999999999999987e63

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 97.0%

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

      1. div-sub 97.0%

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

      2. associate-/l* 97.1%

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

      3. *-inverses 97.1%

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

      4. metadata-eval 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. *-commutative 97.1%

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

   10. Simplified 97.1%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -250 \lor \neg \left(x \leq 1.36 \cdot 10^{-31} \lor \neg \left(x \leq 4.8 \cdot 10^{+30}\right) \land x \leq 2.8 \cdot 10^{+63}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -7:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-226}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))))
   (if (<= x -7.0)
     t_0
     (if (<= x -3.6e-226) 4.0 (if (<= x 2.8e+63) (* (/ z y) -4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double tmp;
	if (x <= -7.0) {
		tmp = t_0;
	} else if (x <= -3.6e-226) {
		tmp = 4.0;
	} else if (x <= 2.8e+63) {
		tmp = (z / y) * -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 <= (-7.0d0)) then
        tmp = t_0
    else if (x <= (-3.6d-226)) then
        tmp = 4.0d0
    else if (x <= 2.8d+63) then
        tmp = (z / y) * (-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 <= -7.0) {
		tmp = t_0;
	} else if (x <= -3.6e-226) {
		tmp = 4.0;
	} else if (x <= 2.8e+63) {
		tmp = (z / y) * -4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	tmp = 0
	if x <= -7.0:
		tmp = t_0
	elif x <= -3.6e-226:
		tmp = 4.0
	elif x <= 2.8e+63:
		tmp = (z / y) * -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 <= -7.0)
		tmp = t_0;
	elseif (x <= -3.6e-226)
		tmp = 4.0;
	elseif (x <= 2.8e+63)
		tmp = Float64(Float64(z / y) * -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 <= -7.0)
		tmp = t_0;
	elseif (x <= -3.6e-226)
		tmp = 4.0;
	elseif (x <= 2.8e+63)
		tmp = (z / y) * -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, -7.0], t$95$0, If[LessEqual[x, -3.6e-226], 4.0, If[LessEqual[x, 2.8e+63], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7 or 2.79999999999999987e63 < x

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.3%

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

      1. +-commutative 94.3%

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

      2. associate--l+ 94.3%

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

      3. +-commutative 94.3%

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

      4. associate-+l- 94.3%

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

      5. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 91.7%

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

      1. associate-*r/ 91.7%

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

      2. neg-mul-1 91.7%

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

   10. Simplified 91.7%

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

   11. Taylor expanded in x around inf 71.3%

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

   if -7 < x < -3.59999999999999994e-226

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.0%

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

      1. div-sub 94.0%

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

      2. associate-/l* 94.1%

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

      3. *-inverses 94.1%

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

      4. metadata-eval 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in z around 0 68.3%

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

   if -3.59999999999999994e-226 < x < 2.79999999999999987e63

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. neg-mul-1 59.7%

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

      2. distribute-neg-frac2 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in z around inf 54.4%

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

      1. *-commutative 54.4%

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

   10. Simplified 54.4%

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

Alternative 4: 52.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -250:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-227}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))))
   (if (<= x -250.0)
     t_0
     (if (<= x -7.2e-227) 4.0 (if (<= x 2.8e+63) (* z (/ -4.0 y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double tmp;
	if (x <= -250.0) {
		tmp = t_0;
	} else if (x <= -7.2e-227) {
		tmp = 4.0;
	} else if (x <= 2.8e+63) {
		tmp = z * (-4.0 / 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 <= (-250.0d0)) then
        tmp = t_0
    else if (x <= (-7.2d-227)) then
        tmp = 4.0d0
    else if (x <= 2.8d+63) then
        tmp = z * ((-4.0d0) / 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 <= -250.0) {
		tmp = t_0;
	} else if (x <= -7.2e-227) {
		tmp = 4.0;
	} else if (x <= 2.8e+63) {
		tmp = z * (-4.0 / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	tmp = 0
	if x <= -250.0:
		tmp = t_0
	elif x <= -7.2e-227:
		tmp = 4.0
	elif x <= 2.8e+63:
		tmp = z * (-4.0 / 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 <= -250.0)
		tmp = t_0;
	elseif (x <= -7.2e-227)
		tmp = 4.0;
	elseif (x <= 2.8e+63)
		tmp = Float64(z * Float64(-4.0 / 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 <= -250.0)
		tmp = t_0;
	elseif (x <= -7.2e-227)
		tmp = 4.0;
	elseif (x <= 2.8e+63)
		tmp = z * (-4.0 / 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, -250.0], t$95$0, If[LessEqual[x, -7.2e-227], 4.0, If[LessEqual[x, 2.8e+63], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -250 or 2.79999999999999987e63 < x

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.3%

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

      1. +-commutative 94.3%

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

      2. associate--l+ 94.3%

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

      3. +-commutative 94.3%

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

      4. associate-+l- 94.3%

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

      5. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 91.7%

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

      1. associate-*r/ 91.7%

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

      2. neg-mul-1 91.7%

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

   10. Simplified 91.7%

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

   11. Taylor expanded in x around inf 71.3%

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

   if -250 < x < -7.1999999999999999e-227

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.0%

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

      1. div-sub 94.0%

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

      2. associate-/l* 94.1%

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

      3. *-inverses 94.1%

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

      4. metadata-eval 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in z around 0 68.3%

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

   if -7.1999999999999999e-227 < x < 2.79999999999999987e63

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. neg-mul-1 59.7%

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

      2. distribute-neg-frac2 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in z around inf 54.4%

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

      1. associate-*r/ 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-/l* 54.3%

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

   10. Simplified 54.3%

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

Alternative 5: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+33} \lor \neg \left(y \leq 1.7 \cdot 10^{+38}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e+33) (not (<= y 1.7e+38)))
   (+ 4.0 (* 4.0 (/ x y)))
   (+ 1.0 (* 4.0 (/ (- x z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e+33) || !(y <= 1.7e+38)) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (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 <= (-2.8d+33)) .or. (.not. (y <= 1.7d+38))) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else
        tmp = 1.0d0 + (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 <= -2.8e+33) || !(y <= 1.7e+38)) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (4.0 * ((x - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e+33) or not (y <= 1.7e+38):
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = 1.0 + (4.0 * ((x - z) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e+33) || !(y <= 1.7e+38))
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(1.0 + 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 <= -2.8e+33) || ~((y <= 1.7e+38)))
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = 1.0 + (4.0 * ((x - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e+33], N[Not[LessEqual[y, 1.7e+38]], $MachinePrecision]], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8000000000000001e33 or 1.69999999999999998e38 < y

   1. Initial program 98.2%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+l- 100.0%

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

      5. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 90.1%

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

      1. associate-*r/ 90.1%

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

      2. neg-mul-1 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in x around 0 90.1%

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

   if -2.8000000000000001e33 < y < 1.69999999999999998e38

   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* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 92.3%

      \[\leadsto 1 + 4 \cdot \color{blue}{\frac{x - z}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+33} \lor \neg \left(y \leq 1.7 \cdot 10^{+38}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+32} \lor \neg \left(y \leq 4.3 \cdot 10^{+39}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+32) (not (<= y 4.3e+39)))
   (+ 4.0 (* 4.0 (/ x y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+32) || !(y <= 4.3e+39)) {
		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 <= (-1.8d+32)) .or. (.not. (y <= 4.3d+39))) 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 <= -1.8e+32) || !(y <= 4.3e+39)) {
		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 <= -1.8e+32) or not (y <= 4.3e+39):
		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 <= -1.8e+32) || !(y <= 4.3e+39))
		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 <= -1.8e+32) || ~((y <= 4.3e+39)))
		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, -1.8e+32], N[Not[LessEqual[y, 4.3e+39]], $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 < -1.7999999999999998e32 or 4.3e39 < y

   1. Initial program 98.2%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+l- 100.0%

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

      5. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 90.1%

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

      1. associate-*r/ 90.1%

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

      2. neg-mul-1 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in x around 0 90.1%

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

   if -1.7999999999999998e32 < y < 4.3e39

   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* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 96.0%

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

   6. Taylor expanded in y around 0 88.4%

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

   7. Taylor expanded in y around 0 87.2%

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

      1. sub-neg 87.2%

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

      2. metadata-eval 87.2%

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

      3. distribute-rgt-in 87.2%

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

      4. neg-mul-1 87.2%

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

      5. unsub-neg 87.2%

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

      6. associate-*l/ 85.8%

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

      7. associate-/l* 91.1%

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

      8. *-inverses 91.1%

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

      9. *-rgt-identity 91.1%

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

   9. Simplified 91.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+32} \lor \neg \left(y \leq 4.3 \cdot 10^{+39}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+44}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+40}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+44) 4.0 (if (<= y 2.4e+40) (* 4.0 (/ (- x z) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+44) {
		tmp = 4.0;
	} else if (y <= 2.4e+40) {
		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 <= (-1.05d+44)) then
        tmp = 4.0d0
    else if (y <= 2.4d+40) 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 <= -1.05e+44) {
		tmp = 4.0;
	} else if (y <= 2.4e+40) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+44:
		tmp = 4.0
	elif y <= 2.4e+40:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+44)
		tmp = 4.0;
	elseif (y <= 2.4e+40)
		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 <= -1.05e+44)
		tmp = 4.0;
	elseif (y <= 2.4e+40)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+44], 4.0, If[LessEqual[y, 2.4e+40], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999993e44 or 2.4e40 < y

   1. Initial program 98.2%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 79.0%

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

      1. div-sub 79.0%

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

      2. associate-/l* 79.1%

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

      3. *-inverses 79.1%

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

      4. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in z around 0 69.0%

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

   if -1.04999999999999993e44 < y < 2.4e40

   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* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 96.1%

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

   6. Taylor expanded in y around 0 88.2%

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

   7. Taylor expanded in y around 0 87.0%

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

      1. sub-neg 87.0%

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

      2. metadata-eval 87.0%

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

      3. distribute-rgt-in 86.9%

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

      4. neg-mul-1 86.9%

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

      5. unsub-neg 86.9%

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

      6. associate-*l/ 85.6%

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

      7. associate-/l* 90.8%

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

      8. *-inverses 90.8%

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

      9. *-rgt-identity 90.8%

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

   9. Simplified 90.8%

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

Alternative 8: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2950 \lor \neg \left(x \leq 1.55 \cdot 10^{-36}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2950.0) (not (<= x 1.55e-36))) (* 4.0 (/ x y)) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2950.0) || !(x <= 1.55e-36)) {
		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 <= (-2950.0d0)) .or. (.not. (x <= 1.55d-36))) 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 <= -2950.0) || !(x <= 1.55e-36)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2950.0) or not (x <= 1.55e-36):
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2950.0) || !(x <= 1.55e-36))
		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 <= -2950.0) || ~((x <= 1.55e-36)))
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2950.0], N[Not[LessEqual[x, 1.55e-36]], $MachinePrecision]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if x < -2950 or 1.5499999999999999e-36 < x

   1. Initial program 99.2%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. associate--l+ 95.5%

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

      3. +-commutative 95.5%

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

      4. associate-+l- 95.5%

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

      5. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. neg-mul-1 86.1%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in x around inf 63.7%

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

   if -2950 < x < 1.5499999999999999e-36

   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* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 97.5%

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

      1. div-sub 97.5%

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

      2. associate-/l* 97.6%

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

      3. *-inverses 97.6%

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

      4. metadata-eval 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in z around 0 51.2%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2950 \lor \neg \left(x \leq 1.55 \cdot 10^{-36}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.0% 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 99.2%

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

   1. associate-/l* 99.9%

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

   2. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around 0 68.6%

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

   1. div-sub 68.6%

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

   2. associate-/l* 68.7%

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

   3. *-inverses 68.7%

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

   4. metadata-eval 68.7%

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

7. Simplified 68.7%

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

8. Taylor expanded in z around 0 36.7%

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

Alternative 10: 7.6% 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 99.2%

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

   1. associate-/l* 99.9%

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

   2. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 39.4%

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

   1. neg-mul-1 39.4%

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

   2. distribute-neg-frac2 39.4%

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

7. Simplified 39.4%

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

8. Taylor expanded in z around 0 8.2%

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

Reproduce

herbie shell --seed 2024100 
(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)))