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

Percentage Accurate: 99.7% → 100.0%

Time: 9.3s

Alternatives: 10

Speedup: 1.4×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 100.0%

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

Alternative 2: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -7.4 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-308}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-252}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+50}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)) (t_1 (* 4.0 (/ x y))))
   (if (<= x -7.4e+95)
     t_1
     (if (<= x -3.5e-308)
       4.0
       (if (<= x 5e-252)
         t_0
         (if (<= x 8.2e-234)
           4.0
           (if (<= x 3.4e-200) t_0 (if (<= x 9.8e+50) 4.0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -7.4e+95) {
		tmp = t_1;
	} else if (x <= -3.5e-308) {
		tmp = 4.0;
	} else if (x <= 5e-252) {
		tmp = t_0;
	} else if (x <= 8.2e-234) {
		tmp = 4.0;
	} else if (x <= 3.4e-200) {
		tmp = t_0;
	} else if (x <= 9.8e+50) {
		tmp = 4.0;
	} 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 = (z * (-4.0d0)) / y
    t_1 = 4.0d0 * (x / y)
    if (x <= (-7.4d+95)) then
        tmp = t_1
    else if (x <= (-3.5d-308)) then
        tmp = 4.0d0
    else if (x <= 5d-252) then
        tmp = t_0
    else if (x <= 8.2d-234) then
        tmp = 4.0d0
    else if (x <= 3.4d-200) then
        tmp = t_0
    else if (x <= 9.8d+50) then
        tmp = 4.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -7.4e+95) {
		tmp = t_1;
	} else if (x <= -3.5e-308) {
		tmp = 4.0;
	} else if (x <= 5e-252) {
		tmp = t_0;
	} else if (x <= 8.2e-234) {
		tmp = 4.0;
	} else if (x <= 3.4e-200) {
		tmp = t_0;
	} else if (x <= 9.8e+50) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	t_1 = 4.0 * (x / y)
	tmp = 0
	if x <= -7.4e+95:
		tmp = t_1
	elif x <= -3.5e-308:
		tmp = 4.0
	elif x <= 5e-252:
		tmp = t_0
	elif x <= 8.2e-234:
		tmp = 4.0
	elif x <= 3.4e-200:
		tmp = t_0
	elif x <= 9.8e+50:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	t_1 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (x <= -7.4e+95)
		tmp = t_1;
	elseif (x <= -3.5e-308)
		tmp = 4.0;
	elseif (x <= 5e-252)
		tmp = t_0;
	elseif (x <= 8.2e-234)
		tmp = 4.0;
	elseif (x <= 3.4e-200)
		tmp = t_0;
	elseif (x <= 9.8e+50)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	t_1 = 4.0 * (x / y);
	tmp = 0.0;
	if (x <= -7.4e+95)
		tmp = t_1;
	elseif (x <= -3.5e-308)
		tmp = 4.0;
	elseif (x <= 5e-252)
		tmp = t_0;
	elseif (x <= 8.2e-234)
		tmp = 4.0;
	elseif (x <= 3.4e-200)
		tmp = t_0;
	elseif (x <= 9.8e+50)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.4e+95], t$95$1, If[LessEqual[x, -3.5e-308], 4.0, If[LessEqual[x, 5e-252], t$95$0, If[LessEqual[x, 8.2e-234], 4.0, If[LessEqual[x, 3.4e-200], t$95$0, If[LessEqual[x, 9.8e+50], 4.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4000000000000003e95 or 9.8000000000000003e50 < x

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 100.0%

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

      10. sub-neg 100.0%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. distribute-lft-in 85.3%

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

      2. metadata-eval 85.3%

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

      3. associate-+r+ 85.3%

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

      4. metadata-eval 85.3%

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

      5. associate-*r/ 85.3%

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

      6. *-commutative 85.3%

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

      7. associate-*r/ 85.1%

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

   7. Simplified 85.1%

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

      1. associate-*r/ 85.3%

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

      2. *-commutative 85.3%

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

   9. Applied egg-rr 85.3%

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

   10. Taylor expanded in x around inf 75.7%

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

   if -7.4000000000000003e95 < x < -3.5e-308 or 5.00000000000000008e-252 < x < 8.20000000000000021e-234 or 3.4000000000000003e-200 < x < 9.8000000000000003e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 55.6%

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

   if -3.5e-308 < x < 5.00000000000000008e-252 or 8.20000000000000021e-234 < x < 3.4000000000000003e-200

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around inf 79.8%

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

      1. associate-*r/ 79.8%

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

   9. Simplified 79.8%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+95}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-308}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-252}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-200}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+50}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-303}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-252}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-201}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+50}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))) (t_1 (* 4.0 (/ x y))))
   (if (<= x -6.5e+95)
     t_1
     (if (<= x -3.4e-303)
       4.0
       (if (<= x 5.2e-252)
         t_0
         (if (<= x 7.2e-234)
           4.0
           (if (<= x 4.4e-201) t_0 (if (<= x 6.5e+50) 4.0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -6.5e+95) {
		tmp = t_1;
	} else if (x <= -3.4e-303) {
		tmp = 4.0;
	} else if (x <= 5.2e-252) {
		tmp = t_0;
	} else if (x <= 7.2e-234) {
		tmp = 4.0;
	} else if (x <= 4.4e-201) {
		tmp = t_0;
	} else if (x <= 6.5e+50) {
		tmp = 4.0;
	} 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 = z * ((-4.0d0) / y)
    t_1 = 4.0d0 * (x / y)
    if (x <= (-6.5d+95)) then
        tmp = t_1
    else if (x <= (-3.4d-303)) then
        tmp = 4.0d0
    else if (x <= 5.2d-252) then
        tmp = t_0
    else if (x <= 7.2d-234) then
        tmp = 4.0d0
    else if (x <= 4.4d-201) then
        tmp = t_0
    else if (x <= 6.5d+50) then
        tmp = 4.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -6.5e+95) {
		tmp = t_1;
	} else if (x <= -3.4e-303) {
		tmp = 4.0;
	} else if (x <= 5.2e-252) {
		tmp = t_0;
	} else if (x <= 7.2e-234) {
		tmp = 4.0;
	} else if (x <= 4.4e-201) {
		tmp = t_0;
	} else if (x <= 6.5e+50) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	t_1 = 4.0 * (x / y)
	tmp = 0
	if x <= -6.5e+95:
		tmp = t_1
	elif x <= -3.4e-303:
		tmp = 4.0
	elif x <= 5.2e-252:
		tmp = t_0
	elif x <= 7.2e-234:
		tmp = 4.0
	elif x <= 4.4e-201:
		tmp = t_0
	elif x <= 6.5e+50:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	t_1 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (x <= -6.5e+95)
		tmp = t_1;
	elseif (x <= -3.4e-303)
		tmp = 4.0;
	elseif (x <= 5.2e-252)
		tmp = t_0;
	elseif (x <= 7.2e-234)
		tmp = 4.0;
	elseif (x <= 4.4e-201)
		tmp = t_0;
	elseif (x <= 6.5e+50)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	t_1 = 4.0 * (x / y);
	tmp = 0.0;
	if (x <= -6.5e+95)
		tmp = t_1;
	elseif (x <= -3.4e-303)
		tmp = 4.0;
	elseif (x <= 5.2e-252)
		tmp = t_0;
	elseif (x <= 7.2e-234)
		tmp = 4.0;
	elseif (x <= 4.4e-201)
		tmp = t_0;
	elseif (x <= 6.5e+50)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+95], t$95$1, If[LessEqual[x, -3.4e-303], 4.0, If[LessEqual[x, 5.2e-252], t$95$0, If[LessEqual[x, 7.2e-234], 4.0, If[LessEqual[x, 4.4e-201], t$95$0, If[LessEqual[x, 6.5e+50], 4.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5e95 or 6.5000000000000003e50 < x

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 100.0%

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

      10. sub-neg 100.0%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. distribute-lft-in 85.3%

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

      2. metadata-eval 85.3%

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

      3. associate-+r+ 85.3%

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

      4. metadata-eval 85.3%

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

      5. associate-*r/ 85.3%

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

      6. *-commutative 85.3%

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

      7. associate-*r/ 85.1%

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

   7. Simplified 85.1%

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

      1. associate-*r/ 85.3%

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

      2. *-commutative 85.3%

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

   9. Applied egg-rr 85.3%

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

   10. Taylor expanded in x around inf 75.7%

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

   if -6.5e95 < x < -3.4e-303 or 5.1999999999999998e-252 < x < 7.1999999999999997e-234 or 4.4e-201 < x < 6.5000000000000003e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 55.6%

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

   if -3.4e-303 < x < 5.1999999999999998e-252 or 7.1999999999999997e-234 < x < 4.4e-201

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 79.8%

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

      3. associate-*r/ 79.5%

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

   9. Simplified 79.5%

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

Alternative 4: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+70} \lor \neg \left(z \leq -4.8 \cdot 10^{+14}\right) \land \left(z \leq -4.8 \cdot 10^{-21} \lor \neg \left(z \leq 1.9 \cdot 10^{+87}\right)\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+70)
         (and (not (<= z -4.8e+14)) (or (<= z -4.8e-21) (not (<= z 1.9e+87)))))
   (* 4.0 (/ (- x z) y))
   (+ 4.0 (* x (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+70) || (!(z <= -4.8e+14) && ((z <= -4.8e-21) || !(z <= 1.9e+87)))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (x * (4.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.35d+70)) .or. (.not. (z <= (-4.8d+14))) .and. (z <= (-4.8d-21)) .or. (.not. (z <= 1.9d+87))) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+70) || (!(z <= -4.8e+14) && ((z <= -4.8e-21) || !(z <= 1.9e+87)))) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e+70) or (not (z <= -4.8e+14) and ((z <= -4.8e-21) or not (z <= 1.9e+87))):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e+70) || (!(z <= -4.8e+14) && ((z <= -4.8e-21) || !(z <= 1.9e+87))))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e+70) || (~((z <= -4.8e+14)) && ((z <= -4.8e-21) || ~((z <= 1.9e+87)))))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e+70], And[N[Not[LessEqual[z, -4.8e+14]], $MachinePrecision], Or[LessEqual[z, -4.8e-21], N[Not[LessEqual[z, 1.9e+87]], $MachinePrecision]]]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e70 or -4.8e14 < z < -4.7999999999999999e-21 or 1.90000000000000006e87 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 83.1%

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

   if -1.35e70 < z < -4.8e14 or -4.7999999999999999e-21 < z < 1.90000000000000006e87

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 99.9%

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

      10. sub-neg 99.9%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 90.9%

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

      1. distribute-lft-in 90.9%

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

      2. metadata-eval 90.9%

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

      3. associate-+r+ 90.9%

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

      4. metadata-eval 90.9%

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

      5. associate-*r/ 90.9%

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

      6. *-commutative 90.9%

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

      7. associate-*r/ 90.9%

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

   7. Simplified 90.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+70} \lor \neg \left(z \leq -4.8 \cdot 10^{+14}\right) \land \left(z \leq -4.8 \cdot 10^{-21} \lor \neg \left(z \leq 1.9 \cdot 10^{+87}\right)\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+94} \lor \neg \left(x \leq 6.5 \cdot 10^{+50}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.6e+94) (not (<= x 6.5e+50)))
   (* 4.0 (/ (- x z) y))
   (+ 4.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.6e+94) || !(x <= 6.5e+50)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-4.6d+94)) .or. (.not. (x <= 6.5d+50))) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.6e+94) || !(x <= 6.5e+50)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.6e+94) or not (x <= 6.5e+50):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.6e+94) || !(x <= 6.5e+50))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.6e+94) || ~((x <= 6.5e+50)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.6e+94], N[Not[LessEqual[x, 6.5e+50]], $MachinePrecision]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999999e94 or 6.5000000000000003e50 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 90.4%

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

   if -4.5999999999999999e94 < x < 6.5000000000000003e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around 0 88.0%

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

      1. associate-*r/ 88.0%

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

   6. Simplified 88.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+94} \lor \neg \left(x \leq 6.5 \cdot 10^{+50}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+95} \lor \neg \left(x \leq 8.6 \cdot 10^{+50}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e+95) (not (<= x 8.6e+50)))
   (* 4.0 (/ (- x z) y))
   (+ 4.0 (* z (/ -4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e+95) || !(x <= 8.6e+50)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (z * (-4.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.7d+95)) .or. (.not. (x <= 8.6d+50))) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0 + (z * ((-4.0d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e+95) || !(x <= 8.6e+50)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0 + (z * (-4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e+95) or not (x <= 8.6e+50):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0 + (z * (-4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e+95) || !(x <= 8.6e+50))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(4.0 + Float64(z * Float64(-4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.7e+95) || ~((x <= 8.6e+50)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0 + (z * (-4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e+95], N[Not[LessEqual[x, 8.6e+50]], $MachinePrecision]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e95 or 8.5999999999999994e50 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 90.4%

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

   if -2.7e95 < x < 8.5999999999999994e50

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 100.0%

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

      10. sub-neg 100.0%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. sub-neg 88.0%

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

      2. distribute-lft-in 88.0%

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

      3. metadata-eval 88.0%

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

      4. associate-+r+ 88.0%

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

      5. metadata-eval 88.0%

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

      6. neg-mul-1 88.0%

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

      7. associate-*r* 88.0%

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

      8. metadata-eval 88.0%

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

      9. associate-*r/ 88.0%

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

      10. *-commutative 88.0%

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

      11. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+95} \lor \neg \left(x \leq 8.6 \cdot 10^{+50}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+104}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+121}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+104) 4.0 (if (<= y 6e+121) (* 4.0 (/ (- x z) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+104) {
		tmp = 4.0;
	} else if (y <= 6e+121) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.2d+104)) then
        tmp = 4.0d0
    else if (y <= 6d+121) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+104) {
		tmp = 4.0;
	} else if (y <= 6e+121) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+104:
		tmp = 4.0
	elif y <= 6e+121:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+104)
		tmp = 4.0;
	elseif (y <= 6e+121)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e+104)
		tmp = 4.0;
	elseif (y <= 6e+121)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+104], 4.0, If[LessEqual[y, 6e+121], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999997e104 or 6.0000000000000005e121 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.1%

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

   if -4.1999999999999997e104 < y < 6.0000000000000005e121

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around 0 81.3%

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

Alternative 8: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+94} \lor \neg \left(x \leq 5.4 \cdot 10^{+50}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e+94) (not (<= x 5.4e+50))) (* 4.0 (/ x y)) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+94) || !(x <= 5.4e+50)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.4d+94)) .or. (.not. (x <= 5.4d+50))) then
        tmp = 4.0d0 * (x / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+94) || !(x <= 5.4e+50)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e+94) or not (x <= 5.4e+50):
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e+94) || !(x <= 5.4e+50))
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.4e+94) || ~((x <= 5.4e+50)))
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e+94], N[Not[LessEqual[x, 5.4e+50]], $MachinePrecision]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999983e94 or 5.4e50 < x

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub-neg 99.9%

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

      8. associate--r+ 99.9%

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

      9. div-sub 100.0%

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

      10. sub-neg 100.0%

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

      11. associate-*l/ 100.0%

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

      12. *-inverses 100.0%

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

      13. metadata-eval 100.0%

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

      14. distribute-frac-neg2 100.0%

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

      15. remove-double-neg 100.0%

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

      16. distribute-neg-out 100.0%

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

      17. +-commutative 100.0%

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

      18. sub-neg 100.0%

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

      19. distribute-frac-neg 100.0%

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

      20. distribute-frac-neg2 100.0%

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

      21. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. distribute-lft-in 85.3%

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

      2. metadata-eval 85.3%

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

      3. associate-+r+ 85.3%

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

      4. metadata-eval 85.3%

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

      5. associate-*r/ 85.3%

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

      6. *-commutative 85.3%

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

      7. associate-*r/ 85.1%

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

   7. Simplified 85.1%

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

      1. associate-*r/ 85.3%

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

      2. *-commutative 85.3%

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

   9. Applied egg-rr 85.3%

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

   10. Taylor expanded in x around inf 75.7%

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

   if -2.39999999999999983e94 < x < 5.4e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 51.7%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+94} \lor \neg \left(x \leq 5.4 \cdot 10^{+50}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 36.2%

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

Alternative 10: 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 99.9%

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

3. Taylor expanded in x around inf 41.8%

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

   1. *-commutative 41.8%

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

5. Simplified 41.8%

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

6. Taylor expanded in x around 0 8.0%

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

Reproduce

herbie shell --seed 2024110 
(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)))