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

Percentage Accurate: 99.9% → 99.9%

Time: 5.5s

Alternatives: 9

Speedup: 1.0×

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

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - 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 * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - 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 * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - 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 * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

2. Final simplification 100.0%

   \[\leadsto 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

Alternative 2: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z}{y} \cdot -4\\ t_1 := 1 + \frac{x}{\frac{y}{4}}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-259}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-292}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-208}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (/ z y) -4.0))) (t_1 (+ 1.0 (/ x (/ y 4.0)))))
   (if (<= x -1e+15)
     t_1
     (if (<= x -2.15e-259)
       2.0
       (if (<= x 3.4e-292)
         t_0
         (if (<= x 2.7e-208)
           2.0
           (if (<= x 7.8e-59) t_0 (if (<= x 1.85e+27) 2.0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + (x / (y / 4.0));
	double tmp;
	if (x <= -1e+15) {
		tmp = t_1;
	} else if (x <= -2.15e-259) {
		tmp = 2.0;
	} else if (x <= 3.4e-292) {
		tmp = t_0;
	} else if (x <= 2.7e-208) {
		tmp = 2.0;
	} else if (x <= 7.8e-59) {
		tmp = t_0;
	} else if (x <= 1.85e+27) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	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 = 1.0d0 + ((z / y) * (-4.0d0))
    t_1 = 1.0d0 + (x / (y / 4.0d0))
    if (x <= (-1d+15)) then
        tmp = t_1
    else if (x <= (-2.15d-259)) then
        tmp = 2.0d0
    else if (x <= 3.4d-292) then
        tmp = t_0
    else if (x <= 2.7d-208) then
        tmp = 2.0d0
    else if (x <= 7.8d-59) then
        tmp = t_0
    else if (x <= 1.85d+27) then
        tmp = 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + (x / (y / 4.0));
	double tmp;
	if (x <= -1e+15) {
		tmp = t_1;
	} else if (x <= -2.15e-259) {
		tmp = 2.0;
	} else if (x <= 3.4e-292) {
		tmp = t_0;
	} else if (x <= 2.7e-208) {
		tmp = 2.0;
	} else if (x <= 7.8e-59) {
		tmp = t_0;
	} else if (x <= 1.85e+27) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z / y) * -4.0)
	t_1 = 1.0 + (x / (y / 4.0))
	tmp = 0
	if x <= -1e+15:
		tmp = t_1
	elif x <= -2.15e-259:
		tmp = 2.0
	elif x <= 3.4e-292:
		tmp = t_0
	elif x <= 2.7e-208:
		tmp = 2.0
	elif x <= 7.8e-59:
		tmp = t_0
	elif x <= 1.85e+27:
		tmp = 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z / y) * -4.0))
	t_1 = Float64(1.0 + Float64(x / Float64(y / 4.0)))
	tmp = 0.0
	if (x <= -1e+15)
		tmp = t_1;
	elseif (x <= -2.15e-259)
		tmp = 2.0;
	elseif (x <= 3.4e-292)
		tmp = t_0;
	elseif (x <= 2.7e-208)
		tmp = 2.0;
	elseif (x <= 7.8e-59)
		tmp = t_0;
	elseif (x <= 1.85e+27)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z / y) * -4.0);
	t_1 = 1.0 + (x / (y / 4.0));
	tmp = 0.0;
	if (x <= -1e+15)
		tmp = t_1;
	elseif (x <= -2.15e-259)
		tmp = 2.0;
	elseif (x <= 3.4e-292)
		tmp = t_0;
	elseif (x <= 2.7e-208)
		tmp = 2.0;
	elseif (x <= 7.8e-59)
		tmp = t_0;
	elseif (x <= 1.85e+27)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x / N[(y / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+15], t$95$1, If[LessEqual[x, -2.15e-259], 2.0, If[LessEqual[x, 3.4e-292], t$95$0, If[LessEqual[x, 2.7e-208], 2.0, If[LessEqual[x, 7.8e-59], t$95$0, If[LessEqual[x, 1.85e+27], 2.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e15 or 1.85000000000000001e27 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. fma-def 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.25, x\right)} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.25, x\right) - z\right)} \]

   4. Taylor expanded in x around inf 68.8%

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

      1. associate-*r/ 68.8%

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

      2. *-commutative 68.8%

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

      3. associate-/l* 68.8%

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

   6. Simplified 68.8%

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

   if -1e15 < x < -2.15e-259 or 3.40000000000000017e-292 < x < 2.7e-208 or 7.80000000000000038e-59 < x < 1.85000000000000001e27

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.9%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*l/ 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. associate-/l* 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      12. distribute-rgt-neg-in 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      13. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      14. associate-/l* 99.9%

          \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      15. *-commutative 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      16. neg-mul-1 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      17. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

          \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

   3. Simplified 99.9%

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

      1. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

      2. associate-/l* 99.9%

         \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   6. Taylor expanded in x around inf 70.8%

      \[\leadsto 2 + \frac{4}{\color{blue}{\frac{y}{x}}} \]

   7. Taylor expanded in y around inf 61.4%

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

   if -2.15e-259 < x < 3.40000000000000017e-292 or 2.7e-208 < x < 7.80000000000000038e-59

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 100.0%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. fma-def 100.0%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.25, x\right)} - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.25, x\right) - z\right)} \]

   4. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+15}:\\ \;\;\;\;1 + \frac{x}{\frac{y}{4}}\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-259}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-292}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-208}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\frac{y}{4}}\\ \end{array} \]

Alternative 3: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := 1 + \frac{z}{y} \cdot -4\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-158}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))) (t_1 (+ 1.0 (* (/ z y) -4.0))))
   (if (<= y -2.3e+63)
     2.0
     (if (<= y -1.05e-204)
       t_1
       (if (<= y 1.2e-158)
         t_0
         (if (<= y 4e-35) t_1 (if (<= y 1.4e+45) t_0 2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = 1.0 + ((z / y) * -4.0);
	double tmp;
	if (y <= -2.3e+63) {
		tmp = 2.0;
	} else if (y <= -1.05e-204) {
		tmp = t_1;
	} else if (y <= 1.2e-158) {
		tmp = t_0;
	} else if (y <= 4e-35) {
		tmp = t_1;
	} else if (y <= 1.4e+45) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / y)
    t_1 = 1.0d0 + ((z / y) * (-4.0d0))
    if (y <= (-2.3d+63)) then
        tmp = 2.0d0
    else if (y <= (-1.05d-204)) then
        tmp = t_1
    else if (y <= 1.2d-158) then
        tmp = t_0
    else if (y <= 4d-35) then
        tmp = t_1
    else if (y <= 1.4d+45) then
        tmp = t_0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = 1.0 + ((z / y) * -4.0);
	double tmp;
	if (y <= -2.3e+63) {
		tmp = 2.0;
	} else if (y <= -1.05e-204) {
		tmp = t_1;
	} else if (y <= 1.2e-158) {
		tmp = t_0;
	} else if (y <= 4e-35) {
		tmp = t_1;
	} else if (y <= 1.4e+45) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	t_1 = 1.0 + ((z / y) * -4.0)
	tmp = 0
	if y <= -2.3e+63:
		tmp = 2.0
	elif y <= -1.05e-204:
		tmp = t_1
	elif y <= 1.2e-158:
		tmp = t_0
	elif y <= 4e-35:
		tmp = t_1
	elif y <= 1.4e+45:
		tmp = t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	t_1 = Float64(1.0 + Float64(Float64(z / y) * -4.0))
	tmp = 0.0
	if (y <= -2.3e+63)
		tmp = 2.0;
	elseif (y <= -1.05e-204)
		tmp = t_1;
	elseif (y <= 1.2e-158)
		tmp = t_0;
	elseif (y <= 4e-35)
		tmp = t_1;
	elseif (y <= 1.4e+45)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / y);
	t_1 = 1.0 + ((z / y) * -4.0);
	tmp = 0.0;
	if (y <= -2.3e+63)
		tmp = 2.0;
	elseif (y <= -1.05e-204)
		tmp = t_1;
	elseif (y <= 1.2e-158)
		tmp = t_0;
	elseif (y <= 4e-35)
		tmp = t_1;
	elseif (y <= 1.4e+45)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+63], 2.0, If[LessEqual[y, -1.05e-204], t$95$1, If[LessEqual[y, 1.2e-158], t$95$0, If[LessEqual[y, 4e-35], t$95$1, If[LessEqual[y, 1.4e+45], t$95$0, 2.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999993e63 or 1.4e45 < y

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.9%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*l/ 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. associate-/l* 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      12. distribute-rgt-neg-in 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      13. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      14. associate-/l* 99.9%

          \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      15. *-commutative 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      16. neg-mul-1 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      17. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

          \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

   3. Simplified 99.9%

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

      1. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

      2. associate-/l* 99.9%

         \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   6. Taylor expanded in x around inf 87.9%

      \[\leadsto 2 + \frac{4}{\color{blue}{\frac{y}{x}}} \]

   7. Taylor expanded in y around inf 67.3%

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

   if -2.29999999999999993e63 < y < -1.05000000000000005e-204 or 1.20000000000000004e-158 < y < 4.00000000000000003e-35

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. fma-def 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.25, x\right)} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.25, x\right) - z\right)} \]

   4. Taylor expanded in z around inf 49.8%

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

      1. *-commutative 49.8%

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

   6. Simplified 49.8%

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

   if -1.05000000000000005e-204 < y < 1.20000000000000004e-158 or 4.00000000000000003e-35 < y < 1.4e45

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. fma-def 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.25, x\right)} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.25, x\right) - z\right)} \]

   4. Taylor expanded in x around inf 65.8%

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

      1. associate-*r/ 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-/l* 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in x around inf 64.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-204}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-158}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-35}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+45}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 4: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+82} \lor \neg \left(z \leq 2.2 \cdot 10^{+96} \lor \neg \left(z \leq 4.5 \cdot 10^{+177}\right) \land z \leq 2.35 \cdot 10^{+201}\right):\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e+82)
         (not
          (or (<= z 2.2e+96) (and (not (<= z 4.5e+177)) (<= z 2.35e+201)))))
   (+ 1.0 (* (/ z y) -4.0))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e+82) || !((z <= 2.2e+96) || (!(z <= 4.5e+177) && (z <= 2.35e+201)))) {
		tmp = 1.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (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 <= (-4d+82)) .or. (.not. (z <= 2.2d+96) .or. (.not. (z <= 4.5d+177)) .and. (z <= 2.35d+201))) then
        tmp = 1.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 2.0d0 + (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 <= -4e+82) || !((z <= 2.2e+96) || (!(z <= 4.5e+177) && (z <= 2.35e+201)))) {
		tmp = 1.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e+82) or not ((z <= 2.2e+96) or (not (z <= 4.5e+177) and (z <= 2.35e+201))):
		tmp = 1.0 + ((z / y) * -4.0)
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e+82) || !((z <= 2.2e+96) || (!(z <= 4.5e+177) && (z <= 2.35e+201))))
		tmp = Float64(1.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e+82) || ~(((z <= 2.2e+96) || (~((z <= 4.5e+177)) && (z <= 2.35e+201)))))
		tmp = 1.0 + ((z / y) * -4.0);
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e+82], N[Not[Or[LessEqual[z, 2.2e+96], And[N[Not[LessEqual[z, 4.5e+177]], $MachinePrecision], LessEqual[z, 2.35e+201]]]], $MachinePrecision]], N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999999e82 or 2.1999999999999999e96 < z < 4.4999999999999997e177 or 2.3499999999999999e201 < z

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. fma-def 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.25, x\right)} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.25, x\right) - z\right)} \]

   4. Taylor expanded in z around inf 76.2%

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

      1. *-commutative 76.2%

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

   6. Simplified 76.2%

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

   if -3.9999999999999999e82 < z < 2.1999999999999999e96 or 4.4999999999999997e177 < z < 2.3499999999999999e201

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.9%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*l/ 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. associate-/l* 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      12. distribute-rgt-neg-in 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      13. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      14. associate-/l* 99.9%

          \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      15. *-commutative 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      16. neg-mul-1 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      17. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

          \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

   3. Simplified 99.9%

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

      1. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

      2. associate-/l* 99.8%

         \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   6. Taylor expanded in x around inf 88.4%

      \[\leadsto 2 + \frac{4}{\color{blue}{\frac{y}{x}}} \]
   7. Step-by-step derivation

      1. div-inv 88.4%

         \[\leadsto 2 + \color{blue}{4 \cdot \frac{1}{\frac{y}{x}}} \]

      2. clear-num 88.5%

         \[\leadsto 2 + 4 \cdot \color{blue}{\frac{x}{y}} \]

      3. *-commutative 88.5%

         \[\leadsto 2 + \color{blue}{\frac{x}{y} \cdot 4} \]

   8. Applied egg-rr 88.5%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+82} \lor \neg \left(z \leq 2.2 \cdot 10^{+96} \lor \neg \left(z \leq 4.5 \cdot 10^{+177}\right) \land z \leq 2.35 \cdot 10^{+201}\right):\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 86.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-9} \lor \neg \left(x \leq 4.8 \cdot 10^{+25}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 - 4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e-9) (not (<= x 4.8e+25)))
   (+ 2.0 (* 4.0 (/ x y)))
   (- 2.0 (* 4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-9) || !(x <= 4.8e+25)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 - (4.0 * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-9d-9)) .or. (.not. (x <= 4.8d+25))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 - (4.0d0 * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-9) || !(x <= 4.8e+25)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 - (4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e-9) or not (x <= 4.8e+25):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 - (4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e-9) || !(x <= 4.8e+25))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 - Float64(4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9e-9) || ~((x <= 4.8e+25)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 2.0 - (4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e-9], N[Not[LessEqual[x, 4.8e+25]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 - N[(4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999953e-9 or 4.79999999999999992e25 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.8%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*l/ 99.8%

         \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* 99.8%

         \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. metadata-eval 99.8%

         \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. associate-/l* 99.8%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      12. distribute-rgt-neg-in 99.8%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      13. distribute-lft-neg-out 99.8%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      14. associate-/l* 99.8%

          \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      15. *-commutative 99.8%

          \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      16. neg-mul-1 99.8%

          \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      17. distribute-lft-neg-out 99.8%

          \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      18. *-inverses 99.8%

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

      19. metadata-eval 99.8%

          \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

   3. Simplified 99.8%

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

      1. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

      2. associate-/l* 99.8%

         \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   6. Taylor expanded in x around inf 83.0%

      \[\leadsto 2 + \frac{4}{\color{blue}{\frac{y}{x}}} \]
   7. Step-by-step derivation

      1. div-inv 83.0%

         \[\leadsto 2 + \color{blue}{4 \cdot \frac{1}{\frac{y}{x}}} \]

      2. clear-num 83.2%

         \[\leadsto 2 + 4 \cdot \color{blue}{\frac{x}{y}} \]

      3. *-commutative 83.2%

         \[\leadsto 2 + \color{blue}{\frac{x}{y} \cdot 4} \]

   8. Applied egg-rr 83.2%

      \[\leadsto 2 + \color{blue}{\frac{x}{y} \cdot 4} \]

   if -8.99999999999999953e-9 < x < 4.79999999999999992e25

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.9%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*l/ 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. associate-/l* 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      12. distribute-rgt-neg-in 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      13. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      14. associate-/l* 99.9%

          \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      15. *-commutative 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      16. neg-mul-1 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      17. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

          \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

   3. Simplified 99.9%

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

      1. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

      2. associate-/l* 99.9%

         \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   6. Taylor expanded in x around 0 92.3%

      \[\leadsto 2 + \frac{4}{\color{blue}{-1 \cdot \frac{y}{z}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 92.3%

         \[\leadsto 2 + \frac{4}{\color{blue}{\frac{-1 \cdot y}{z}}} \]

      2. neg-mul-1 92.3%

         \[\leadsto 2 + \frac{4}{\frac{\color{blue}{-y}}{z}} \]

   8. Simplified 92.3%

      \[\leadsto 2 + \frac{4}{\color{blue}{\frac{-y}{z}}} \]
   9. Step-by-step derivation

      1. frac-2neg 92.3%

         \[\leadsto 2 + \color{blue}{\frac{-4}{-\frac{-y}{z}}} \]

      2. div-inv 92.3%

         \[\leadsto 2 + \color{blue}{\left(-4\right) \cdot \frac{1}{-\frac{-y}{z}}} \]

      3. distribute-neg-frac 92.3%

         \[\leadsto 2 + \left(-4\right) \cdot \frac{1}{\color{blue}{\frac{-\left(-y\right)}{z}}} \]

      4. remove-double-neg 92.3%

         \[\leadsto 2 + \left(-4\right) \cdot \frac{1}{\frac{\color{blue}{y}}{z}} \]

      5. add-sqr-sqrt 46.5%

         \[\leadsto 2 + \left(-4\right) \cdot \frac{1}{\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{z}} \]

      6. sqrt-unprod 65.8%

         \[\leadsto 2 + \left(-4\right) \cdot \frac{1}{\frac{\color{blue}{\sqrt{y \cdot y}}}{z}} \]

      7. sqr-neg 65.8%

         \[\leadsto 2 + \left(-4\right) \cdot \frac{1}{\frac{\sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}}{z}} \]

      8. sqrt-unprod 23.0%

         \[\leadsto 2 + \left(-4\right) \cdot \frac{1}{\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{z}} \]

      9. add-sqr-sqrt 52.5%

         \[\leadsto 2 + \left(-4\right) \cdot \frac{1}{\frac{\color{blue}{-y}}{z}} \]

      10. clear-num 52.5%

          \[\leadsto 2 + \left(-4\right) \cdot \color{blue}{\frac{z}{-y}} \]

      11. cancel-sign-sub-inv 52.5%

          \[\leadsto \color{blue}{2 - 4 \cdot \frac{z}{-y}} \]

      12. clear-num 52.5%

          \[\leadsto 2 - 4 \cdot \color{blue}{\frac{1}{\frac{-y}{z}}} \]

      13. div-inv 52.5%

          \[\leadsto 2 - \color{blue}{\frac{4}{\frac{-y}{z}}} \]

      14. div-inv 52.5%

          \[\leadsto 2 - \color{blue}{4 \cdot \frac{1}{\frac{-y}{z}}} \]

      15. clear-num 52.5%

          \[\leadsto 2 - 4 \cdot \color{blue}{\frac{z}{-y}} \]

      16. add-sqr-sqrt 23.0%

          \[\leadsto 2 - 4 \cdot \frac{z}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

      17. sqrt-unprod 65.8%

          \[\leadsto 2 - 4 \cdot \frac{z}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

      18. sqr-neg 65.8%

          \[\leadsto 2 - 4 \cdot \frac{z}{\sqrt{\color{blue}{y \cdot y}}} \]

      19. sqrt-unprod 46.5%

          \[\leadsto 2 - 4 \cdot \frac{z}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

      20. add-sqr-sqrt 92.3%

          \[\leadsto 2 - 4 \cdot \frac{z}{\color{blue}{y}} \]

   10. Applied egg-rr 92.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-9} \lor \neg \left(x \leq 4.8 \cdot 10^{+25}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 - 4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 6: 53.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+46}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+71) 2.0 (if (<= y 3.4e+46) (* 4.0 (/ x y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+71) {
		tmp = 2.0;
	} else if (y <= 3.4e+46) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.5d+71)) then
        tmp = 2.0d0
    else if (y <= 3.4d+46) then
        tmp = 4.0d0 * (x / y)
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+71) {
		tmp = 2.0;
	} else if (y <= 3.4e+46) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e+71:
		tmp = 2.0
	elif y <= 3.4e+46:
		tmp = 4.0 * (x / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+71)
		tmp = 2.0;
	elseif (y <= 3.4e+46)
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.5e+71)
		tmp = 2.0;
	elseif (y <= 3.4e+46)
		tmp = 4.0 * (x / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+71], 2.0, If[LessEqual[y, 3.4e+46], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e71 or 3.3999999999999998e46 < y

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. associate--l+ 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

      4. distribute-lft-in 99.9%

         \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

      5. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*l/ 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* 99.9%

         \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. associate-/l* 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      12. distribute-rgt-neg-in 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      13. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      14. associate-/l* 99.9%

          \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      15. *-commutative 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      16. neg-mul-1 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      17. distribute-lft-neg-out 99.9%

          \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

          \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

   3. Simplified 99.9%

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

      1. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

      2. associate-/l* 99.9%

         \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

   6. Taylor expanded in x around inf 87.9%

      \[\leadsto 2 + \frac{4}{\color{blue}{\frac{y}{x}}} \]

   7. Taylor expanded in y around inf 67.3%

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

   if -5.5e71 < y < 3.3999999999999998e46

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

      3. fma-def 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.25, x\right)} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.25, x\right) - z\right)} \]

   4. Taylor expanded in x around inf 51.0%

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

      1. associate-*r/ 51.0%

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

      2. *-commutative 51.0%

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

      3. associate-/l* 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in x around inf 48.7%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+46}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 2 + \frac{4}{y} \cdot \left(x - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 2.0 (* (/ 4.0 y) (- x z))))

C

double code(double x, double y, double z) {
	return 2.0 + ((4.0 / y) * (x - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 + ((4.0d0 / y) * (x - z))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 + ((4.0 / y) * (x - z));
}

Python

def code(x, y, z):
	return 2.0 + ((4.0 / y) * (x - z))

Julia

function code(x, y, z)
	return Float64(2.0 + Float64(Float64(4.0 / y) * Float64(x - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 + ((4.0 / y) * (x - z));
end

Wolfram

code[x_, y_, z_] := N[(2.0 + N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

   2. +-commutative 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

   3. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

   4. distribute-lft-in 99.8%

      \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

   5. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

   6. associate-*l/ 99.9%

      \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   7. *-commutative 99.9%

      \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   8. associate-/l* 99.9%

      \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   9. metadata-eval 99.9%

      \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   10. metadata-eval 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   11. associate-/l* 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   12. distribute-rgt-neg-in 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   13. distribute-lft-neg-out 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   14. associate-/l* 99.9%

       \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   15. *-commutative 99.9%

       \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   16. neg-mul-1 99.9%

       \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   17. distribute-lft-neg-out 99.9%

       \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   18. *-inverses 99.9%

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

   19. metadata-eval 99.9%

       \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{2 + \frac{4}{y} \cdot \left(x - z\right)} \]

4. Final simplification 99.9%

   \[\leadsto 2 + \frac{4}{y} \cdot \left(x - z\right) \]

Alternative 8: 8.1% 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%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

   2. +-commutative 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

   3. fma-def 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.25, x\right)} - z\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.25, x\right) - z\right)} \]

4. Taylor expanded in z around inf 36.8%

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

   1. *-commutative 36.8%

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

6. Simplified 36.8%

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

7. Taylor expanded in z around 0 8.3%

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

8. Final simplification 8.3%

   \[\leadsto 1 \]

Alternative 9: 33.9% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

double code(double x, double y, double z) {
	return 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

   2. +-commutative 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

   3. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

   4. distribute-lft-in 99.8%

      \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

   5. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

   6. associate-*l/ 99.9%

      \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   7. *-commutative 99.9%

      \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   8. associate-/l* 99.9%

      \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   9. metadata-eval 99.9%

      \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   10. metadata-eval 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   11. associate-/l* 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   12. distribute-rgt-neg-in 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   13. distribute-lft-neg-out 99.9%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   14. associate-/l* 99.9%

       \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   15. *-commutative 99.9%

       \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   16. neg-mul-1 99.9%

       \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   17. distribute-lft-neg-out 99.9%

       \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   18. *-inverses 99.9%

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

   19. metadata-eval 99.9%

       \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

3. Simplified 99.9%

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

   1. associate-*l/ 100.0%

      \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

   2. associate-/l* 99.8%

      \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

5. Applied egg-rr 99.8%

   \[\leadsto 2 + \color{blue}{\frac{4}{\frac{y}{x - z}}} \]

6. Taylor expanded in x around inf 72.3%

   \[\leadsto 2 + \frac{4}{\color{blue}{\frac{y}{x}}} \]

7. Taylor expanded in y around inf 35.7%

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

8. Final simplification 35.7%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))