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

Percentage Accurate: 99.8% → 100.0%

Time: 5.6s

Alternatives: 8

Speedup: 1.4×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Final simplification 100.0%

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

Alternative 2: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := \frac{z \cdot -4}{y}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+64}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-217}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-25}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))) (t_1 (/ (* z -4.0) y)))
   (if (<= y -2.65e+64)
     4.0
     (if (<= y -6.5e-129)
       t_1
       (if (<= y -1.45e-217)
         t_0
         (if (<= y 2.3e-265) t_1 (if (<= y 3.4e-25) t_0 4.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = (z * -4.0) / y;
	double tmp;
	if (y <= -2.65e+64) {
		tmp = 4.0;
	} else if (y <= -6.5e-129) {
		tmp = t_1;
	} else if (y <= -1.45e-217) {
		tmp = t_0;
	} else if (y <= 2.3e-265) {
		tmp = t_1;
	} else if (y <= 3.4e-25) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / y)
    t_1 = (z * (-4.0d0)) / y
    if (y <= (-2.65d+64)) then
        tmp = 4.0d0
    else if (y <= (-6.5d-129)) then
        tmp = t_1
    else if (y <= (-1.45d-217)) then
        tmp = t_0
    else if (y <= 2.3d-265) then
        tmp = t_1
    else if (y <= 3.4d-25) then
        tmp = t_0
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = (z * -4.0) / y;
	double tmp;
	if (y <= -2.65e+64) {
		tmp = 4.0;
	} else if (y <= -6.5e-129) {
		tmp = t_1;
	} else if (y <= -1.45e-217) {
		tmp = t_0;
	} else if (y <= 2.3e-265) {
		tmp = t_1;
	} else if (y <= 3.4e-25) {
		tmp = t_0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	t_1 = (z * -4.0) / y
	tmp = 0
	if y <= -2.65e+64:
		tmp = 4.0
	elif y <= -6.5e-129:
		tmp = t_1
	elif y <= -1.45e-217:
		tmp = t_0
	elif y <= 2.3e-265:
		tmp = t_1
	elif y <= 3.4e-25:
		tmp = t_0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	t_1 = Float64(Float64(z * -4.0) / y)
	tmp = 0.0
	if (y <= -2.65e+64)
		tmp = 4.0;
	elseif (y <= -6.5e-129)
		tmp = t_1;
	elseif (y <= -1.45e-217)
		tmp = t_0;
	elseif (y <= 2.3e-265)
		tmp = t_1;
	elseif (y <= 3.4e-25)
		tmp = t_0;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / y);
	t_1 = (z * -4.0) / y;
	tmp = 0.0;
	if (y <= -2.65e+64)
		tmp = 4.0;
	elseif (y <= -6.5e-129)
		tmp = t_1;
	elseif (y <= -1.45e-217)
		tmp = t_0;
	elseif (y <= 2.3e-265)
		tmp = t_1;
	elseif (y <= 3.4e-25)
		tmp = t_0;
	else
		tmp = 4.0;
	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[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.65e+64], 4.0, If[LessEqual[y, -6.5e-129], t$95$1, If[LessEqual[y, -1.45e-217], t$95$0, If[LessEqual[y, 2.3e-265], t$95$1, If[LessEqual[y, 3.4e-25], t$95$0, 4.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6500000000000001e64 or 3.40000000000000002e-25 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 68.6%

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

   if -2.6500000000000001e64 < y < -6.49999999999999952e-129 or -1.44999999999999991e-217 < y < 2.2999999999999999e-265

   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 x around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. fma-define 67.0%

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

      3. div-sub 67.0%

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

      4. associate-/l* 67.1%

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

      5. *-inverses 67.1%

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

      6. metadata-eval 67.1%

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

      7. fma-define 67.1%

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

      8. +-commutative 67.1%

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

      9. sub-neg 67.1%

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

      10. distribute-lft-in 67.1%

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

      11. metadata-eval 67.1%

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

      12. associate-+r+ 67.1%

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

      13. metadata-eval 67.1%

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

      14. neg-mul-1 67.1%

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

      15. associate-*r* 67.1%

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

      16. metadata-eval 67.1%

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

      17. *-commutative 67.1%

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

      18. associate-*l/ 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around inf 57.5%

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

      1. associate-*r/ 57.5%

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

   8. Simplified 57.5%

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

   if -6.49999999999999952e-129 < y < -1.44999999999999991e-217 or 2.2999999999999999e-265 < y < 3.40000000000000002e-25

   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 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. associate-+r- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 61.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+64}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-217}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-265}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-25}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+77}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-7} \lor \neg \left(y \leq 4.1 \cdot 10^{+42}\right) \land y \leq 1.46 \cdot 10^{+128}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e+77)
   4.0
   (if (or (<= y 7.5e-7) (and (not (<= y 4.1e+42)) (<= y 1.46e+128)))
     (* (- x z) (/ 4.0 y))
     4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+77) {
		tmp = 4.0;
	} else if ((y <= 7.5e-7) || (!(y <= 4.1e+42) && (y <= 1.46e+128))) {
		tmp = (x - z) * (4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3d+77)) then
        tmp = 4.0d0
    else if ((y <= 7.5d-7) .or. (.not. (y <= 4.1d+42)) .and. (y <= 1.46d+128)) then
        tmp = (x - z) * (4.0d0 / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+77) {
		tmp = 4.0;
	} else if ((y <= 7.5e-7) || (!(y <= 4.1e+42) && (y <= 1.46e+128))) {
		tmp = (x - z) * (4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e+77:
		tmp = 4.0
	elif (y <= 7.5e-7) or (not (y <= 4.1e+42) and (y <= 1.46e+128)):
		tmp = (x - z) * (4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e+77)
		tmp = 4.0;
	elseif ((y <= 7.5e-7) || (!(y <= 4.1e+42) && (y <= 1.46e+128)))
		tmp = Float64(Float64(x - z) * Float64(4.0 / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e+77)
		tmp = 4.0;
	elseif ((y <= 7.5e-7) || (~((y <= 4.1e+42)) && (y <= 1.46e+128)))
		tmp = (x - z) * (4.0 / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e+77], 4.0, If[Or[LessEqual[y, 7.5e-7], And[N[Not[LessEqual[y, 4.1e+42]], $MachinePrecision], LessEqual[y, 1.46e+128]]], N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999998e77 or 7.5000000000000002e-7 < y < 4.1e42 or 1.4599999999999999e128 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 77.8%

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

   if -2.9999999999999998e77 < y < 7.5000000000000002e-7 or 4.1e42 < y < 1.4599999999999999e128

   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 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. associate-+r- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.2%

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

      1. associate-*r/ 89.2%

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

      2. associate-*l/ 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+77}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-7} \lor \neg \left(y \leq 4.1 \cdot 10^{+42}\right) \land y \leq 1.46 \cdot 10^{+128}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 + \frac{z \cdot -4}{y}\\ \mathbf{if}\;y \leq -1.18 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-32}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 4.0 (/ (* z -4.0) y))))
   (if (<= y -1.18e+70)
     t_0
     (if (<= y 4.4e-32)
       (* (- x z) (/ 4.0 y))
       (if (<= y 6e+107) t_0 (+ 4.0 (/ (* 4.0 x) y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 + ((z * -4.0) / y);
	double tmp;
	if (y <= -1.18e+70) {
		tmp = t_0;
	} else if (y <= 4.4e-32) {
		tmp = (x - z) * (4.0 / y);
	} else if (y <= 6e+107) {
		tmp = t_0;
	} else {
		tmp = 4.0 + ((4.0 * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 + ((z * (-4.0d0)) / y)
    if (y <= (-1.18d+70)) then
        tmp = t_0
    else if (y <= 4.4d-32) then
        tmp = (x - z) * (4.0d0 / y)
    else if (y <= 6d+107) then
        tmp = t_0
    else
        tmp = 4.0d0 + ((4.0d0 * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 + ((z * -4.0) / y);
	double tmp;
	if (y <= -1.18e+70) {
		tmp = t_0;
	} else if (y <= 4.4e-32) {
		tmp = (x - z) * (4.0 / y);
	} else if (y <= 6e+107) {
		tmp = t_0;
	} else {
		tmp = 4.0 + ((4.0 * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 + ((z * -4.0) / y)
	tmp = 0
	if y <= -1.18e+70:
		tmp = t_0
	elif y <= 4.4e-32:
		tmp = (x - z) * (4.0 / y)
	elif y <= 6e+107:
		tmp = t_0
	else:
		tmp = 4.0 + ((4.0 * x) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 + Float64(Float64(z * -4.0) / y))
	tmp = 0.0
	if (y <= -1.18e+70)
		tmp = t_0;
	elseif (y <= 4.4e-32)
		tmp = Float64(Float64(x - z) * Float64(4.0 / y));
	elseif (y <= 6e+107)
		tmp = t_0;
	else
		tmp = Float64(4.0 + Float64(Float64(4.0 * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 + ((z * -4.0) / y);
	tmp = 0.0;
	if (y <= -1.18e+70)
		tmp = t_0;
	elseif (y <= 4.4e-32)
		tmp = (x - z) * (4.0 / y);
	elseif (y <= 6e+107)
		tmp = t_0;
	else
		tmp = 4.0 + ((4.0 * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.18e+70], t$95$0, If[LessEqual[y, 4.4e-32], N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+107], t$95$0, N[(4.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.18000000000000001e70 or 4.4e-32 < y < 6.00000000000000046e107

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 88.5%

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

      1. +-commutative 88.5%

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

      2. fma-define 88.5%

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

      3. div-sub 88.5%

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

      4. associate-/l* 88.6%

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

      5. *-inverses 88.6%

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

      6. metadata-eval 88.6%

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

      7. fma-define 88.6%

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

      8. +-commutative 88.6%

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

      9. sub-neg 88.6%

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

      10. distribute-lft-in 88.6%

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

      11. metadata-eval 88.6%

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

      12. associate-+r+ 88.7%

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

      13. metadata-eval 88.7%

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

      14. neg-mul-1 88.7%

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

      15. associate-*r* 88.7%

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

      16. metadata-eval 88.7%

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

      17. *-commutative 88.7%

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

      18. associate-*l/ 88.7%

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

   5. Simplified 88.7%

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

   if -1.18000000000000001e70 < y < 4.4e-32

   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 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. associate-+r- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 92.5%

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

      1. associate-*r/ 92.5%

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

      2. associate-*l/ 92.3%

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

   8. Simplified 92.3%

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

   if 6.00000000000000046e107 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      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 94.4%

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

      1. distribute-lft-in 94.4%

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

      2. metadata-eval 94.4%

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

      3. associate-+r+ 94.4%

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

      4. metadata-eval 94.4%

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

      5. associate-*r/ 94.4%

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

   7. Simplified 94.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+70}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-32}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+107}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+66} \lor \neg \left(y \leq 4.5 \cdot 10^{-39}\right):\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e+66) (not (<= y 4.5e-39)))
   (+ 4.0 (/ (* 4.0 x) y))
   (* (- x z) (/ 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+66) || !(y <= 4.5e-39)) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else {
		tmp = (x - z) * (4.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-8d+66)) .or. (.not. (y <= 4.5d-39))) then
        tmp = 4.0d0 + ((4.0d0 * x) / y)
    else
        tmp = (x - z) * (4.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+66) || !(y <= 4.5e-39)) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else {
		tmp = (x - z) * (4.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e+66) or not (y <= 4.5e-39):
		tmp = 4.0 + ((4.0 * x) / y)
	else:
		tmp = (x - z) * (4.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e+66) || !(y <= 4.5e-39))
		tmp = Float64(4.0 + Float64(Float64(4.0 * x) / y));
	else
		tmp = Float64(Float64(x - z) * Float64(4.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8e+66) || ~((y <= 4.5e-39)))
		tmp = 4.0 + ((4.0 * x) / y);
	else
		tmp = (x - z) * (4.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e+66], N[Not[LessEqual[y, 4.5e-39]], $MachinePrecision]], N[(4.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999956e66 or 4.5000000000000001e-39 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 99.9%

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

      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 84.6%

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

      1. distribute-lft-in 84.6%

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

      2. metadata-eval 84.6%

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

      3. associate-+r+ 84.6%

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

      4. metadata-eval 84.6%

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

      5. associate-*r/ 84.6%

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

   7. Simplified 84.6%

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

   if -7.99999999999999956e66 < y < 4.5000000000000001e-39

   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 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. associate-+r- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 92.4%

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

      1. associate-*r/ 92.4%

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

      2. associate-*l/ 92.2%

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

   8. Simplified 92.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+66} \lor \neg \left(y \leq 4.5 \cdot 10^{-39}\right):\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+67}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-25}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+67) 4.0 (if (<= y 3.4e-25) (* 4.0 (/ x y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+67) {
		tmp = 4.0;
	} else if (y <= 3.4e-25) {
		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 (y <= (-4.2d+67)) then
        tmp = 4.0d0
    else if (y <= 3.4d-25) 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 (y <= -4.2e+67) {
		tmp = 4.0;
	} else if (y <= 3.4e-25) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+67:
		tmp = 4.0
	elif y <= 3.4e-25:
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+67)
		tmp = 4.0;
	elseif (y <= 3.4e-25)
		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 (y <= -4.2e+67)
		tmp = 4.0;
	elseif (y <= 3.4e-25)
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+67], 4.0, If[LessEqual[y, 3.4e-25], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2000000000000003e67 or 3.40000000000000002e-25 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 69.2%

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

   if -4.2000000000000003e67 < y < 3.40000000000000002e-25

   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 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. associate-+r- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 49.4%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+67}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-25}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $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 0 100.0%

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

   1. distribute-lft-out 100.0%

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

   2. associate-+r- 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 8: 34.9% 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 35.6%

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

4. Final simplification 35.6%

   \[\leadsto 4 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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)))