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

Percentage Accurate: 99.7% → 99.9%

Time: 6.1s

Alternatives: 8

Speedup: 1.4×

• 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% 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 100.0%

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

   1. +-commutative 100.0%

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

   2. associate-*l/ 99.8%

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

   3. *-commutative 99.8%

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

   4. fma-def 99.8%

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

   5. +-commutative 99.8%

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

   6. associate--l+ 99.8%

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

   7. +-commutative 99.8%

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

   8. associate-+l- 99.8%

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

   9. sub-neg 99.8%

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

   10. remove-double-neg 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. +-commutative 99.8%

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

   13. distribute-neg-in 99.8%

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

   14. distribute-lft-neg-out 99.8%

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

   15. sub-neg 99.8%

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

   16. distribute-lft-neg-out 99.8%

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

   17. distribute-rgt-neg-in 99.8%

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

   18. fma-neg 99.8%

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

   19. metadata-eval 99.8%

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

   20. remove-double-neg 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x - \mathsf{fma}\left(y, -0.75, z\right), \frac{4}{y}, 1\right)} \]
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: 55.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z}{y} + 1\\ t_1 := 1 + x \cdot \frac{4}{y}\\ \mathbf{if}\;y \leq -1650000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* -4.0 (/ z y)) 1.0)) (t_1 (+ 1.0 (* x (/ 4.0 y)))))
   (if (<= y -1650000000.0)
     4.0
     (if (<= y -2.2e-308)
       t_1
       (if (<= y 5.6e-251)
         t_0
         (if (<= y 8.6e-157) t_1 (if (<= y 1.8e+36) t_0 4.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (y <= -1650000000.0) {
		tmp = 4.0;
	} else if (y <= -2.2e-308) {
		tmp = t_1;
	} else if (y <= 5.6e-251) {
		tmp = t_0;
	} else if (y <= 8.6e-157) {
		tmp = t_1;
	} else if (y <= 1.8e+36) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((-4.0d0) * (z / y)) + 1.0d0
    t_1 = 1.0d0 + (x * (4.0d0 / y))
    if (y <= (-1650000000.0d0)) then
        tmp = 4.0d0
    else if (y <= (-2.2d-308)) then
        tmp = t_1
    else if (y <= 5.6d-251) then
        tmp = t_0
    else if (y <= 8.6d-157) then
        tmp = t_1
    else if (y <= 1.8d+36) then
        tmp = t_0
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (y <= -1650000000.0) {
		tmp = 4.0;
	} else if (y <= -2.2e-308) {
		tmp = t_1;
	} else if (y <= 5.6e-251) {
		tmp = t_0;
	} else if (y <= 8.6e-157) {
		tmp = t_1;
	} else if (y <= 1.8e+36) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * (z / y)) + 1.0
	t_1 = 1.0 + (x * (4.0 / y))
	tmp = 0
	if y <= -1650000000.0:
		tmp = 4.0
	elif y <= -2.2e-308:
		tmp = t_1
	elif y <= 5.6e-251:
		tmp = t_0
	elif y <= 8.6e-157:
		tmp = t_1
	elif y <= 1.8e+36:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * Float64(z / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(x * Float64(4.0 / y)))
	tmp = 0.0
	if (y <= -1650000000.0)
		tmp = 4.0;
	elseif (y <= -2.2e-308)
		tmp = t_1;
	elseif (y <= 5.6e-251)
		tmp = t_0;
	elseif (y <= 8.6e-157)
		tmp = t_1;
	elseif (y <= 1.8e+36)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * (z / y)) + 1.0;
	t_1 = 1.0 + (x * (4.0 / y));
	tmp = 0.0;
	if (y <= -1650000000.0)
		tmp = 4.0;
	elseif (y <= -2.2e-308)
		tmp = t_1;
	elseif (y <= 5.6e-251)
		tmp = t_0;
	elseif (y <= 8.6e-157)
		tmp = t_1;
	elseif (y <= 1.8e+36)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1650000000.0], 4.0, If[LessEqual[y, -2.2e-308], t$95$1, If[LessEqual[y, 5.6e-251], t$95$0, If[LessEqual[y, 8.6e-157], t$95$1, If[LessEqual[y, 1.8e+36], t$95$0, 4.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e9 or 1.7999999999999999e36 < y

   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. +-commutative 99.9%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l- 99.7%

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

      9. sub-neg 99.7%

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

      10. remove-double-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. distribute-lft-neg-out 99.7%

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

      15. sub-neg 99.7%

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

      16. distribute-lft-neg-out 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-neg 99.7%

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

      19. metadata-eval 99.7%

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

      20. remove-double-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 70.3%

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

   if -1.65e9 < y < -2.2000000000000002e-308 or 5.59999999999999978e-251 < y < 8.5999999999999995e-157

   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/ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 64.3%

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

   if -2.2000000000000002e-308 < y < 5.59999999999999978e-251 or 8.5999999999999995e-157 < y < 1.7999999999999999e36

   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/ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 64.6%

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

      1. *-commutative 64.6%

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

   7. Simplified 64.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1650000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-308}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-251}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-157}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z}{y} + 1\\ t_1 := 1 + \frac{4 \cdot x}{y}\\ \mathbf{if}\;y \leq -3100000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* -4.0 (/ z y)) 1.0)) (t_1 (+ 1.0 (/ (* 4.0 x) y))))
   (if (<= y -3100000000.0)
     4.0
     (if (<= y 1.32e-301)
       t_1
       (if (<= y 3.5e-253)
         t_0
         (if (<= y 1.6e-158) t_1 (if (<= y 1.15e+37) t_0 4.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (y <= -3100000000.0) {
		tmp = 4.0;
	} else if (y <= 1.32e-301) {
		tmp = t_1;
	} else if (y <= 3.5e-253) {
		tmp = t_0;
	} else if (y <= 1.6e-158) {
		tmp = t_1;
	} else if (y <= 1.15e+37) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((-4.0d0) * (z / y)) + 1.0d0
    t_1 = 1.0d0 + ((4.0d0 * x) / y)
    if (y <= (-3100000000.0d0)) then
        tmp = 4.0d0
    else if (y <= 1.32d-301) then
        tmp = t_1
    else if (y <= 3.5d-253) then
        tmp = t_0
    else if (y <= 1.6d-158) then
        tmp = t_1
    else if (y <= 1.15d+37) then
        tmp = t_0
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (y <= -3100000000.0) {
		tmp = 4.0;
	} else if (y <= 1.32e-301) {
		tmp = t_1;
	} else if (y <= 3.5e-253) {
		tmp = t_0;
	} else if (y <= 1.6e-158) {
		tmp = t_1;
	} else if (y <= 1.15e+37) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * (z / y)) + 1.0
	t_1 = 1.0 + ((4.0 * x) / y)
	tmp = 0
	if y <= -3100000000.0:
		tmp = 4.0
	elif y <= 1.32e-301:
		tmp = t_1
	elif y <= 3.5e-253:
		tmp = t_0
	elif y <= 1.6e-158:
		tmp = t_1
	elif y <= 1.15e+37:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * Float64(z / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	tmp = 0.0
	if (y <= -3100000000.0)
		tmp = 4.0;
	elseif (y <= 1.32e-301)
		tmp = t_1;
	elseif (y <= 3.5e-253)
		tmp = t_0;
	elseif (y <= 1.6e-158)
		tmp = t_1;
	elseif (y <= 1.15e+37)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * (z / y)) + 1.0;
	t_1 = 1.0 + ((4.0 * x) / y);
	tmp = 0.0;
	if (y <= -3100000000.0)
		tmp = 4.0;
	elseif (y <= 1.32e-301)
		tmp = t_1;
	elseif (y <= 3.5e-253)
		tmp = t_0;
	elseif (y <= 1.6e-158)
		tmp = t_1;
	elseif (y <= 1.15e+37)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3100000000.0], 4.0, If[LessEqual[y, 1.32e-301], t$95$1, If[LessEqual[y, 3.5e-253], t$95$0, If[LessEqual[y, 1.6e-158], t$95$1, If[LessEqual[y, 1.15e+37], t$95$0, 4.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e9 or 1.15000000000000001e37 < y

   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. +-commutative 99.9%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l- 99.7%

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

      9. sub-neg 99.7%

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

      10. remove-double-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. distribute-lft-neg-out 99.7%

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

      15. sub-neg 99.7%

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

      16. distribute-lft-neg-out 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-neg 99.7%

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

      19. metadata-eval 99.7%

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

      20. remove-double-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 70.3%

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

   if -3.1e9 < y < 1.3200000000000001e-301 or 3.50000000000000022e-253 < y < 1.59999999999999998e-158

   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/ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 64.4%

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

      1. associate-*r/ 64.4%

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

      2. *-commutative 64.4%

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

   7. Simplified 64.4%

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

   if 1.3200000000000001e-301 < y < 3.50000000000000022e-253 or 1.59999999999999998e-158 < y < 1.15000000000000001e37

   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/ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 64.6%

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

      1. *-commutative 64.6%

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

   7. Simplified 64.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3100000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-301}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-158}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+37}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+130} \lor \neg \left(z \leq 2.2 \cdot 10^{+101}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.6e+130) (not (<= z 2.2e+101)))
   (+ (* -4.0 (/ z y)) 1.0)
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+130) || !(z <= 2.2e+101)) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.6d+130)) .or. (.not. (z <= 2.2d+101))) then
        tmp = ((-4.0d0) * (z / y)) + 1.0d0
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.6e+130) || !(z <= 2.2e+101)) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.6e+130) or not (z <= 2.2e+101):
		tmp = (-4.0 * (z / y)) + 1.0
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.6e+130) || !(z <= 2.2e+101))
		tmp = Float64(Float64(-4.0 * Float64(z / y)) + 1.0);
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.6e+130) || ~((z <= 2.2e+101)))
		tmp = (-4.0 * (z / y)) + 1.0;
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.6e+130], N[Not[LessEqual[z, 2.2e+101]], $MachinePrecision]], N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6000000000000001e130 or 2.2000000000000001e101 < z

   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/ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. *-commutative 76.6%

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

   7. Simplified 76.6%

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

   if -3.6000000000000001e130 < z < 2.2000000000000001e101

   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. +-commutative 99.9%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-def 99.8%

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

      5. +-commutative 99.8%

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

      6. associate--l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

      9. sub-neg 99.8%

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

      10. remove-double-neg 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-neg-in 99.8%

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

      14. distribute-lft-neg-out 99.8%

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

      15. sub-neg 99.8%

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

      16. distribute-lft-neg-out 99.8%

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

      17. distribute-rgt-neg-in 99.8%

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

      18. fma-neg 99.8%

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

      19. metadata-eval 99.8%

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

      20. remove-double-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - \mathsf{fma}\left(y, -0.75, z\right), \frac{4}{y}, 1\right)} \]
   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 92.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+130} \lor \neg \left(z \leq 2.2 \cdot 10^{+101}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+46} \lor \neg \left(z \leq 3.1 \cdot 10^{+97}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.02e+46) (not (<= z 3.1e+97)))
   (+ 4.0 (* -4.0 (/ z y)))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02e+46) || !(z <= 3.1e+97)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.02d+46)) .or. (.not. (z <= 3.1d+97))) then
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02e+46) || !(z <= 3.1e+97)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.02e+46) or not (z <= 3.1e+97):
		tmp = 4.0 + (-4.0 * (z / y))
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.02e+46) || !(z <= 3.1e+97))
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.02e+46) || ~((z <= 3.1e+97)))
		tmp = 4.0 + (-4.0 * (z / y));
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.02e+46], N[Not[LessEqual[z, 3.1e+97]], $MachinePrecision]], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0199999999999999e46 or 3.09999999999999981e97 < z

   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. +-commutative 100.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l- 99.7%

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

      9. sub-neg 99.7%

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

      10. remove-double-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. distribute-lft-neg-out 99.7%

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

      15. sub-neg 99.7%

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

      16. distribute-lft-neg-out 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-neg 99.7%

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

      19. metadata-eval 99.7%

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

      20. remove-double-neg 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - \mathsf{fma}\left(y, -0.75, z\right), \frac{4}{y}, 1\right)} \]
   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 88.2%

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

      1. +-commutative 88.2%

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

   10. Simplified 88.2%

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

   if -1.0199999999999999e46 < z < 3.09999999999999981e97

   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. +-commutative 99.9%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-def 99.8%

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

      5. +-commutative 99.8%

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

      6. associate--l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l- 99.8%

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

      9. sub-neg 99.8%

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

      10. remove-double-neg 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-neg-in 99.8%

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

      14. distribute-lft-neg-out 99.8%

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

      15. sub-neg 99.8%

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

      16. distribute-lft-neg-out 99.8%

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

      17. distribute-rgt-neg-in 99.8%

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

      18. fma-neg 99.8%

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

      19. metadata-eval 99.8%

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

      20. remove-double-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - \mathsf{fma}\left(y, -0.75, z\right), \frac{4}{y}, 1\right)} \]
   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 94.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+46} \lor \neg \left(z \leq 3.1 \cdot 10^{+97}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5600000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5600000000.0) 4.0 (if (<= y 1.5e+67) (+ 1.0 (* x (/ 4.0 y))) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5600000000.0) {
		tmp = 4.0;
	} else if (y <= 1.5e+67) {
		tmp = 1.0 + (x * (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 <= (-5600000000.0d0)) then
        tmp = 4.0d0
    else if (y <= 1.5d+67) then
        tmp = 1.0d0 + (x * (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 <= -5600000000.0) {
		tmp = 4.0;
	} else if (y <= 1.5e+67) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5600000000.0:
		tmp = 4.0
	elif y <= 1.5e+67:
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5600000000.0)
		tmp = 4.0;
	elseif (y <= 1.5e+67)
		tmp = Float64(1.0 + Float64(x * 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 <= -5600000000.0)
		tmp = 4.0;
	elseif (y <= 1.5e+67)
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5600000000.0], 4.0, If[LessEqual[y, 1.5e+67], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e9 or 1.50000000000000005e67 < y

   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. +-commutative 99.9%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l- 99.7%

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

      9. sub-neg 99.7%

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

      10. remove-double-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. distribute-lft-neg-out 99.7%

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

      15. sub-neg 99.7%

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

      16. distribute-lft-neg-out 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-neg 99.7%

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

      19. metadata-eval 99.7%

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

      20. remove-double-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 70.9%

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

   if -5.6e9 < y < 1.50000000000000005e67

   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/ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 51.6%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5600000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 7.7% 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 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/ 99.8%

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

   2. +-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf 38.1%

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

6. Taylor expanded in y around inf 8.8%

   \[\leadsto \color{blue}{1} \]

7. Final simplification 8.8%

   \[\leadsto 1 \]
8. Add Preprocessing

Alternative 8: 35.0% 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 100.0%

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

   1. +-commutative 100.0%

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

   2. associate-*l/ 99.8%

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

   3. *-commutative 99.8%

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

   4. fma-def 99.8%

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

   5. +-commutative 99.8%

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

   6. associate--l+ 99.8%

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

   7. +-commutative 99.8%

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

   8. associate-+l- 99.8%

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

   9. sub-neg 99.8%

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

   10. remove-double-neg 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. +-commutative 99.8%

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

   13. distribute-neg-in 99.8%

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

   14. distribute-lft-neg-out 99.8%

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

   15. sub-neg 99.8%

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

   16. distribute-lft-neg-out 99.8%

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

   17. distribute-rgt-neg-in 99.8%

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

   18. fma-neg 99.8%

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

   19. metadata-eval 99.8%

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

   20. remove-double-neg 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 41.8%

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

6. Final simplification 41.8%

   \[\leadsto 4 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024013 
(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)))