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

Percentage Accurate: 99.8% → 100.0%

Time: 8.6s

Alternatives: 10

Speedup: 1.2×

• 20.4% 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, 1.2× speedup

Math

\[\begin{array}{l} \\ 1 + \left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (+ (/ (* 4.0 (- x z)) y) 3.0)))

C

double code(double x, double y, double z) {
	return 1.0 + (((4.0 * (x - z)) / y) + 3.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (((4.0d0 * (x - z)) / y) + 3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (((4.0 * (x - z)) / y) + 3.0);
}

Python

def code(x, y, z):
	return 1.0 + (((4.0 * (x - z)) / y) + 3.0)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(Float64(4.0 * Float64(x - z)) / y) + 3.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (((4.0 * (x - z)) / y) + 3.0);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 100.0%

   \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
4. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. associate-*r/ 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

   \[\leadsto 1 + \left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right) \]
7. Add Preprocessing

Alternative 2: 57.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + z \cdot \frac{-4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-63}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* z (/ -4.0 y)))) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= x -1.32e+118)
     t_1
     (if (<= x -2.8e+79)
       t_0
       (if (<= x -6.5e+45)
         t_1
         (if (<= x -3e-63) 4.0 (if (<= x 9.5e+46) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (z * (-4.0 / y));
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -1.32e+118) {
		tmp = t_1;
	} else if (x <= -2.8e+79) {
		tmp = t_0;
	} else if (x <= -6.5e+45) {
		tmp = t_1;
	} else if (x <= -3e-63) {
		tmp = 4.0;
	} else if (x <= 9.5e+46) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + (z * ((-4.0d0) / y))
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (x <= (-1.32d+118)) then
        tmp = t_1
    else if (x <= (-2.8d+79)) then
        tmp = t_0
    else if (x <= (-6.5d+45)) then
        tmp = t_1
    else if (x <= (-3d-63)) then
        tmp = 4.0d0
    else if (x <= 9.5d+46) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (z * (-4.0 / y));
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -1.32e+118) {
		tmp = t_1;
	} else if (x <= -2.8e+79) {
		tmp = t_0;
	} else if (x <= -6.5e+45) {
		tmp = t_1;
	} else if (x <= -3e-63) {
		tmp = 4.0;
	} else if (x <= 9.5e+46) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (z * (-4.0 / y))
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if x <= -1.32e+118:
		tmp = t_1
	elif x <= -2.8e+79:
		tmp = t_0
	elif x <= -6.5e+45:
		tmp = t_1
	elif x <= -3e-63:
		tmp = 4.0
	elif x <= 9.5e+46:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(z * Float64(-4.0 / y)))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -1.32e+118)
		tmp = t_1;
	elseif (x <= -2.8e+79)
		tmp = t_0;
	elseif (x <= -6.5e+45)
		tmp = t_1;
	elseif (x <= -3e-63)
		tmp = 4.0;
	elseif (x <= 9.5e+46)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (z * (-4.0 / y));
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (x <= -1.32e+118)
		tmp = t_1;
	elseif (x <= -2.8e+79)
		tmp = t_0;
	elseif (x <= -6.5e+45)
		tmp = t_1;
	elseif (x <= -3e-63)
		tmp = 4.0;
	elseif (x <= 9.5e+46)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.32e+118], t$95$1, If[LessEqual[x, -2.8e+79], t$95$0, If[LessEqual[x, -6.5e+45], t$95$1, If[LessEqual[x, -3e-63], 4.0, If[LessEqual[x, 9.5e+46], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3199999999999999e118 or -2.8000000000000001e79 < x < -6.50000000000000034e45 or 9.5000000000000008e46 < x

   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 inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -1.3199999999999999e118 < x < -2.8000000000000001e79 or -2.99999999999999979e-63 < x < 9.5000000000000008e46

   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 z around inf 56.7%

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

      1. metadata-eval 56.7%

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

      2. distribute-lft-neg-in 56.7%

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

      3. *-lft-identity 56.7%

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

      4. associate-*l/ 56.5%

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

      5. associate-*l* 56.5%

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

      6. *-commutative 56.5%

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

      7. distribute-rgt-neg-in 56.5%

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

      8. associate-*r/ 56.5%

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

      9. metadata-eval 56.5%

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

      10. distribute-neg-frac 56.5%

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

      11. metadata-eval 56.5%

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

   5. Simplified 56.5%

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

   if -6.50000000000000034e45 < x < -2.99999999999999979e-63

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 71.0%

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

      1. div-sub 71.0%

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

      2. associate-/l* 71.1%

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

      3. *-inverses 71.1%

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

      4. metadata-eval 71.1%

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

      5. sub-neg 71.1%

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

      6. distribute-lft-in 71.1%

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

      7. metadata-eval 71.1%

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

      8. distribute-rgt-neg-in 71.1%

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

      9. *-lft-identity 71.1%

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

      10. associate-*l/ 71.1%

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

      11. associate-*l* 71.1%

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

      12. *-commutative 71.1%

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

      13. distribute-rgt-neg-in 71.1%

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

      14. associate-*r/ 71.1%

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

      15. metadata-eval 71.1%

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

      16. distribute-neg-frac 71.1%

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

      17. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around 0 66.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+118}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+45}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-63}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-65}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+52}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= x -1.1e+119)
     t_1
     (if (<= x -2.35e+75)
       t_0
       (if (<= x -1.9e+47)
         t_1
         (if (<= x -6e-65) 4.0 (if (<= x 1.95e+52) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -1.1e+119) {
		tmp = t_1;
	} else if (x <= -2.35e+75) {
		tmp = t_0;
	} else if (x <= -1.9e+47) {
		tmp = t_1;
	} else if (x <= -6e-65) {
		tmp = 4.0;
	} else if (x <= 1.95e+52) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (x <= (-1.1d+119)) then
        tmp = t_1
    else if (x <= (-2.35d+75)) then
        tmp = t_0
    else if (x <= (-1.9d+47)) then
        tmp = t_1
    else if (x <= (-6d-65)) then
        tmp = 4.0d0
    else if (x <= 1.95d+52) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -1.1e+119) {
		tmp = t_1;
	} else if (x <= -2.35e+75) {
		tmp = t_0;
	} else if (x <= -1.9e+47) {
		tmp = t_1;
	} else if (x <= -6e-65) {
		tmp = 4.0;
	} else if (x <= 1.95e+52) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z * -4.0) / y)
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if x <= -1.1e+119:
		tmp = t_1
	elif x <= -2.35e+75:
		tmp = t_0
	elif x <= -1.9e+47:
		tmp = t_1
	elif x <= -6e-65:
		tmp = 4.0
	elif x <= 1.95e+52:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -1.1e+119)
		tmp = t_1;
	elseif (x <= -2.35e+75)
		tmp = t_0;
	elseif (x <= -1.9e+47)
		tmp = t_1;
	elseif (x <= -6e-65)
		tmp = 4.0;
	elseif (x <= 1.95e+52)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z * -4.0) / y);
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (x <= -1.1e+119)
		tmp = t_1;
	elseif (x <= -2.35e+75)
		tmp = t_0;
	elseif (x <= -1.9e+47)
		tmp = t_1;
	elseif (x <= -6e-65)
		tmp = 4.0;
	elseif (x <= 1.95e+52)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+119], t$95$1, If[LessEqual[x, -2.35e+75], t$95$0, If[LessEqual[x, -1.9e+47], t$95$1, If[LessEqual[x, -6e-65], 4.0, If[LessEqual[x, 1.95e+52], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1000000000000001e119 or -2.34999999999999992e75 < x < -1.9000000000000002e47 or 1.95e52 < x

   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 inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -1.1000000000000001e119 < x < -2.34999999999999992e75 or -5.99999999999999996e-65 < x < 1.95e52

   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 z around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-*l/ 56.7%

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

   5. Simplified 56.7%

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

   if -1.9000000000000002e47 < x < -5.99999999999999996e-65

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 71.0%

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

      1. div-sub 71.0%

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

      2. associate-/l* 71.1%

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

      3. *-inverses 71.1%

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

      4. metadata-eval 71.1%

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

      5. sub-neg 71.1%

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

      6. distribute-lft-in 71.1%

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

      7. metadata-eval 71.1%

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

      8. distribute-rgt-neg-in 71.1%

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

      9. *-lft-identity 71.1%

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

      10. associate-*l/ 71.1%

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

      11. associate-*l* 71.1%

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

      12. *-commutative 71.1%

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

      13. distribute-rgt-neg-in 71.1%

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

      14. associate-*r/ 71.1%

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

      15. metadata-eval 71.1%

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

      16. distribute-neg-frac 71.1%

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

      17. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around 0 66.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+119}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+75}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+47}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-65}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+52}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+118} \lor \neg \left(x \leq -2.1 \cdot 10^{+79} \lor \neg \left(x \leq -2.2 \cdot 10^{-55}\right) \land x \leq 1.8 \cdot 10^{+44}\right):\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.32e+118)
         (not (or (<= x -2.1e+79) (and (not (<= x -2.2e-55)) (<= x 1.8e+44)))))
   (+ 1.0 (+ 3.0 (* 4.0 (/ x y))))
   (+ 4.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.32e+118) || !((x <= -2.1e+79) || (!(x <= -2.2e-55) && (x <= 1.8e+44)))) {
		tmp = 1.0 + (3.0 + (4.0 * (x / y)));
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.32d+118)) .or. (.not. (x <= (-2.1d+79)) .or. (.not. (x <= (-2.2d-55))) .and. (x <= 1.8d+44))) then
        tmp = 1.0d0 + (3.0d0 + (4.0d0 * (x / y)))
    else
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.32e+118) || !((x <= -2.1e+79) || (!(x <= -2.2e-55) && (x <= 1.8e+44)))) {
		tmp = 1.0 + (3.0 + (4.0 * (x / y)));
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.32e+118) or not ((x <= -2.1e+79) or (not (x <= -2.2e-55) and (x <= 1.8e+44))):
		tmp = 1.0 + (3.0 + (4.0 * (x / y)))
	else:
		tmp = 4.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.32e+118) || !((x <= -2.1e+79) || (!(x <= -2.2e-55) && (x <= 1.8e+44))))
		tmp = Float64(1.0 + Float64(3.0 + Float64(4.0 * Float64(x / y))));
	else
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.32e+118) || ~(((x <= -2.1e+79) || (~((x <= -2.2e-55)) && (x <= 1.8e+44)))))
		tmp = 1.0 + (3.0 + (4.0 * (x / y)));
	else
		tmp = 4.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.32e+118], N[Not[Or[LessEqual[x, -2.1e+79], And[N[Not[LessEqual[x, -2.2e-55]], $MachinePrecision], LessEqual[x, 1.8e+44]]]], $MachinePrecision]], N[(1.0 + N[(3.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3199999999999999e118 or -2.10000000000000008e79 < x < -2.2e-55 or 1.8e44 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 89.2%

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

   if -1.3199999999999999e118 < x < -2.10000000000000008e79 or -2.2e-55 < x < 1.8e44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.0%

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

      1. div-sub 94.0%

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

      2. associate-/l* 94.1%

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

      3. *-inverses 94.1%

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

      4. metadata-eval 94.1%

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

      5. sub-neg 94.1%

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

      6. distribute-lft-in 94.1%

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

      7. metadata-eval 94.1%

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

      8. distribute-rgt-neg-in 94.1%

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

      9. *-lft-identity 94.1%

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

      10. associate-*l/ 93.9%

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

      11. associate-*l* 93.9%

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

      12. *-commutative 93.9%

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

      13. distribute-rgt-neg-in 93.9%

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

      14. associate-*r/ 93.9%

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

      15. metadata-eval 93.9%

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

      16. distribute-neg-frac 93.9%

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

      17. metadata-eval 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in z around 0 94.1%

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

      1. associate-*r/ 94.1%

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

   8. Simplified 94.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+118} \lor \neg \left(x \leq -2.1 \cdot 10^{+79} \lor \neg \left(x \leq -2.2 \cdot 10^{-55}\right) \land x \leq 1.8 \cdot 10^{+44}\right):\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 + \frac{z \cdot -4}{y}\\ t_1 := 1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{+52}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 4.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (+ 3.0 (* 4.0 (/ x y))))))
   (if (<= x -1.32e+118)
     t_1
     (if (<= x -1.6e+76)
       t_0
       (if (<= x -2.75e-55)
         t_1
         (if (<= x 5.9e+52) t_0 (+ 1.0 (/ 4.0 (/ y (- x z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (3.0 + (4.0 * (x / y)));
	double tmp;
	if (x <= -1.32e+118) {
		tmp = t_1;
	} else if (x <= -1.6e+76) {
		tmp = t_0;
	} else if (x <= -2.75e-55) {
		tmp = t_1;
	} else if (x <= 5.9e+52) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (4.0 / (y / (x - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + (3.0d0 + (4.0d0 * (x / y)))
    if (x <= (-1.32d+118)) then
        tmp = t_1
    else if (x <= (-1.6d+76)) then
        tmp = t_0
    else if (x <= (-2.75d-55)) then
        tmp = t_1
    else if (x <= 5.9d+52) then
        tmp = t_0
    else
        tmp = 1.0d0 + (4.0d0 / (y / (x - z)))
    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 t_1 = 1.0 + (3.0 + (4.0 * (x / y)));
	double tmp;
	if (x <= -1.32e+118) {
		tmp = t_1;
	} else if (x <= -1.6e+76) {
		tmp = t_0;
	} else if (x <= -2.75e-55) {
		tmp = t_1;
	} else if (x <= 5.9e+52) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (4.0 / (y / (x - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 + ((z * -4.0) / y)
	t_1 = 1.0 + (3.0 + (4.0 * (x / y)))
	tmp = 0
	if x <= -1.32e+118:
		tmp = t_1
	elif x <= -1.6e+76:
		tmp = t_0
	elif x <= -2.75e-55:
		tmp = t_1
	elif x <= 5.9e+52:
		tmp = t_0
	else:
		tmp = 1.0 + (4.0 / (y / (x - z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(3.0 + Float64(4.0 * Float64(x / y))))
	tmp = 0.0
	if (x <= -1.32e+118)
		tmp = t_1;
	elseif (x <= -1.6e+76)
		tmp = t_0;
	elseif (x <= -2.75e-55)
		tmp = t_1;
	elseif (x <= 5.9e+52)
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(4.0 / Float64(y / Float64(x - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 + ((z * -4.0) / y);
	t_1 = 1.0 + (3.0 + (4.0 * (x / y)));
	tmp = 0.0;
	if (x <= -1.32e+118)
		tmp = t_1;
	elseif (x <= -1.6e+76)
		tmp = t_0;
	elseif (x <= -2.75e-55)
		tmp = t_1;
	elseif (x <= 5.9e+52)
		tmp = t_0;
	else
		tmp = 1.0 + (4.0 / (y / (x - z)));
	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]}, Block[{t$95$1 = N[(1.0 + N[(3.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.32e+118], t$95$1, If[LessEqual[x, -1.6e+76], t$95$0, If[LessEqual[x, -2.75e-55], t$95$1, If[LessEqual[x, 5.9e+52], t$95$0, N[(1.0 + N[(4.0 / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3199999999999999e118 or -1.59999999999999988e76 < x < -2.7499999999999999e-55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 92.7%

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

   if -1.3199999999999999e118 < x < -1.59999999999999988e76 or -2.7499999999999999e-55 < x < 5.89999999999999996e52

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.0%

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

      1. div-sub 94.0%

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

      2. associate-/l* 94.1%

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

      3. *-inverses 94.1%

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

      4. metadata-eval 94.1%

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

      5. sub-neg 94.1%

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

      6. distribute-lft-in 94.1%

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

      7. metadata-eval 94.1%

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

      8. distribute-rgt-neg-in 94.1%

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

      9. *-lft-identity 94.1%

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

      10. associate-*l/ 93.9%

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

      11. associate-*l* 93.9%

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

      12. *-commutative 93.9%

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

      13. distribute-rgt-neg-in 93.9%

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

      14. associate-*r/ 93.9%

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

      15. metadata-eval 93.9%

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

      16. distribute-neg-frac 93.9%

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

      17. metadata-eval 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in z around 0 94.1%

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

      1. associate-*r/ 94.1%

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

   8. Simplified 94.1%

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

   if 5.89999999999999996e52 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. clear-num 86.6%

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

      2. inv-pow 86.6%

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

      3. *-un-lft-identity 86.6%

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

      4. times-frac 86.6%

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

      5. metadata-eval 86.6%

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

   5. Applied egg-rr 86.6%

      \[\leadsto 1 + \color{blue}{{\left(0.25 \cdot \frac{y}{x - z}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 86.6%

         \[\leadsto 1 + \color{blue}{\frac{1}{0.25 \cdot \frac{y}{x - z}}} \]

      2. associate-/r* 86.6%

         \[\leadsto 1 + \color{blue}{\frac{\frac{1}{0.25}}{\frac{y}{x - z}}} \]

      3. metadata-eval 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+118}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-55}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{+52}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 + \frac{z \cdot -4}{y}\\ t_1 := 1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4 \cdot \left(x - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 4.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (+ 3.0 (* 4.0 (/ x y))))))
   (if (<= x -1.7e+118)
     t_1
     (if (<= x -6.2e+78)
       t_0
       (if (<= x -2.25e-55)
         t_1
         (if (<= x 4.05e+43) t_0 (+ 1.0 (/ (* 4.0 (- x z)) y))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (3.0 + (4.0 * (x / y)));
	double tmp;
	if (x <= -1.7e+118) {
		tmp = t_1;
	} else if (x <= -6.2e+78) {
		tmp = t_0;
	} else if (x <= -2.25e-55) {
		tmp = t_1;
	} else if (x <= 4.05e+43) {
		tmp = t_0;
	} else {
		tmp = 1.0 + ((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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + (3.0d0 + (4.0d0 * (x / y)))
    if (x <= (-1.7d+118)) then
        tmp = t_1
    else if (x <= (-6.2d+78)) then
        tmp = t_0
    else if (x <= (-2.25d-55)) then
        tmp = t_1
    else if (x <= 4.05d+43) then
        tmp = t_0
    else
        tmp = 1.0d0 + ((4.0d0 * (x - z)) / 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 t_1 = 1.0 + (3.0 + (4.0 * (x / y)));
	double tmp;
	if (x <= -1.7e+118) {
		tmp = t_1;
	} else if (x <= -6.2e+78) {
		tmp = t_0;
	} else if (x <= -2.25e-55) {
		tmp = t_1;
	} else if (x <= 4.05e+43) {
		tmp = t_0;
	} else {
		tmp = 1.0 + ((4.0 * (x - z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 + ((z * -4.0) / y)
	t_1 = 1.0 + (3.0 + (4.0 * (x / y)))
	tmp = 0
	if x <= -1.7e+118:
		tmp = t_1
	elif x <= -6.2e+78:
		tmp = t_0
	elif x <= -2.25e-55:
		tmp = t_1
	elif x <= 4.05e+43:
		tmp = t_0
	else:
		tmp = 1.0 + ((4.0 * (x - z)) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(3.0 + Float64(4.0 * Float64(x / y))))
	tmp = 0.0
	if (x <= -1.7e+118)
		tmp = t_1;
	elseif (x <= -6.2e+78)
		tmp = t_0;
	elseif (x <= -2.25e-55)
		tmp = t_1;
	elseif (x <= 4.05e+43)
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(Float64(4.0 * Float64(x - z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 + ((z * -4.0) / y);
	t_1 = 1.0 + (3.0 + (4.0 * (x / y)));
	tmp = 0.0;
	if (x <= -1.7e+118)
		tmp = t_1;
	elseif (x <= -6.2e+78)
		tmp = t_0;
	elseif (x <= -2.25e-55)
		tmp = t_1;
	elseif (x <= 4.05e+43)
		tmp = t_0;
	else
		tmp = 1.0 + ((4.0 * (x - z)) / 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]}, Block[{t$95$1 = N[(1.0 + N[(3.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+118], t$95$1, If[LessEqual[x, -6.2e+78], t$95$0, If[LessEqual[x, -2.25e-55], t$95$1, If[LessEqual[x, 4.05e+43], t$95$0, N[(1.0 + N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999993e118 or -6.2e78 < x < -2.24999999999999985e-55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 92.7%

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

   if -1.69999999999999993e118 < x < -6.2e78 or -2.24999999999999985e-55 < x < 4.0499999999999998e43

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.0%

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

      1. div-sub 94.0%

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

      2. associate-/l* 94.0%

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

      3. *-inverses 94.0%

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

      4. metadata-eval 94.0%

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

      5. sub-neg 94.0%

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

      6. distribute-lft-in 94.0%

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

      7. metadata-eval 94.0%

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

      8. distribute-rgt-neg-in 94.0%

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

      9. *-lft-identity 94.0%

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

      10. associate-*l/ 93.9%

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

      11. associate-*l* 93.9%

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

      12. *-commutative 93.9%

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

      13. distribute-rgt-neg-in 93.9%

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

      14. associate-*r/ 93.9%

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

      15. metadata-eval 93.9%

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

      16. distribute-neg-frac 93.9%

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

      17. metadata-eval 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in z around 0 94.0%

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

      1. associate-*r/ 94.0%

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

   8. Simplified 94.0%

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

   if 4.0499999999999998e43 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.9%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+118}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-55}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{+43}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4 \cdot \left(x - z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+34} \lor \neg \left(z \leq 1.25 \cdot 10^{+58}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.6e+34) (not (<= z 1.25e+58))) (+ 1.0 (* z (/ -4.0 y))) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e+34) || !(z <= 1.25e+58)) {
		tmp = 1.0 + (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 ((z <= (-2.6d+34)) .or. (.not. (z <= 1.25d+58))) then
        tmp = 1.0d0 + (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 ((z <= -2.6e+34) || !(z <= 1.25e+58)) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.6e+34) or not (z <= 1.25e+58):
		tmp = 1.0 + (z * (-4.0 / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.6e+34) || !(z <= 1.25e+58))
		tmp = Float64(1.0 + Float64(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 ((z <= -2.6e+34) || ~((z <= 1.25e+58)))
		tmp = 1.0 + (z * (-4.0 / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.6e+34], N[Not[LessEqual[z, 1.25e+58]], $MachinePrecision]], N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999997e34 or 1.24999999999999996e58 < z

   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 z around inf 67.0%

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

      1. metadata-eval 67.0%

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

      2. distribute-lft-neg-in 67.0%

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

      3. *-lft-identity 67.0%

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

      4. associate-*l/ 66.9%

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

      5. associate-*l* 66.9%

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

      6. *-commutative 66.9%

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

      7. distribute-rgt-neg-in 66.9%

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

      8. associate-*r/ 66.9%

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

      9. metadata-eval 66.9%

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

      10. distribute-neg-frac 66.9%

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

      11. metadata-eval 66.9%

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

   5. Simplified 66.9%

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

   if -2.59999999999999997e34 < z < 1.24999999999999996e58

   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 58.6%

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

      1. div-sub 58.6%

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

      2. associate-/l* 58.6%

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

      3. *-inverses 58.6%

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

      4. metadata-eval 58.6%

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

      5. sub-neg 58.6%

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

      6. distribute-lft-in 58.6%

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

      7. metadata-eval 58.6%

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

      8. distribute-rgt-neg-in 58.6%

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

      9. *-lft-identity 58.6%

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

      10. associate-*l/ 58.6%

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

      11. associate-*l* 58.6%

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

      12. *-commutative 58.6%

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

      13. distribute-rgt-neg-in 58.6%

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

      14. associate-*r/ 58.6%

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

      15. metadata-eval 58.6%

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

      16. distribute-neg-frac 58.6%

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

      17. metadata-eval 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in z around 0 49.3%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+34} \lor \neg \left(z \leq 1.25 \cdot 10^{+58}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+118} \lor \neg \left(x \leq 7.8 \cdot 10^{+100}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.75e+118) (not (<= x 7.8e+100)))
   (+ 1.0 (* 4.0 (/ x y)))
   (+ 4.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e+118) || !(x <= 7.8e+100)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.75d+118)) .or. (.not. (x <= 7.8d+100))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e+118) || !(x <= 7.8e+100)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.75e+118) or not (x <= 7.8e+100):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.75e+118) || !(x <= 7.8e+100))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.75e+118) || ~((x <= 7.8e+100)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 4.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.75e+118], N[Not[LessEqual[x, 7.8e+100]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000008e118 or 7.8e100 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.6%

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

      1. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -1.75000000000000008e118 < x < 7.8e100

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.3%

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

      1. div-sub 85.3%

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

      2. associate-/l* 85.3%

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

      3. *-inverses 85.3%

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

      4. metadata-eval 85.3%

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

      5. sub-neg 85.3%

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

      6. distribute-lft-in 85.3%

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

      7. metadata-eval 85.3%

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

      8. distribute-rgt-neg-in 85.3%

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

      9. *-lft-identity 85.3%

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

      10. associate-*l/ 85.2%

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

      11. associate-*l* 85.2%

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

      12. *-commutative 85.2%

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

      13. distribute-rgt-neg-in 85.2%

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

      14. associate-*r/ 85.2%

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

      15. metadata-eval 85.2%

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

      16. distribute-neg-frac 85.2%

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

      17. metadata-eval 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around 0 85.3%

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

      1. associate-*r/ 85.3%

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

   8. Simplified 85.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+118} \lor \neg \left(x \leq 7.8 \cdot 10^{+100}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 1 + \left(3 + \frac{4}{\frac{y}{x - z}}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (+ 3.0 (/ 4.0 (/ y (- x z))))))

C

double code(double x, double y, double z) {
	return 1.0 + (3.0 + (4.0 / (y / (x - z))));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (3.0d0 + (4.0d0 / (y / (x - z))))
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (3.0 + (4.0 / (y / (x - z))));
}

Python

def code(x, y, z):
	return 1.0 + (3.0 + (4.0 / (y / (x - z))))

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(3.0 + Float64(4.0 / Float64(y / Float64(x - z)))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (3.0 + (4.0 / (y / (x - z))));
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(3.0 + N[(4.0 / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 100.0%

   \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
4. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. associate-*r/ 100.0%

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

5. Simplified 100.0%

   \[\leadsto 1 + \color{blue}{\left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right)} \]
6. Step-by-step derivation

   1. clear-num 69.8%

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

   2. inv-pow 69.8%

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

   3. *-un-lft-identity 69.8%

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

   4. times-frac 69.8%

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

   5. metadata-eval 69.8%

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

7. Applied egg-rr 99.8%

   \[\leadsto 1 + \left(\color{blue}{{\left(0.25 \cdot \frac{y}{x - z}\right)}^{-1}} + 3\right) \]
8. Step-by-step derivation

   1. unpow-1 69.8%

      \[\leadsto 1 + \color{blue}{\frac{1}{0.25 \cdot \frac{y}{x - z}}} \]

   2. associate-/r* 69.8%

      \[\leadsto 1 + \color{blue}{\frac{\frac{1}{0.25}}{\frac{y}{x - z}}} \]

   3. metadata-eval 69.8%

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

9. Simplified 99.8%

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

10. Final simplification 99.8%

    \[\leadsto 1 + \left(3 + \frac{4}{\frac{y}{x - z}}\right) \]
11. Add Preprocessing

Alternative 10: 34.3% 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 x around 0 68.2%

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

   1. div-sub 68.2%

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

   2. associate-/l* 68.2%

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

   3. *-inverses 68.2%

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

   4. metadata-eval 68.2%

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

   5. sub-neg 68.2%

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

   6. distribute-lft-in 68.2%

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

   7. metadata-eval 68.2%

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

   8. distribute-rgt-neg-in 68.2%

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

   9. *-lft-identity 68.2%

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

   10. associate-*l/ 68.1%

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

   11. associate-*l* 68.1%

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

   12. *-commutative 68.1%

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

   13. distribute-rgt-neg-in 68.1%

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

   14. associate-*r/ 68.1%

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

   15. metadata-eval 68.1%

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

   16. distribute-neg-frac 68.1%

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

   17. metadata-eval 68.1%

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

5. Simplified 68.1%

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

6. Taylor expanded in z around 0 37.2%

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

7. Final simplification 37.2%

   \[\leadsto 4 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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)))