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

Percentage Accurate: 99.8% → 100.0%

Time: 9.2s

Alternatives: 11

Speedup: 1.4×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% 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 99.6%

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

   1. +-commutative 99.6%

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

   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: 54.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := \frac{z \cdot -4}{y}\\ \mathbf{if}\;y \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-193}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-285}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 290000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))) (t_1 (/ (* z -4.0) y)))
   (if (<= y -1.26e+85)
     4.0
     (if (<= y -6.4e+18)
       t_1
       (if (<= y -1.4e-7)
         4.0
         (if (<= y -2.9e-193)
           t_0
           (if (<= y -1.12e-260)
             t_1
             (if (<= y -9.8e-285)
               t_0
               (if (<= y 7e-201)
                 t_1
                 (if (<= y 4.7e-147)
                   t_0
                   (if (<= y 290000.0)
                     t_1
                     (if (<= y 1.15e+54)
                       t_0
                       (if (<= y 1.95e+62) t_1 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 <= -1.26e+85) {
		tmp = 4.0;
	} else if (y <= -6.4e+18) {
		tmp = t_1;
	} else if (y <= -1.4e-7) {
		tmp = 4.0;
	} else if (y <= -2.9e-193) {
		tmp = t_0;
	} else if (y <= -1.12e-260) {
		tmp = t_1;
	} else if (y <= -9.8e-285) {
		tmp = t_0;
	} else if (y <= 7e-201) {
		tmp = t_1;
	} else if (y <= 4.7e-147) {
		tmp = t_0;
	} else if (y <= 290000.0) {
		tmp = t_1;
	} else if (y <= 1.15e+54) {
		tmp = t_0;
	} else if (y <= 1.95e+62) {
		tmp = t_1;
	} 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 <= (-1.26d+85)) then
        tmp = 4.0d0
    else if (y <= (-6.4d+18)) then
        tmp = t_1
    else if (y <= (-1.4d-7)) then
        tmp = 4.0d0
    else if (y <= (-2.9d-193)) then
        tmp = t_0
    else if (y <= (-1.12d-260)) then
        tmp = t_1
    else if (y <= (-9.8d-285)) then
        tmp = t_0
    else if (y <= 7d-201) then
        tmp = t_1
    else if (y <= 4.7d-147) then
        tmp = t_0
    else if (y <= 290000.0d0) then
        tmp = t_1
    else if (y <= 1.15d+54) then
        tmp = t_0
    else if (y <= 1.95d+62) then
        tmp = t_1
    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 <= -1.26e+85) {
		tmp = 4.0;
	} else if (y <= -6.4e+18) {
		tmp = t_1;
	} else if (y <= -1.4e-7) {
		tmp = 4.0;
	} else if (y <= -2.9e-193) {
		tmp = t_0;
	} else if (y <= -1.12e-260) {
		tmp = t_1;
	} else if (y <= -9.8e-285) {
		tmp = t_0;
	} else if (y <= 7e-201) {
		tmp = t_1;
	} else if (y <= 4.7e-147) {
		tmp = t_0;
	} else if (y <= 290000.0) {
		tmp = t_1;
	} else if (y <= 1.15e+54) {
		tmp = t_0;
	} else if (y <= 1.95e+62) {
		tmp = t_1;
	} 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 <= -1.26e+85:
		tmp = 4.0
	elif y <= -6.4e+18:
		tmp = t_1
	elif y <= -1.4e-7:
		tmp = 4.0
	elif y <= -2.9e-193:
		tmp = t_0
	elif y <= -1.12e-260:
		tmp = t_1
	elif y <= -9.8e-285:
		tmp = t_0
	elif y <= 7e-201:
		tmp = t_1
	elif y <= 4.7e-147:
		tmp = t_0
	elif y <= 290000.0:
		tmp = t_1
	elif y <= 1.15e+54:
		tmp = t_0
	elif y <= 1.95e+62:
		tmp = t_1
	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 <= -1.26e+85)
		tmp = 4.0;
	elseif (y <= -6.4e+18)
		tmp = t_1;
	elseif (y <= -1.4e-7)
		tmp = 4.0;
	elseif (y <= -2.9e-193)
		tmp = t_0;
	elseif (y <= -1.12e-260)
		tmp = t_1;
	elseif (y <= -9.8e-285)
		tmp = t_0;
	elseif (y <= 7e-201)
		tmp = t_1;
	elseif (y <= 4.7e-147)
		tmp = t_0;
	elseif (y <= 290000.0)
		tmp = t_1;
	elseif (y <= 1.15e+54)
		tmp = t_0;
	elseif (y <= 1.95e+62)
		tmp = t_1;
	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 <= -1.26e+85)
		tmp = 4.0;
	elseif (y <= -6.4e+18)
		tmp = t_1;
	elseif (y <= -1.4e-7)
		tmp = 4.0;
	elseif (y <= -2.9e-193)
		tmp = t_0;
	elseif (y <= -1.12e-260)
		tmp = t_1;
	elseif (y <= -9.8e-285)
		tmp = t_0;
	elseif (y <= 7e-201)
		tmp = t_1;
	elseif (y <= 4.7e-147)
		tmp = t_0;
	elseif (y <= 290000.0)
		tmp = t_1;
	elseif (y <= 1.15e+54)
		tmp = t_0;
	elseif (y <= 1.95e+62)
		tmp = t_1;
	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, -1.26e+85], 4.0, If[LessEqual[y, -6.4e+18], t$95$1, If[LessEqual[y, -1.4e-7], 4.0, If[LessEqual[y, -2.9e-193], t$95$0, If[LessEqual[y, -1.12e-260], t$95$1, If[LessEqual[y, -9.8e-285], t$95$0, If[LessEqual[y, 7e-201], t$95$1, If[LessEqual[y, 4.7e-147], t$95$0, If[LessEqual[y, 290000.0], t$95$1, If[LessEqual[y, 1.15e+54], t$95$0, If[LessEqual[y, 1.95e+62], t$95$1, 4.0]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.26000000000000003e85 or -6.4e18 < y < -1.4000000000000001e-7 or 1.95e62 < 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. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 78.2%

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

   if -1.26000000000000003e85 < y < -6.4e18 or -2.90000000000000007e-193 < y < -1.12000000000000004e-260 or -9.79999999999999949e-285 < y < 7.00000000000000016e-201 or 4.69999999999999989e-147 < y < 2.9e5 or 1.14999999999999997e54 < y < 1.95e62

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-*l/ 69.8%

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

   7. Simplified 69.8%

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

   if -1.4000000000000001e-7 < y < -2.90000000000000007e-193 or -1.12000000000000004e-260 < y < -9.79999999999999949e-285 or 7.00000000000000016e-201 < y < 4.69999999999999989e-147 or 2.9e5 < y < 1.14999999999999997e54

   1. Initial program 98.5%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 69.2%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-193}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-260}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-285}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-201}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-147}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 290000:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := z \cdot \frac{-4}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+84}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-17}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-191}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-280}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 11.6:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))) (t_1 (* z (/ -4.0 y))))
   (if (<= y -4.8e+84)
     4.0
     (if (<= y -2.75e+19)
       t_1
       (if (<= y -9e-17)
         4.0
         (if (<= y -1.6e-191)
           t_0
           (if (<= y -5.5e-261)
             t_1
             (if (<= y -5.5e-280)
               t_0
               (if (<= y 1.05e-200)
                 t_1
                 (if (<= y 3e-146)
                   t_0
                   (if (<= y 11.6) t_1 (if (<= y 4.5e+62) 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 <= -4.8e+84) {
		tmp = 4.0;
	} else if (y <= -2.75e+19) {
		tmp = t_1;
	} else if (y <= -9e-17) {
		tmp = 4.0;
	} else if (y <= -1.6e-191) {
		tmp = t_0;
	} else if (y <= -5.5e-261) {
		tmp = t_1;
	} else if (y <= -5.5e-280) {
		tmp = t_0;
	} else if (y <= 1.05e-200) {
		tmp = t_1;
	} else if (y <= 3e-146) {
		tmp = t_0;
	} else if (y <= 11.6) {
		tmp = t_1;
	} else if (y <= 4.5e+62) {
		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 <= (-4.8d+84)) then
        tmp = 4.0d0
    else if (y <= (-2.75d+19)) then
        tmp = t_1
    else if (y <= (-9d-17)) then
        tmp = 4.0d0
    else if (y <= (-1.6d-191)) then
        tmp = t_0
    else if (y <= (-5.5d-261)) then
        tmp = t_1
    else if (y <= (-5.5d-280)) then
        tmp = t_0
    else if (y <= 1.05d-200) then
        tmp = t_1
    else if (y <= 3d-146) then
        tmp = t_0
    else if (y <= 11.6d0) then
        tmp = t_1
    else if (y <= 4.5d+62) 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 <= -4.8e+84) {
		tmp = 4.0;
	} else if (y <= -2.75e+19) {
		tmp = t_1;
	} else if (y <= -9e-17) {
		tmp = 4.0;
	} else if (y <= -1.6e-191) {
		tmp = t_0;
	} else if (y <= -5.5e-261) {
		tmp = t_1;
	} else if (y <= -5.5e-280) {
		tmp = t_0;
	} else if (y <= 1.05e-200) {
		tmp = t_1;
	} else if (y <= 3e-146) {
		tmp = t_0;
	} else if (y <= 11.6) {
		tmp = t_1;
	} else if (y <= 4.5e+62) {
		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 <= -4.8e+84:
		tmp = 4.0
	elif y <= -2.75e+19:
		tmp = t_1
	elif y <= -9e-17:
		tmp = 4.0
	elif y <= -1.6e-191:
		tmp = t_0
	elif y <= -5.5e-261:
		tmp = t_1
	elif y <= -5.5e-280:
		tmp = t_0
	elif y <= 1.05e-200:
		tmp = t_1
	elif y <= 3e-146:
		tmp = t_0
	elif y <= 11.6:
		tmp = t_1
	elif y <= 4.5e+62:
		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(z * Float64(-4.0 / y))
	tmp = 0.0
	if (y <= -4.8e+84)
		tmp = 4.0;
	elseif (y <= -2.75e+19)
		tmp = t_1;
	elseif (y <= -9e-17)
		tmp = 4.0;
	elseif (y <= -1.6e-191)
		tmp = t_0;
	elseif (y <= -5.5e-261)
		tmp = t_1;
	elseif (y <= -5.5e-280)
		tmp = t_0;
	elseif (y <= 1.05e-200)
		tmp = t_1;
	elseif (y <= 3e-146)
		tmp = t_0;
	elseif (y <= 11.6)
		tmp = t_1;
	elseif (y <= 4.5e+62)
		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 <= -4.8e+84)
		tmp = 4.0;
	elseif (y <= -2.75e+19)
		tmp = t_1;
	elseif (y <= -9e-17)
		tmp = 4.0;
	elseif (y <= -1.6e-191)
		tmp = t_0;
	elseif (y <= -5.5e-261)
		tmp = t_1;
	elseif (y <= -5.5e-280)
		tmp = t_0;
	elseif (y <= 1.05e-200)
		tmp = t_1;
	elseif (y <= 3e-146)
		tmp = t_0;
	elseif (y <= 11.6)
		tmp = t_1;
	elseif (y <= 4.5e+62)
		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[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+84], 4.0, If[LessEqual[y, -2.75e+19], t$95$1, If[LessEqual[y, -9e-17], 4.0, If[LessEqual[y, -1.6e-191], t$95$0, If[LessEqual[y, -5.5e-261], t$95$1, If[LessEqual[y, -5.5e-280], t$95$0, If[LessEqual[y, 1.05e-200], t$95$1, If[LessEqual[y, 3e-146], t$95$0, If[LessEqual[y, 11.6], t$95$1, If[LessEqual[y, 4.5e+62], t$95$0, 4.0]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999999e84 or -2.75e19 < y < -8.99999999999999957e-17 or 4.49999999999999999e62 < 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. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 78.2%

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

   if -4.7999999999999999e84 < y < -2.75e19 or -1.6000000000000002e-191 < y < -5.50000000000000042e-261 or -5.50000000000000001e-280 < y < 1.05e-200 or 3.00000000000000019e-146 < y < 11.5999999999999996

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 96.6%

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

      1. *-commutative 96.6%

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

   7. Simplified 96.6%

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

      1. div-sub 91.1%

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

   9. Applied egg-rr 91.1%

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

   10. Taylor expanded in x around 0 70.2%

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

       1. metadata-eval 70.2%

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

       2. distribute-lft-neg-in 70.2%

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

       3. *-lft-identity 70.2%

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

       4. associate-*l/ 70.0%

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

       5. associate-*l* 70.0%

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

       6. *-commutative 70.0%

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

       7. distribute-rgt-neg-in 70.0%

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

       8. associate-*r/ 70.0%

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

       9. metadata-eval 70.0%

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

       10. distribute-neg-frac 70.0%

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

       11. metadata-eval 70.0%

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

   12. Simplified 70.0%

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

   if -8.99999999999999957e-17 < y < -1.6000000000000002e-191 or -5.50000000000000042e-261 < y < -5.50000000000000001e-280 or 1.05e-200 < y < 3.00000000000000019e-146 or 11.5999999999999996 < y < 4.49999999999999999e62

   1. Initial program 98.6%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 68.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+84}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-17}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-191}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-280}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-146}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 11.6:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+40} \lor \neg \left(z \leq 10^{-10} \lor \neg \left(z \leq 8 \cdot 10^{+14}\right) \land z \leq 1.75 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.2e+40)
         (not (or (<= z 1e-10) (and (not (<= z 8e+14)) (<= z 1.75e+158)))))
   (/ (* z -4.0) y)
   (* 4.0 (/ (+ x y) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e+40) || !((z <= 1e-10) || (!(z <= 8e+14) && (z <= 1.75e+158)))) {
		tmp = (z * -4.0) / y;
	} else {
		tmp = 4.0 * ((x + y) / 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 <= (-1.2d+40)) .or. (.not. (z <= 1d-10) .or. (.not. (z <= 8d+14)) .and. (z <= 1.75d+158))) then
        tmp = (z * (-4.0d0)) / y
    else
        tmp = 4.0d0 * ((x + y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e+40) || !((z <= 1e-10) || (!(z <= 8e+14) && (z <= 1.75e+158)))) {
		tmp = (z * -4.0) / y;
	} else {
		tmp = 4.0 * ((x + y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.2e+40) or not ((z <= 1e-10) or (not (z <= 8e+14) and (z <= 1.75e+158))):
		tmp = (z * -4.0) / y
	else:
		tmp = 4.0 * ((x + y) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.2e+40) || !((z <= 1e-10) || (!(z <= 8e+14) && (z <= 1.75e+158))))
		tmp = Float64(Float64(z * -4.0) / y);
	else
		tmp = Float64(4.0 * Float64(Float64(x + y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.2e+40) || ~(((z <= 1e-10) || (~((z <= 8e+14)) && (z <= 1.75e+158)))))
		tmp = (z * -4.0) / y;
	else
		tmp = 4.0 * ((x + y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.2e+40], N[Not[Or[LessEqual[z, 1e-10], And[N[Not[LessEqual[z, 8e+14]], $MachinePrecision], LessEqual[z, 1.75e+158]]]], $MachinePrecision]], N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision], N[(4.0 * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e40 or 1.00000000000000004e-10 < z < 8e14 or 1.7500000000000001e158 < z

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 79.4%

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

   7. Simplified 79.4%

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

   if -1.2e40 < z < 1.00000000000000004e-10 or 8e14 < z < 1.7500000000000001e158

   1. Initial program 99.4%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.4%

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

      1. distribute-lft-out 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in z around 0 89.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+40} \lor \neg \left(z \leq 10^{-10} \lor \neg \left(z \leq 8 \cdot 10^{+14}\right) \land z \leq 1.75 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+77} \lor \neg \left(y \leq -3.5 \cdot 10^{+20} \lor \neg \left(y \leq -7.5 \cdot 10^{-74}\right) \land y \leq 3.1 \cdot 10^{+56}\right):\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.45e+77)
         (not (or (<= y -3.5e+20) (and (not (<= y -7.5e-74)) (<= y 3.1e+56)))))
   (* 4.0 (/ (+ x y) y))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e+77) || !((y <= -3.5e+20) || (!(y <= -7.5e-74) && (y <= 3.1e+56)))) {
		tmp = 4.0 * ((x + y) / y);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.45d+77)) .or. (.not. (y <= (-3.5d+20)) .or. (.not. (y <= (-7.5d-74))) .and. (y <= 3.1d+56))) then
        tmp = 4.0d0 * ((x + y) / y)
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e+77) || !((y <= -3.5e+20) || (!(y <= -7.5e-74) && (y <= 3.1e+56)))) {
		tmp = 4.0 * ((x + y) / y);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.45e+77) or not ((y <= -3.5e+20) or (not (y <= -7.5e-74) and (y <= 3.1e+56))):
		tmp = 4.0 * ((x + y) / y)
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.45e+77) || !((y <= -3.5e+20) || (!(y <= -7.5e-74) && (y <= 3.1e+56))))
		tmp = Float64(4.0 * Float64(Float64(x + y) / y));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.45e+77) || ~(((y <= -3.5e+20) || (~((y <= -7.5e-74)) && (y <= 3.1e+56)))))
		tmp = 4.0 * ((x + y) / y);
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.45e+77], N[Not[Or[LessEqual[y, -3.5e+20], And[N[Not[LessEqual[y, -7.5e-74]], $MachinePrecision], LessEqual[y, 3.1e+56]]]], $MachinePrecision]], N[(4.0 * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e77 or -3.5e20 < y < -7.5e-74 or 3.10000000000000005e56 < 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. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.9%

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

      1. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 89.1%

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

   if -1.4500000000000001e77 < y < -3.5e20 or -7.5e-74 < y < 3.10000000000000005e56

   1. Initial program 99.3%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.9%

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

      1. *-commutative 95.9%

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

   7. Simplified 95.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+77} \lor \neg \left(y \leq -3.5 \cdot 10^{+20} \lor \neg \left(y \leq -7.5 \cdot 10^{-74}\right) \land y \leq 3.1 \cdot 10^{+56}\right):\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x + y}{y}\\ t_1 := 4 \cdot \frac{x - z}{y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+77}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-75}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ (+ x y) y))) (t_1 (* 4.0 (/ (- x z) y))))
   (if (<= y -1.2e+77)
     t_0
     (if (<= y -5.6e+20)
       t_1
       (if (<= y -6e-75)
         (+ 4.0 (/ (* 4.0 x) y))
         (if (<= y 1.06e+59) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * ((x + y) / y);
	double t_1 = 4.0 * ((x - z) / y);
	double tmp;
	if (y <= -1.2e+77) {
		tmp = t_0;
	} else if (y <= -5.6e+20) {
		tmp = t_1;
	} else if (y <= -6e-75) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if (y <= 1.06e+59) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * ((x + y) / y)
    t_1 = 4.0d0 * ((x - z) / y)
    if (y <= (-1.2d+77)) then
        tmp = t_0
    else if (y <= (-5.6d+20)) then
        tmp = t_1
    else if (y <= (-6d-75)) then
        tmp = 4.0d0 + ((4.0d0 * x) / y)
    else if (y <= 1.06d+59) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * ((x + y) / y);
	double t_1 = 4.0 * ((x - z) / y);
	double tmp;
	if (y <= -1.2e+77) {
		tmp = t_0;
	} else if (y <= -5.6e+20) {
		tmp = t_1;
	} else if (y <= -6e-75) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if (y <= 1.06e+59) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * ((x + y) / y)
	t_1 = 4.0 * ((x - z) / y)
	tmp = 0
	if y <= -1.2e+77:
		tmp = t_0
	elif y <= -5.6e+20:
		tmp = t_1
	elif y <= -6e-75:
		tmp = 4.0 + ((4.0 * x) / y)
	elif y <= 1.06e+59:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(Float64(x + y) / y))
	t_1 = Float64(4.0 * Float64(Float64(x - z) / y))
	tmp = 0.0
	if (y <= -1.2e+77)
		tmp = t_0;
	elseif (y <= -5.6e+20)
		tmp = t_1;
	elseif (y <= -6e-75)
		tmp = Float64(4.0 + Float64(Float64(4.0 * x) / y));
	elseif (y <= 1.06e+59)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * ((x + y) / y);
	t_1 = 4.0 * ((x - z) / y);
	tmp = 0.0;
	if (y <= -1.2e+77)
		tmp = t_0;
	elseif (y <= -5.6e+20)
		tmp = t_1;
	elseif (y <= -6e-75)
		tmp = 4.0 + ((4.0 * x) / y);
	elseif (y <= 1.06e+59)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+77], t$95$0, If[LessEqual[y, -5.6e+20], t$95$1, If[LessEqual[y, -6e-75], N[(4.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+59], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1999999999999999e77 or 1.0600000000000001e59 < 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. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.9%

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

      1. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 89.0%

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

   if -1.1999999999999999e77 < y < -5.6e20 or -5.9999999999999997e-75 < y < 1.0600000000000001e59

   1. Initial program 99.3%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.9%

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

      1. *-commutative 95.9%

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

   7. Simplified 95.9%

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

   if -5.6e20 < y < -5.9999999999999997e-75

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub-neg 99.8%

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

      8. associate--r+ 99.8%

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

      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 89.4%

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

      1. distribute-lft-in 89.4%

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

      2. metadata-eval 89.4%

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

      3. associate-+r+ 89.4%

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

      4. metadata-eval 89.4%

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

      5. *-commutative 89.4%

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

      6. associate-*l/ 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+77}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+20}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-75}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+59}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+39} \lor \neg \left(z \leq 7.8 \cdot 10^{-17}\right):\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.8e+39) (not (<= z 7.8e-17)))
   (+ 4.0 (/ (* z -4.0) y))
   (* 4.0 (/ (+ x y) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.8e+39) || !(z <= 7.8e-17)) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 * ((x + y) / 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 <= (-9.8d+39)) .or. (.not. (z <= 7.8d-17))) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    else
        tmp = 4.0d0 * ((x + y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.8e+39) || !(z <= 7.8e-17)) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 * ((x + y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.8e+39) or not (z <= 7.8e-17):
		tmp = 4.0 + ((z * -4.0) / y)
	else:
		tmp = 4.0 * ((x + y) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.8e+39) || !(z <= 7.8e-17))
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = Float64(4.0 * Float64(Float64(x + y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.8e+39) || ~((z <= 7.8e-17)))
		tmp = 4.0 + ((z * -4.0) / y);
	else
		tmp = 4.0 * ((x + y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.8e+39], N[Not[LessEqual[z, 7.8e-17]], $MachinePrecision]], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999974e39 or 7.79999999999999979e-17 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

      4. associate--l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r+ 100.0%

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

      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 91.2%

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

      1. sub-neg 91.2%

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

      2. distribute-lft-in 91.2%

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

      3. metadata-eval 91.2%

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

      4. associate-+r+ 91.2%

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

      5. metadata-eval 91.2%

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

      6. neg-mul-1 91.2%

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

      7. associate-*r* 91.2%

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

      8. metadata-eval 91.2%

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

      9. *-commutative 91.2%

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

      10. associate-*l/ 91.2%

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

   7. Simplified 91.2%

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

   if -9.79999999999999974e39 < z < 7.79999999999999979e-17

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.3%

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

      1. distribute-lft-out 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in z around 0 93.1%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+39} \lor \neg \left(z \leq 7.8 \cdot 10^{-17}\right):\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-7}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e-7) 4.0 (if (<= y 5.5e+61) (* 4.0 (/ x y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e-7) {
		tmp = 4.0;
	} else if (y <= 5.5e+61) {
		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 <= (-1.55d-7)) then
        tmp = 4.0d0
    else if (y <= 5.5d+61) 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 <= -1.55e-7) {
		tmp = 4.0;
	} else if (y <= 5.5e+61) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e-7:
		tmp = 4.0
	elif y <= 5.5e+61:
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e-7)
		tmp = 4.0;
	elseif (y <= 5.5e+61)
		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 <= -1.55e-7)
		tmp = 4.0;
	elseif (y <= 5.5e+61)
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e-7], 4.0, If[LessEqual[y, 5.5e+61], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e-7 or 5.50000000000000036e61 < 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. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 72.1%

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

   if -1.55e-7 < y < 5.50000000000000036e61

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 47.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-7}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. associate-/l* 99.9%

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

   2. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 10: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. associate-/l* 99.9%

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

   2. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 99.6%

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

   1. distribute-lft-out 99.6%

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

7. Simplified 99.6%

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

8. Final simplification 99.6%

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

Alternative 11: 34.6% 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 99.6%

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

   1. associate-/l* 99.9%

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

   2. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 35.2%

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

6. Final simplification 35.2%

   \[\leadsto 4 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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)))