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

Percentage Accurate: 99.8% → 99.9%

Time: 6.5s

Alternatives: 13

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% 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: 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. Add Preprocessing

Alternative 2: 86.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot \left(x - z\right)}{y}\\ t_1 := 4 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+37}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+130}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 (- x z)) y))) (t_1 (+ 4.0 (* -4.0 (/ z y)))))
   (if (<= z -1.7e+129)
     t_1
     (if (<= z -5.8e-19)
       t_0
       (if (<= z 1.25e+37)
         (+ 4.0 (* 4.0 (/ x y)))
         (if (<= z 7.2e+130) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * (x - z)) / y);
	double t_1 = 4.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.7e+129) {
		tmp = t_1;
	} else if (z <= -5.8e-19) {
		tmp = t_0;
	} else if (z <= 1.25e+37) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if (z <= 7.2e+130) {
		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 + ((4.0d0 * (x - z)) / y)
    t_1 = 4.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-1.7d+129)) then
        tmp = t_1
    else if (z <= (-5.8d-19)) then
        tmp = t_0
    else if (z <= 1.25d+37) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else if (z <= 7.2d+130) 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 + ((4.0 * (x - z)) / y);
	double t_1 = 4.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.7e+129) {
		tmp = t_1;
	} else if (z <= -5.8e-19) {
		tmp = t_0;
	} else if (z <= 1.25e+37) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if (z <= 7.2e+130) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * (x - z)) / y)
	t_1 = 4.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -1.7e+129:
		tmp = t_1
	elif z <= -5.8e-19:
		tmp = t_0
	elif z <= 1.25e+37:
		tmp = 4.0 + (4.0 * (x / y))
	elif z <= 7.2e+130:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * Float64(x - z)) / y))
	t_1 = Float64(4.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -1.7e+129)
		tmp = t_1;
	elseif (z <= -5.8e-19)
		tmp = t_0;
	elseif (z <= 1.25e+37)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	elseif (z <= 7.2e+130)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * (x - z)) / y);
	t_1 = 4.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -1.7e+129)
		tmp = t_1;
	elseif (z <= -5.8e-19)
		tmp = t_0;
	elseif (z <= 1.25e+37)
		tmp = 4.0 + (4.0 * (x / y));
	elseif (z <= 7.2e+130)
		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[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+129], t$95$1, If[LessEqual[z, -5.8e-19], t$95$0, If[LessEqual[z, 1.25e+37], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+130], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000009e129 or 7.2000000000000002e130 < 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 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 94.0%

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

   7. Taylor expanded in z around 0 94.0%

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

   if -1.70000000000000009e129 < z < -5.8e-19 or 1.24999999999999997e37 < z < 7.2000000000000002e130

   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 86.5%

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

   if -5.8e-19 < z < 1.24999999999999997e37

   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 90.9%

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

      1. associate-*r/ 90.9%

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

      2. associate-*l/ 90.8%

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

      3. associate-/r/ 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in y around inf 90.9%

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

Alternative 3: 86.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \left(x - z\right) \cdot \frac{4}{y}\\ t_1 := 4 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+35}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+131}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (- x z) (/ 4.0 y)))) (t_1 (+ 4.0 (* -4.0 (/ z y)))))
   (if (<= z -1.75e+130)
     t_1
     (if (<= z -1.9e-18)
       t_0
       (if (<= z 8e+35)
         (+ 4.0 (* 4.0 (/ x y)))
         (if (<= z 2.6e+131) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((x - z) * (4.0 / y));
	double t_1 = 4.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.75e+130) {
		tmp = t_1;
	} else if (z <= -1.9e-18) {
		tmp = t_0;
	} else if (z <= 8e+35) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if (z <= 2.6e+131) {
		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 + ((x - z) * (4.0d0 / y))
    t_1 = 4.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-1.75d+130)) then
        tmp = t_1
    else if (z <= (-1.9d-18)) then
        tmp = t_0
    else if (z <= 8d+35) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else if (z <= 2.6d+131) 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 + ((x - z) * (4.0 / y));
	double t_1 = 4.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.75e+130) {
		tmp = t_1;
	} else if (z <= -1.9e-18) {
		tmp = t_0;
	} else if (z <= 8e+35) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if (z <= 2.6e+131) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((x - z) * (4.0 / y))
	t_1 = 4.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -1.75e+130:
		tmp = t_1
	elif z <= -1.9e-18:
		tmp = t_0
	elif z <= 8e+35:
		tmp = 4.0 + (4.0 * (x / y))
	elif z <= 2.6e+131:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(x - z) * Float64(4.0 / y)))
	t_1 = Float64(4.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -1.75e+130)
		tmp = t_1;
	elseif (z <= -1.9e-18)
		tmp = t_0;
	elseif (z <= 8e+35)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	elseif (z <= 2.6e+131)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((x - z) * (4.0 / y));
	t_1 = 4.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -1.75e+130)
		tmp = t_1;
	elseif (z <= -1.9e-18)
		tmp = t_0;
	elseif (z <= 8e+35)
		tmp = 4.0 + (4.0 * (x / y));
	elseif (z <= 2.6e+131)
		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[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+130], t$95$1, If[LessEqual[z, -1.9e-18], t$95$0, If[LessEqual[z, 8e+35], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+131], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75e130 or 2.6e131 < 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 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 94.0%

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

   7. Taylor expanded in z around 0 94.0%

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

   if -1.75e130 < z < -1.8999999999999999e-18 or 7.9999999999999997e35 < z < 2.6e131

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. *-lft-identity 86.5%

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

      2. associate-*l/ 86.3%

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

      3. associate-*r* 86.3%

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

      4. associate-*r/ 86.3%

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

      5. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

   if -1.8999999999999999e-18 < z < 7.9999999999999997e35

   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 90.9%

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

      1. associate-*r/ 90.9%

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

      2. associate-*l/ 90.8%

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

      3. associate-/r/ 90.8%

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

   8. Simplified 90.8%

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

   9. Taylor expanded in y around inf 90.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+130}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-18}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+35}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+131}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+76} \lor \neg \left(y \leq -1.55 \cdot 10^{-23}\right) \land y \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+161)
   4.0
   (if (or (<= y -2.65e+76) (and (not (<= y -1.55e-23)) (<= y 1.55e-18)))
     (/ (* z -4.0) y)
     4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+161) {
		tmp = 4.0;
	} else if ((y <= -2.65e+76) || (!(y <= -1.55e-23) && (y <= 1.55e-18))) {
		tmp = (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 <= (-1.4d+161)) then
        tmp = 4.0d0
    else if ((y <= (-2.65d+76)) .or. (.not. (y <= (-1.55d-23))) .and. (y <= 1.55d-18)) then
        tmp = (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 <= -1.4e+161) {
		tmp = 4.0;
	} else if ((y <= -2.65e+76) || (!(y <= -1.55e-23) && (y <= 1.55e-18))) {
		tmp = (z * -4.0) / y;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+161:
		tmp = 4.0
	elif (y <= -2.65e+76) or (not (y <= -1.55e-23) and (y <= 1.55e-18)):
		tmp = (z * -4.0) / y
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+161)
		tmp = 4.0;
	elseif ((y <= -2.65e+76) || (!(y <= -1.55e-23) && (y <= 1.55e-18)))
		tmp = Float64(Float64(z * -4.0) / y);
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e+161)
		tmp = 4.0;
	elseif ((y <= -2.65e+76) || (~((y <= -1.55e-23)) && (y <= 1.55e-18)))
		tmp = (z * -4.0) / y;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+161], 4.0, If[Or[LessEqual[y, -2.65e+76], And[N[Not[LessEqual[y, -1.55e-23]], $MachinePrecision], LessEqual[y, 1.55e-18]]], N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e161 or -2.65000000000000008e76 < y < -1.5499999999999999e-23 or 1.55000000000000003e-18 < 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 77.3%

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

   7. Taylor expanded in z around 0 61.1%

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

   if -1.4000000000000001e161 < y < -2.65000000000000008e76 or -1.5499999999999999e-23 < y < 1.55000000000000003e-18

   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 59.5%

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

   7. Taylor expanded in z around inf 53.8%

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

      1. associate-*r/ 53.8%

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

   9. Simplified 53.8%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+76} \lor \neg \left(y \leq -1.55 \cdot 10^{-23}\right) \land y \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+80} \lor \neg \left(y \leq -8.2 \cdot 10^{-23}\right) \land y \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+161)
   4.0
   (if (or (<= y -1.75e+80) (and (not (<= y -8.2e-23)) (<= y 1.55e-18)))
     (* z (/ -4.0 y))
     4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+161) {
		tmp = 4.0;
	} else if ((y <= -1.75e+80) || (!(y <= -8.2e-23) && (y <= 1.55e-18))) {
		tmp = 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 <= (-1.4d+161)) then
        tmp = 4.0d0
    else if ((y <= (-1.75d+80)) .or. (.not. (y <= (-8.2d-23))) .and. (y <= 1.55d-18)) then
        tmp = 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 <= -1.4e+161) {
		tmp = 4.0;
	} else if ((y <= -1.75e+80) || (!(y <= -8.2e-23) && (y <= 1.55e-18))) {
		tmp = z * (-4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+161:
		tmp = 4.0
	elif (y <= -1.75e+80) or (not (y <= -8.2e-23) and (y <= 1.55e-18)):
		tmp = z * (-4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+161)
		tmp = 4.0;
	elseif ((y <= -1.75e+80) || (!(y <= -8.2e-23) && (y <= 1.55e-18)))
		tmp = 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 <= -1.4e+161)
		tmp = 4.0;
	elseif ((y <= -1.75e+80) || (~((y <= -8.2e-23)) && (y <= 1.55e-18)))
		tmp = z * (-4.0 / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+161], 4.0, If[Or[LessEqual[y, -1.75e+80], And[N[Not[LessEqual[y, -8.2e-23]], $MachinePrecision], LessEqual[y, 1.55e-18]]], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e161 or -1.74999999999999997e80 < y < -8.20000000000000059e-23 or 1.55000000000000003e-18 < 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 77.3%

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

   7. Taylor expanded in z around 0 61.1%

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

   if -1.4000000000000001e161 < y < -1.74999999999999997e80 or -8.20000000000000059e-23 < y < 1.55000000000000003e-18

   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 59.5%

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

   7. Taylor expanded in z around inf 53.8%

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

      1. *-commutative 53.8%

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

      2. associate-*l/ 53.8%

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

      3. associate-*r/ 53.6%

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

   9. Simplified 53.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+80} \lor \neg \left(y \leq -8.2 \cdot 10^{-23}\right) \land y \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-22}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;\frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+161)
   4.0
   (if (<= y -1.65e+90)
     (* z (/ -4.0 y))
     (if (<= y -1.45e-22) 4.0 (if (<= y 1.55e-18) (/ -4.0 (/ y z)) 4.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+161) {
		tmp = 4.0;
	} else if (y <= -1.65e+90) {
		tmp = z * (-4.0 / y);
	} else if (y <= -1.45e-22) {
		tmp = 4.0;
	} else if (y <= 1.55e-18) {
		tmp = -4.0 / (y / z);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.4d+161)) then
        tmp = 4.0d0
    else if (y <= (-1.65d+90)) then
        tmp = z * ((-4.0d0) / y)
    else if (y <= (-1.45d-22)) then
        tmp = 4.0d0
    else if (y <= 1.55d-18) then
        tmp = (-4.0d0) / (y / z)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+161) {
		tmp = 4.0;
	} else if (y <= -1.65e+90) {
		tmp = z * (-4.0 / y);
	} else if (y <= -1.45e-22) {
		tmp = 4.0;
	} else if (y <= 1.55e-18) {
		tmp = -4.0 / (y / z);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+161:
		tmp = 4.0
	elif y <= -1.65e+90:
		tmp = z * (-4.0 / y)
	elif y <= -1.45e-22:
		tmp = 4.0
	elif y <= 1.55e-18:
		tmp = -4.0 / (y / z)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+161)
		tmp = 4.0;
	elseif (y <= -1.65e+90)
		tmp = Float64(z * Float64(-4.0 / y));
	elseif (y <= -1.45e-22)
		tmp = 4.0;
	elseif (y <= 1.55e-18)
		tmp = Float64(-4.0 / Float64(y / z));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e+161)
		tmp = 4.0;
	elseif (y <= -1.65e+90)
		tmp = z * (-4.0 / y);
	elseif (y <= -1.45e-22)
		tmp = 4.0;
	elseif (y <= 1.55e-18)
		tmp = -4.0 / (y / z);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+161], 4.0, If[LessEqual[y, -1.65e+90], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-22], 4.0, If[LessEqual[y, 1.55e-18], N[(-4.0 / N[(y / z), $MachinePrecision]), $MachinePrecision], 4.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4000000000000001e161 or -1.65000000000000004e90 < y < -1.4500000000000001e-22 or 1.55000000000000003e-18 < 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 77.3%

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

   7. Taylor expanded in z around 0 61.1%

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

   if -1.4000000000000001e161 < y < -1.65000000000000004e90

   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 61.4%

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

   7. Taylor expanded in z around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l/ 50.2%

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

      3. associate-*r/ 49.9%

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

   9. Simplified 49.9%

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

   if -1.4500000000000001e-22 < y < 1.55000000000000003e-18

   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 59.3%

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

   7. Taylor expanded in z around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-*l/ 54.1%

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

      3. associate-*r/ 54.0%

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

   9. Simplified 54.0%

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

       1. associate-*r/ 54.1%

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

       2. *-commutative 54.1%

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

       3. associate-*r/ 54.1%

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

       4. clear-num 54.0%

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

       5. un-div-inv 54.0%

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

   11. Applied egg-rr 54.0%

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

Alternative 7: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+66} \lor \neg \left(z \leq 1.22 \cdot 10^{+33}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.2e+66) (not (<= z 1.22e+33)))
   (+ 4.0 (* -4.0 (/ z y)))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.2e+66) || !(z <= 1.22e+33)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.2d+66)) .or. (.not. (z <= 1.22d+33))) then
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.2e+66) || !(z <= 1.22e+33)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.2e+66) or not (z <= 1.22e+33):
		tmp = 4.0 + (-4.0 * (z / y))
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.2e+66) || !(z <= 1.22e+33))
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.2e+66) || ~((z <= 1.22e+33)))
		tmp = 4.0 + (-4.0 * (z / y));
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.2e+66], N[Not[LessEqual[z, 1.22e+33]], $MachinePrecision]], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999989e66 or 1.22000000000000005e33 < 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 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 85.8%

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

   7. Taylor expanded in z around 0 85.8%

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

   if -8.19999999999999989e66 < z < 1.22000000000000005e33

   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 87.1%

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

      1. associate-*r/ 87.1%

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

      2. associate-*l/ 86.9%

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

      3. associate-/r/ 87.0%

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

   8. Simplified 87.0%

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

   9. Taylor expanded in y around inf 87.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+66} \lor \neg \left(z \leq 1.22 \cdot 10^{+33}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+136} \lor \neg \left(x \leq 6.2 \cdot 10^{+128}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e+136) (not (<= x 6.2e+128)))
   (+ 1.0 (* 4.0 (/ x y)))
   (+ 4.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e+136) || !(x <= 6.2e+128)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3.3d+136)) .or. (.not. (x <= 6.2d+128))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e+136) || !(x <= 6.2e+128)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e+136) or not (x <= 6.2e+128):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e+136) || !(x <= 6.2e+128))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.3e+136) || ~((x <= 6.2e+128)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 4.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e+136], N[Not[LessEqual[x, 6.2e+128]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999992e136 or 6.20000000000000008e128 < 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 83.1%

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

      1. *-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -3.29999999999999992e136 < x < 6.20000000000000008e128

   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 82.2%

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

   7. Taylor expanded in z around 0 82.2%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+136} \lor \neg \left(x \leq 6.2 \cdot 10^{+128}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-29} \lor \neg \left(x \leq 5.2 \cdot 10^{+87}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-29) (not (<= x 5.2e+87)))
   (+ 1.0 (* 4.0 (/ x y)))
   (+ 1.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-29) || !(x <= 5.2e+87)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + ((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 <= (-2.1d-29)) .or. (.not. (x <= 5.2d+87))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 1.0d0 + ((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 <= -2.1e-29) || !(x <= 5.2e+87)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-29) or not (x <= 5.2e+87):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 1.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-29) || !(x <= 5.2e+87))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(1.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e-29) || ~((x <= 5.2e+87)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 1.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-29], N[Not[LessEqual[x, 5.2e+87]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999989e-29 or 5.19999999999999997e87 < 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 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -2.09999999999999989e-29 < x < 5.19999999999999997e87

   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 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-*l/ 56.6%

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

   5. Simplified 56.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-29} \lor \neg \left(x \leq 5.2 \cdot 10^{+87}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-37} \lor \neg \left(x \leq 5.8 \cdot 10^{+87}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e-37) (not (<= x 5.8e+87)))
   (+ 1.0 (* 4.0 (/ x y)))
   (+ 1.0 (* z (/ -4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-37) || !(x <= 5.8e+87)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (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 <= (-1.7d-37)) .or. (.not. (x <= 5.8d+87))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 1.0d0 + (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 <= -1.7e-37) || !(x <= 5.8e+87)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (z * (-4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e-37) or not (x <= 5.8e+87):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 1.0 + (z * (-4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e-37) || !(x <= 5.8e+87))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(1.0 + Float64(z * Float64(-4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.7e-37) || ~((x <= 5.8e+87)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 1.0 + (z * (-4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-37], N[Not[LessEqual[x, 5.8e+87]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000009e-37 or 5.7999999999999996e87 < 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 67.2%

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

      1. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if -1.70000000000000009e-37 < x < 5.7999999999999996e87

   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 56.9%

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

      1. metadata-eval 56.9%

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

      2. distribute-lft-neg-in 56.9%

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

      3. *-lft-identity 56.9%

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

      4. associate-*l/ 56.7%

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

      5. associate-*l* 56.7%

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

      6. *-commutative 56.7%

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

      7. distribute-rgt-neg-in 56.7%

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

      8. associate-*r/ 56.7%

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

      9. metadata-eval 56.7%

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

      10. distribute-neg-frac 56.7%

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

      11. metadata-eval 56.7%

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

   5. Simplified 56.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-37} \lor \neg \left(x \leq 5.8 \cdot 10^{+87}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-26} \lor \neg \left(z \leq 1.05 \cdot 10^{+36}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.1e-26) (not (<= z 1.05e+36))) (+ 1.0 (* z (/ -4.0 y))) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-26) || !(z <= 1.05e+36)) {
		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 <= (-4.1d-26)) .or. (.not. (z <= 1.05d+36))) 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 <= -4.1e-26) || !(z <= 1.05e+36)) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.1e-26) or not (z <= 1.05e+36):
		tmp = 1.0 + (z * (-4.0 / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.1e-26) || !(z <= 1.05e+36))
		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 <= -4.1e-26) || ~((z <= 1.05e+36)))
		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, -4.1e-26], N[Not[LessEqual[z, 1.05e+36]], $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 < -4.0999999999999999e-26 or 1.05000000000000002e36 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 64.4%

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

      1. metadata-eval 64.4%

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

      2. distribute-lft-neg-in 64.4%

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

      3. *-lft-identity 64.4%

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

      4. associate-*l/ 64.2%

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

      5. associate-*l* 64.2%

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

      6. *-commutative 64.2%

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

      7. distribute-rgt-neg-in 64.2%

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

      8. associate-*r/ 64.2%

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

      9. metadata-eval 64.2%

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

      10. distribute-neg-frac 64.2%

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

      11. metadata-eval 64.2%

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

   5. Simplified 64.2%

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

   if -4.0999999999999999e-26 < z < 1.05000000000000002e36

   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 53.7%

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

   7. Taylor expanded in z around 0 45.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-26} \lor \neg \left(z \leq 1.05 \cdot 10^{+36}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.8% 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 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 67.5%

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

7. Taylor expanded in z around 0 31.5%

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

Alternative 13: 7.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 39.3%

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

   1. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in x around 0 7.7%

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

Reproduce

herbie shell --seed 2024107 
(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)))