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

Percentage Accurate: 99.7% → 99.9%

Time: 6.4s

Alternatives: 9

Speedup: 1.2×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% 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: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + z \cdot \frac{-4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-57}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7200000000000:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2.7e+49)
     t_1
     (if (<= x -1.12e-57)
       4.0
       (if (<= x 1.05e-79)
         t_0
         (if (<= x 7200000000000.0) 4.0 (if (<= x 8.2e+65) 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 <= -2.7e+49) {
		tmp = t_1;
	} else if (x <= -1.12e-57) {
		tmp = 4.0;
	} else if (x <= 1.05e-79) {
		tmp = t_0;
	} else if (x <= 7200000000000.0) {
		tmp = 4.0;
	} else if (x <= 8.2e+65) {
		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 <= (-2.7d+49)) then
        tmp = t_1
    else if (x <= (-1.12d-57)) then
        tmp = 4.0d0
    else if (x <= 1.05d-79) then
        tmp = t_0
    else if (x <= 7200000000000.0d0) then
        tmp = 4.0d0
    else if (x <= 8.2d+65) 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 <= -2.7e+49) {
		tmp = t_1;
	} else if (x <= -1.12e-57) {
		tmp = 4.0;
	} else if (x <= 1.05e-79) {
		tmp = t_0;
	} else if (x <= 7200000000000.0) {
		tmp = 4.0;
	} else if (x <= 8.2e+65) {
		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 <= -2.7e+49:
		tmp = t_1
	elif x <= -1.12e-57:
		tmp = 4.0
	elif x <= 1.05e-79:
		tmp = t_0
	elif x <= 7200000000000.0:
		tmp = 4.0
	elif x <= 8.2e+65:
		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 <= -2.7e+49)
		tmp = t_1;
	elseif (x <= -1.12e-57)
		tmp = 4.0;
	elseif (x <= 1.05e-79)
		tmp = t_0;
	elseif (x <= 7200000000000.0)
		tmp = 4.0;
	elseif (x <= 8.2e+65)
		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 <= -2.7e+49)
		tmp = t_1;
	elseif (x <= -1.12e-57)
		tmp = 4.0;
	elseif (x <= 1.05e-79)
		tmp = t_0;
	elseif (x <= 7200000000000.0)
		tmp = 4.0;
	elseif (x <= 8.2e+65)
		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, -2.7e+49], t$95$1, If[LessEqual[x, -1.12e-57], 4.0, If[LessEqual[x, 1.05e-79], t$95$0, If[LessEqual[x, 7200000000000.0], 4.0, If[LessEqual[x, 8.2e+65], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7000000000000001e49 or 8.2000000000000003e65 < 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 75.5%

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

      1. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -2.7000000000000001e49 < x < -1.12e-57 or 1.05e-79 < x < 7.2e12

   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 63.3%

      \[\leadsto 1 + \color{blue}{3} \]

   if -1.12e-57 < x < 1.05e-79 or 7.2e12 < x < 8.2000000000000003e65

   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 z around inf 61.6%

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

      1. metadata-eval 61.6%

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

      2. distribute-lft-neg-in 61.6%

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

      3. *-lft-identity 61.6%

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

      4. associate-*l/ 61.4%

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

      5. associate-*l* 61.4%

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

      6. *-commutative 61.4%

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

      7. distribute-rgt-neg-in 61.4%

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

      8. associate-*r/ 61.4%

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

      9. metadata-eval 61.4%

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

      10. distribute-neg-frac 61.4%

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

      11. metadata-eval 61.4%

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

   5. Simplified 61.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-57}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-79}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 7200000000000:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-80}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6000000000000:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2.7e+49)
     t_1
     (if (<= x -2.9e-55)
       4.0
       (if (<= x 2.05e-80)
         t_0
         (if (<= x 6000000000000.0) 4.0 (if (<= x 8.2e+65) 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 <= -2.7e+49) {
		tmp = t_1;
	} else if (x <= -2.9e-55) {
		tmp = 4.0;
	} else if (x <= 2.05e-80) {
		tmp = t_0;
	} else if (x <= 6000000000000.0) {
		tmp = 4.0;
	} else if (x <= 8.2e+65) {
		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 <= (-2.7d+49)) then
        tmp = t_1
    else if (x <= (-2.9d-55)) then
        tmp = 4.0d0
    else if (x <= 2.05d-80) then
        tmp = t_0
    else if (x <= 6000000000000.0d0) then
        tmp = 4.0d0
    else if (x <= 8.2d+65) 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 <= -2.7e+49) {
		tmp = t_1;
	} else if (x <= -2.9e-55) {
		tmp = 4.0;
	} else if (x <= 2.05e-80) {
		tmp = t_0;
	} else if (x <= 6000000000000.0) {
		tmp = 4.0;
	} else if (x <= 8.2e+65) {
		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 <= -2.7e+49:
		tmp = t_1
	elif x <= -2.9e-55:
		tmp = 4.0
	elif x <= 2.05e-80:
		tmp = t_0
	elif x <= 6000000000000.0:
		tmp = 4.0
	elif x <= 8.2e+65:
		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 <= -2.7e+49)
		tmp = t_1;
	elseif (x <= -2.9e-55)
		tmp = 4.0;
	elseif (x <= 2.05e-80)
		tmp = t_0;
	elseif (x <= 6000000000000.0)
		tmp = 4.0;
	elseif (x <= 8.2e+65)
		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 <= -2.7e+49)
		tmp = t_1;
	elseif (x <= -2.9e-55)
		tmp = 4.0;
	elseif (x <= 2.05e-80)
		tmp = t_0;
	elseif (x <= 6000000000000.0)
		tmp = 4.0;
	elseif (x <= 8.2e+65)
		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, -2.7e+49], t$95$1, If[LessEqual[x, -2.9e-55], 4.0, If[LessEqual[x, 2.05e-80], t$95$0, If[LessEqual[x, 6000000000000.0], 4.0, If[LessEqual[x, 8.2e+65], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7000000000000001e49 or 8.2000000000000003e65 < 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 75.5%

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

      1. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -2.7000000000000001e49 < x < -2.9e-55 or 2.05e-80 < x < 6e12

   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 63.3%

      \[\leadsto 1 + \color{blue}{3} \]

   if -2.9e-55 < x < 2.05e-80 or 6e12 < x < 8.2000000000000003e65

   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 z around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-*l/ 61.6%

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

   5. Simplified 61.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-80}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 6000000000000:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+25} \lor \neg \left(x \leq 5.2 \cdot 10^{-79} \lor \neg \left(x \leq 115000000000\right) \land x \leq 2.2 \cdot 10^{+66}\right):\\ \;\;\;\;1 + \left(3 + x \cdot \frac{4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5e+25)
         (not
          (or (<= x 5.2e-79)
              (and (not (<= x 115000000000.0)) (<= x 2.2e+66)))))
   (+ 1.0 (+ 3.0 (* x (/ 4.0 y))))
   (+ 1.0 (+ 3.0 (* z (/ -4.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e+25) || !((x <= 5.2e-79) || (!(x <= 115000000000.0) && (x <= 2.2e+66)))) {
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	} else {
		tmp = 1.0 + (3.0 + (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 <= (-5d+25)) .or. (.not. (x <= 5.2d-79) .or. (.not. (x <= 115000000000.0d0)) .and. (x <= 2.2d+66))) then
        tmp = 1.0d0 + (3.0d0 + (x * (4.0d0 / y)))
    else
        tmp = 1.0d0 + (3.0d0 + (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 <= -5e+25) || !((x <= 5.2e-79) || (!(x <= 115000000000.0) && (x <= 2.2e+66)))) {
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	} else {
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5e+25) or not ((x <= 5.2e-79) or (not (x <= 115000000000.0) and (x <= 2.2e+66))):
		tmp = 1.0 + (3.0 + (x * (4.0 / y)))
	else:
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5e+25) || !((x <= 5.2e-79) || (!(x <= 115000000000.0) && (x <= 2.2e+66))))
		tmp = Float64(1.0 + Float64(3.0 + Float64(x * Float64(4.0 / y))));
	else
		tmp = Float64(1.0 + Float64(3.0 + Float64(z * Float64(-4.0 / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5e+25) || ~(((x <= 5.2e-79) || (~((x <= 115000000000.0)) && (x <= 2.2e+66)))))
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	else
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5e+25], N[Not[Or[LessEqual[x, 5.2e-79], And[N[Not[LessEqual[x, 115000000000.0]], $MachinePrecision], LessEqual[x, 2.2e+66]]]], $MachinePrecision]], N[(1.0 + N[(3.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(3.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000024e25 or 5.19999999999999987e-79 < x < 1.15e11 or 2.1999999999999998e66 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   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 90.8%

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

      1. associate-*r/ 90.8%

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

      2. *-commutative 90.8%

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

      3. associate-*r/ 90.7%

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

   8. Simplified 90.7%

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

   if -5.00000000000000024e25 < x < 5.19999999999999987e-79 or 1.15e11 < x < 2.1999999999999998e66

   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 92.2%

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

      1. div-sub 92.2%

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

      2. associate-/l* 92.2%

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

      3. *-inverses 92.2%

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

      4. metadata-eval 92.2%

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

      5. sub-neg 92.2%

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

      6. distribute-lft-in 92.2%

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

      7. metadata-eval 92.2%

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

      8. distribute-rgt-neg-in 92.2%

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

      9. *-lft-identity 92.2%

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

      10. associate-*l/ 92.1%

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

      11. associate-*l* 92.1%

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

      12. *-commutative 92.1%

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

      13. distribute-rgt-neg-in 92.1%

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

      14. associate-*r/ 92.1%

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

      15. metadata-eval 92.1%

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

      16. distribute-neg-frac 92.1%

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

      17. metadata-eval 92.1%

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

   5. Simplified 92.1%

      \[\leadsto 1 + \color{blue}{\left(3 + z \cdot \frac{-4}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+25} \lor \neg \left(x \leq 5.2 \cdot 10^{-79} \lor \neg \left(x \leq 115000000000\right) \land x \leq 2.2 \cdot 10^{+66}\right):\\ \;\;\;\;1 + \left(3 + x \cdot \frac{4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+25} \lor \neg \left(x \leq 5.2 \cdot 10^{-79} \lor \neg \left(x \leq 95000000000\right) \land x \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;1 + \left(3 + x \cdot \frac{4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + \frac{z \cdot -4}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+25)
         (not
          (or (<= x 5.2e-79) (and (not (<= x 95000000000.0)) (<= x 1.2e+67)))))
   (+ 1.0 (+ 3.0 (* x (/ 4.0 y))))
   (+ 1.0 (+ 3.0 (/ (* z -4.0) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+25) || !((x <= 5.2e-79) || (!(x <= 95000000000.0) && (x <= 1.2e+67)))) {
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	} else {
		tmp = 1.0 + (3.0 + ((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 <= (-5.5d+25)) .or. (.not. (x <= 5.2d-79) .or. (.not. (x <= 95000000000.0d0)) .and. (x <= 1.2d+67))) then
        tmp = 1.0d0 + (3.0d0 + (x * (4.0d0 / y)))
    else
        tmp = 1.0d0 + (3.0d0 + ((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 <= -5.5e+25) || !((x <= 5.2e-79) || (!(x <= 95000000000.0) && (x <= 1.2e+67)))) {
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	} else {
		tmp = 1.0 + (3.0 + ((z * -4.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+25) or not ((x <= 5.2e-79) or (not (x <= 95000000000.0) and (x <= 1.2e+67))):
		tmp = 1.0 + (3.0 + (x * (4.0 / y)))
	else:
		tmp = 1.0 + (3.0 + ((z * -4.0) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+25) || !((x <= 5.2e-79) || (!(x <= 95000000000.0) && (x <= 1.2e+67))))
		tmp = Float64(1.0 + Float64(3.0 + Float64(x * Float64(4.0 / y))));
	else
		tmp = Float64(1.0 + Float64(3.0 + Float64(Float64(z * -4.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e+25) || ~(((x <= 5.2e-79) || (~((x <= 95000000000.0)) && (x <= 1.2e+67)))))
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	else
		tmp = 1.0 + (3.0 + ((z * -4.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+25], N[Not[Or[LessEqual[x, 5.2e-79], And[N[Not[LessEqual[x, 95000000000.0]], $MachinePrecision], LessEqual[x, 1.2e+67]]]], $MachinePrecision]], N[(1.0 + N[(3.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(3.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000018e25 or 5.19999999999999987e-79 < x < 9.5e10 or 1.20000000000000001e67 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   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 90.8%

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

      1. associate-*r/ 90.8%

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

      2. *-commutative 90.8%

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

      3. associate-*r/ 90.7%

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

   8. Simplified 90.7%

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

   if -5.50000000000000018e25 < x < 5.19999999999999987e-79 or 9.5e10 < x < 1.20000000000000001e67

   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 0 92.2%

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

      1. associate-*r/ 92.2%

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

   8. Simplified 92.2%

      \[\leadsto 1 + \left(\color{blue}{\frac{-4 \cdot z}{y}} + 3\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+25} \lor \neg \left(x \leq 5.2 \cdot 10^{-79} \lor \neg \left(x \leq 95000000000\right) \land x \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;1 + \left(3 + x \cdot \frac{4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + \frac{z \cdot -4}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+49} \lor \neg \left(x \leq 2.35 \cdot 10^{+88}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.9e+49) (not (<= x 2.35e+88)))
   (+ 1.0 (* 4.0 (/ x y)))
   (+ 1.0 (+ 3.0 (* z (/ -4.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.9e+49) || !(x <= 2.35e+88)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.9d+49)) .or. (.not. (x <= 2.35d+88))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 1.0d0 + (3.0d0 + (z * ((-4.0d0) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.9e+49) || !(x <= 2.35e+88)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.9e+49) or not (x <= 2.35e+88):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.9e+49) || !(x <= 2.35e+88))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(1.0 + Float64(3.0 + Float64(z * Float64(-4.0 / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.9e+49) || ~((x <= 2.35e+88)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.9e+49], N[Not[LessEqual[x, 2.35e+88]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(3.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e49 or 2.35000000000000004e88 < 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 76.5%

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

      1. *-commutative 76.5%

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

   5. Simplified 76.5%

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

   if -2.9e49 < x < 2.35000000000000004e88

   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 87.5%

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

      1. div-sub 87.5%

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

      2. associate-/l* 87.5%

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

      3. *-inverses 87.5%

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

      4. metadata-eval 87.5%

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

      5. sub-neg 87.5%

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

      6. distribute-lft-in 87.5%

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

      7. metadata-eval 87.5%

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

      8. distribute-rgt-neg-in 87.5%

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

      9. *-lft-identity 87.5%

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

      10. associate-*l/ 87.3%

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

      11. associate-*l* 87.3%

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

      12. *-commutative 87.3%

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

      13. distribute-rgt-neg-in 87.3%

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

      14. associate-*r/ 87.3%

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

      15. metadata-eval 87.3%

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

      16. distribute-neg-frac 87.3%

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

      17. metadata-eval 87.3%

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

   5. Simplified 87.3%

      \[\leadsto 1 + \color{blue}{\left(3 + z \cdot \frac{-4}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+49} \lor \neg \left(x \leq 2.35 \cdot 10^{+88}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-12}:\\ \;\;\;\;1 + \left(3 + x \cdot \frac{4}{y}\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+28}:\\ \;\;\;\;1 + \frac{4 \cdot \left(x - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + \frac{z \cdot -4}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.85e-12)
   (+ 1.0 (+ 3.0 (* x (/ 4.0 y))))
   (if (<= y 7.4e+28)
     (+ 1.0 (/ (* 4.0 (- x z)) y))
     (+ 1.0 (+ 3.0 (/ (* z -4.0) y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.85e-12) {
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	} else if (y <= 7.4e+28) {
		tmp = 1.0 + ((4.0 * (x - z)) / y);
	} else {
		tmp = 1.0 + (3.0 + ((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 (y <= (-1.85d-12)) then
        tmp = 1.0d0 + (3.0d0 + (x * (4.0d0 / y)))
    else if (y <= 7.4d+28) then
        tmp = 1.0d0 + ((4.0d0 * (x - z)) / y)
    else
        tmp = 1.0d0 + (3.0d0 + ((z * (-4.0d0)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.85e-12) {
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	} else if (y <= 7.4e+28) {
		tmp = 1.0 + ((4.0 * (x - z)) / y);
	} else {
		tmp = 1.0 + (3.0 + ((z * -4.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.85e-12:
		tmp = 1.0 + (3.0 + (x * (4.0 / y)))
	elif y <= 7.4e+28:
		tmp = 1.0 + ((4.0 * (x - z)) / y)
	else:
		tmp = 1.0 + (3.0 + ((z * -4.0) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.85e-12)
		tmp = Float64(1.0 + Float64(3.0 + Float64(x * Float64(4.0 / y))));
	elseif (y <= 7.4e+28)
		tmp = Float64(1.0 + Float64(Float64(4.0 * Float64(x - z)) / y));
	else
		tmp = Float64(1.0 + Float64(3.0 + Float64(Float64(z * -4.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.85e-12)
		tmp = 1.0 + (3.0 + (x * (4.0 / y)));
	elseif (y <= 7.4e+28)
		tmp = 1.0 + ((4.0 * (x - z)) / y);
	else
		tmp = 1.0 + (3.0 + ((z * -4.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.85e-12], N[(1.0 + N[(3.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e+28], N[(1.0 + N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(3.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.84999999999999999e-12

   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. Taylor expanded in x around inf 84.4%

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

      1. associate-*r/ 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r/ 84.3%

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

   8. Simplified 84.3%

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

   if -1.84999999999999999e-12 < y < 7.3999999999999998e28

   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 95.1%

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

   if 7.3999999999999998e28 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 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 0 88.9%

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

      1. associate-*r/ 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-12}:\\ \;\;\;\;1 + \left(3 + x \cdot \frac{4}{y}\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+28}:\\ \;\;\;\;1 + \frac{4 \cdot \left(x - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + \frac{z \cdot -4}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+44}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e-15) 4.0 (if (<= y 2.25e+44) (+ 1.0 (* z (/ -4.0 y))) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e-15) {
		tmp = 4.0;
	} else if (y <= 2.25e+44) {
		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 (y <= (-5.5d-15)) then
        tmp = 4.0d0
    else if (y <= 2.25d+44) 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 (y <= -5.5e-15) {
		tmp = 4.0;
	} else if (y <= 2.25e+44) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e-15:
		tmp = 4.0
	elif y <= 2.25e+44:
		tmp = 1.0 + (z * (-4.0 / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e-15)
		tmp = 4.0;
	elseif (y <= 2.25e+44)
		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 (y <= -5.5e-15)
		tmp = 4.0;
	elseif (y <= 2.25e+44)
		tmp = 1.0 + (z * (-4.0 / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e-15], 4.0, If[LessEqual[y, 2.25e+44], N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000002e-15 or 2.25e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 65.2%

      \[\leadsto 1 + \color{blue}{3} \]

   if -5.5000000000000002e-15 < y < 2.25e44

   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 z around inf 44.3%

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

      1. metadata-eval 44.3%

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

      2. distribute-lft-neg-in 44.3%

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

      3. *-lft-identity 44.3%

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

      4. associate-*l/ 44.2%

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

      5. associate-*l* 44.2%

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

      6. *-commutative 44.2%

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

      7. distribute-rgt-neg-in 44.2%

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

      8. associate-*r/ 44.2%

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

      9. metadata-eval 44.2%

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

      10. distribute-neg-frac 44.2%

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

      11. metadata-eval 44.2%

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

   5. Simplified 44.2%

      \[\leadsto 1 + \color{blue}{z \cdot \frac{-4}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+44}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 33.6%

   \[\leadsto 1 + \color{blue}{3} \]

4. Final simplification 33.6%

   \[\leadsto 4 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024082 
(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)))