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

Percentage Accurate: 99.8% → 99.9%

Time: 7.1s

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: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \left(x - z\right) \cdot \frac{4}{y}\\ t_1 := 4 + -4 \cdot \frac{z}{y}\\ t_2 := 4 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+129}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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))))
        (t_2 (+ 4.0 (* 4.0 (/ x y)))))
   (if (<= z -1.2e+175)
     t_1
     (if (<= z -3.5e-13)
       t_0
       (if (<= z -2.55e-77)
         t_2
         (if (<= z -2.1e-94)
           t_0
           (if (<= z 3.7e+37) t_2 (if (<= z 3.5e+129) 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 t_2 = 4.0 + (4.0 * (x / y));
	double tmp;
	if (z <= -1.2e+175) {
		tmp = t_1;
	} else if (z <= -3.5e-13) {
		tmp = t_0;
	} else if (z <= -2.55e-77) {
		tmp = t_2;
	} else if (z <= -2.1e-94) {
		tmp = t_0;
	} else if (z <= 3.7e+37) {
		tmp = t_2;
	} else if (z <= 3.5e+129) {
		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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 + ((x - z) * (4.0d0 / y))
    t_1 = 4.0d0 + ((-4.0d0) * (z / y))
    t_2 = 4.0d0 + (4.0d0 * (x / y))
    if (z <= (-1.2d+175)) then
        tmp = t_1
    else if (z <= (-3.5d-13)) then
        tmp = t_0
    else if (z <= (-2.55d-77)) then
        tmp = t_2
    else if (z <= (-2.1d-94)) then
        tmp = t_0
    else if (z <= 3.7d+37) then
        tmp = t_2
    else if (z <= 3.5d+129) 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 t_2 = 4.0 + (4.0 * (x / y));
	double tmp;
	if (z <= -1.2e+175) {
		tmp = t_1;
	} else if (z <= -3.5e-13) {
		tmp = t_0;
	} else if (z <= -2.55e-77) {
		tmp = t_2;
	} else if (z <= -2.1e-94) {
		tmp = t_0;
	} else if (z <= 3.7e+37) {
		tmp = t_2;
	} else if (z <= 3.5e+129) {
		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))
	t_2 = 4.0 + (4.0 * (x / y))
	tmp = 0
	if z <= -1.2e+175:
		tmp = t_1
	elif z <= -3.5e-13:
		tmp = t_0
	elif z <= -2.55e-77:
		tmp = t_2
	elif z <= -2.1e-94:
		tmp = t_0
	elif z <= 3.7e+37:
		tmp = t_2
	elif z <= 3.5e+129:
		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)))
	t_2 = Float64(4.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (z <= -1.2e+175)
		tmp = t_1;
	elseif (z <= -3.5e-13)
		tmp = t_0;
	elseif (z <= -2.55e-77)
		tmp = t_2;
	elseif (z <= -2.1e-94)
		tmp = t_0;
	elseif (z <= 3.7e+37)
		tmp = t_2;
	elseif (z <= 3.5e+129)
		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));
	t_2 = 4.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (z <= -1.2e+175)
		tmp = t_1;
	elseif (z <= -3.5e-13)
		tmp = t_0;
	elseif (z <= -2.55e-77)
		tmp = t_2;
	elseif (z <= -2.1e-94)
		tmp = t_0;
	elseif (z <= 3.7e+37)
		tmp = t_2;
	elseif (z <= 3.5e+129)
		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]}, Block[{t$95$2 = N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+175], t$95$1, If[LessEqual[z, -3.5e-13], t$95$0, If[LessEqual[z, -2.55e-77], t$95$2, If[LessEqual[z, -2.1e-94], t$95$0, If[LessEqual[z, 3.7e+37], t$95$2, If[LessEqual[z, 3.5e+129], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e175 or 3.4999999999999998e129 < 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 93.0%

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

   7. Taylor expanded in z around 0 93.0%

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

   if -1.2e175 < z < -3.5000000000000002e-13 or -2.55000000000000016e-77 < z < -2.1000000000000001e-94 or 3.6999999999999999e37 < z < 3.4999999999999998e129

   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 85.6%

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

      1. *-lft-identity 85.6%

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

      2. associate-*l/ 85.3%

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

      3. associate-*r* 85.3%

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

      4. associate-*r/ 85.3%

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

      5. metadata-eval 85.3%

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

   5. Simplified 85.3%

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

   if -3.5000000000000002e-13 < z < -2.55000000000000016e-77 or -2.1000000000000001e-94 < z < 3.6999999999999999e37

   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 92.1%

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

      1. associate-*r/ 92.1%

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

      2. associate-*l/ 91.9%

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

      3. associate-/r/ 92.0%

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

   8. Simplified 92.0%

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

   9. Taylor expanded in y around inf 92.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+175}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-77}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+129}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-66} \lor \neg \left(x \leq 1.16 \cdot 10^{+27}\right) \land \left(x \leq 1.4 \cdot 10^{+60} \lor \neg \left(x \leq 1.5 \cdot 10^{+77}\right)\right):\\ \;\;\;\;1 + \frac{4 \cdot \left(x - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.7e+134)
   (+ 4.0 (* 4.0 (/ x y)))
   (if (or (<= x -3.4e-66)
           (and (not (<= x 1.16e+27))
                (or (<= x 1.4e+60) (not (<= x 1.5e+77)))))
     (+ 1.0 (/ (* 4.0 (- x z)) y))
     (+ 4.0 (* -4.0 (/ z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.7e+134) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if ((x <= -3.4e-66) || (!(x <= 1.16e+27) && ((x <= 1.4e+60) || !(x <= 1.5e+77)))) {
		tmp = 1.0 + ((4.0 * (x - z)) / 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 <= (-2.7d+134)) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else if ((x <= (-3.4d-66)) .or. (.not. (x <= 1.16d+27)) .and. (x <= 1.4d+60) .or. (.not. (x <= 1.5d+77))) then
        tmp = 1.0d0 + ((4.0d0 * (x - z)) / 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 <= -2.7e+134) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if ((x <= -3.4e-66) || (!(x <= 1.16e+27) && ((x <= 1.4e+60) || !(x <= 1.5e+77)))) {
		tmp = 1.0 + ((4.0 * (x - z)) / y);
	} else {
		tmp = 4.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.7e+134:
		tmp = 4.0 + (4.0 * (x / y))
	elif (x <= -3.4e-66) or (not (x <= 1.16e+27) and ((x <= 1.4e+60) or not (x <= 1.5e+77))):
		tmp = 1.0 + ((4.0 * (x - z)) / y)
	else:
		tmp = 4.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.7e+134)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	elseif ((x <= -3.4e-66) || (!(x <= 1.16e+27) && ((x <= 1.4e+60) || !(x <= 1.5e+77))))
		tmp = Float64(1.0 + Float64(Float64(4.0 * Float64(x - z)) / 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 <= -2.7e+134)
		tmp = 4.0 + (4.0 * (x / y));
	elseif ((x <= -3.4e-66) || (~((x <= 1.16e+27)) && ((x <= 1.4e+60) || ~((x <= 1.5e+77)))))
		tmp = 1.0 + ((4.0 * (x - z)) / y);
	else
		tmp = 4.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.7e+134], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.4e-66], And[N[Not[LessEqual[x, 1.16e+27]], $MachinePrecision], Or[LessEqual[x, 1.4e+60], N[Not[LessEqual[x, 1.5e+77]], $MachinePrecision]]]], N[(1.0 + N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e134

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 93.0%

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

      1. associate-*r/ 93.0%

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

      2. associate-*l/ 92.8%

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

      3. associate-/r/ 92.9%

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

   8. Simplified 92.9%

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

   9. Taylor expanded in y around inf 93.0%

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

   if -2.7e134 < x < -3.39999999999999997e-66 or 1.16e27 < x < 1.4e60 or 1.4999999999999999e77 < 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 83.8%

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

   if -3.39999999999999997e-66 < x < 1.16e27 or 1.4e60 < x < 1.4999999999999999e77

   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 92.1%

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

   7. Taylor expanded in z around 0 92.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-66} \lor \neg \left(x \leq 1.16 \cdot 10^{+27}\right) \land \left(x \leq 1.4 \cdot 10^{+60} \lor \neg \left(x \leq 1.5 \cdot 10^{+77}\right)\right):\\ \;\;\;\;1 + \frac{4 \cdot \left(x - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+68} \lor \neg \left(z \leq -4.8 \cdot 10^{-6} \lor \neg \left(z \leq -2.85 \cdot 10^{-15}\right) \land z \leq 1.35 \cdot 10^{+29}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e+68)
         (not
          (or (<= z -4.8e-6) (and (not (<= z -2.85e-15)) (<= z 1.35e+29)))))
   (+ 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 <= -3.5e+68) || !((z <= -4.8e-6) || (!(z <= -2.85e-15) && (z <= 1.35e+29)))) {
		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 <= (-3.5d+68)) .or. (.not. (z <= (-4.8d-6)) .or. (.not. (z <= (-2.85d-15))) .and. (z <= 1.35d+29))) 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 <= -3.5e+68) || !((z <= -4.8e-6) || (!(z <= -2.85e-15) && (z <= 1.35e+29)))) {
		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 <= -3.5e+68) or not ((z <= -4.8e-6) or (not (z <= -2.85e-15) and (z <= 1.35e+29))):
		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 <= -3.5e+68) || !((z <= -4.8e-6) || (!(z <= -2.85e-15) && (z <= 1.35e+29))))
		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 <= -3.5e+68) || ~(((z <= -4.8e-6) || (~((z <= -2.85e-15)) && (z <= 1.35e+29)))))
		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, -3.5e+68], N[Not[Or[LessEqual[z, -4.8e-6], And[N[Not[LessEqual[z, -2.85e-15]], $MachinePrecision], LessEqual[z, 1.35e+29]]]], $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 < -3.49999999999999977e68 or -4.7999999999999998e-6 < z < -2.8500000000000002e-15 or 1.35e29 < 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 85.5%

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

   7. Taylor expanded in z around 0 85.5%

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

   if -3.49999999999999977e68 < z < -4.7999999999999998e-6 or -2.8500000000000002e-15 < z < 1.35e29

   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 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-*l/ 88.6%

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

      3. associate-/r/ 88.6%

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

   8. Simplified 88.6%

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

   9. Taylor expanded in y around inf 88.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+68} \lor \neg \left(z \leq -4.8 \cdot 10^{-6} \lor \neg \left(z \leq -2.85 \cdot 10^{-15}\right) \land z \leq 1.35 \cdot 10^{+29}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{-9} \lor \neg \left(z \leq -2.15 \cdot 10^{-77} \lor \neg \left(z \leq -2.4 \cdot 10^{-111}\right) \land z \leq 3.5 \cdot 10^{+15}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.42e-9)
         (not
          (or (<= z -2.15e-77) (and (not (<= z -2.4e-111)) (<= z 3.5e+15)))))
   (+ 1.0 (* z (/ -4.0 y)))
   4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.42e-9) || !((z <= -2.15e-77) || (!(z <= -2.4e-111) && (z <= 3.5e+15)))) {
		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 <= (-1.42d-9)) .or. (.not. (z <= (-2.15d-77)) .or. (.not. (z <= (-2.4d-111))) .and. (z <= 3.5d+15))) 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 <= -1.42e-9) || !((z <= -2.15e-77) || (!(z <= -2.4e-111) && (z <= 3.5e+15)))) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.42e-9) or not ((z <= -2.15e-77) or (not (z <= -2.4e-111) and (z <= 3.5e+15))):
		tmp = 1.0 + (z * (-4.0 / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.42e-9) || !((z <= -2.15e-77) || (!(z <= -2.4e-111) && (z <= 3.5e+15))))
		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 <= -1.42e-9) || ~(((z <= -2.15e-77) || (~((z <= -2.4e-111)) && (z <= 3.5e+15)))))
		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, -1.42e-9], N[Not[Or[LessEqual[z, -2.15e-77], And[N[Not[LessEqual[z, -2.4e-111]], $MachinePrecision], LessEqual[z, 3.5e+15]]]], $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 < -1.4200000000000001e-9 or -2.1500000000000001e-77 < z < -2.4000000000000001e-111 or 3.5e15 < 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 62.9%

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

      1. metadata-eval 62.9%

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

      2. distribute-lft-neg-in 62.9%

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

      3. *-lft-identity 62.9%

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

      4. associate-*l/ 62.7%

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

      5. associate-*l* 62.7%

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

      6. *-commutative 62.7%

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

      7. distribute-rgt-neg-in 62.7%

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

      8. associate-*r/ 62.7%

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

      9. metadata-eval 62.7%

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

      10. distribute-neg-frac 62.7%

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

      11. metadata-eval 62.7%

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

   5. Simplified 62.7%

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

   if -1.4200000000000001e-9 < z < -2.1500000000000001e-77 or -2.4000000000000001e-111 < z < 3.5e15

   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 53.2%

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

   7. Taylor expanded in z around 0 46.5%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{-9} \lor \neg \left(z \leq -2.15 \cdot 10^{-77} \lor \neg \left(z \leq -2.4 \cdot 10^{-111}\right) \land z \leq 3.5 \cdot 10^{+15}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-14} \lor \neg \left(z \leq -2.25 \cdot 10^{-76} \lor \neg \left(z \leq -2.45 \cdot 10^{-113}\right) \land z \leq 4.7 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.2e-14)
         (not
          (or (<= z -2.25e-76) (and (not (<= z -2.45e-113)) (<= z 4.7e+16)))))
   (/ (* z -4.0) y)
   4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.2e-14) || !((z <= -2.25e-76) || (!(z <= -2.45e-113) && (z <= 4.7e+16)))) {
		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 ((z <= (-7.2d-14)) .or. (.not. (z <= (-2.25d-76)) .or. (.not. (z <= (-2.45d-113))) .and. (z <= 4.7d+16))) 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 ((z <= -7.2e-14) || !((z <= -2.25e-76) || (!(z <= -2.45e-113) && (z <= 4.7e+16)))) {
		tmp = (z * -4.0) / y;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.2e-14) or not ((z <= -2.25e-76) or (not (z <= -2.45e-113) and (z <= 4.7e+16))):
		tmp = (z * -4.0) / y
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.2e-14) || !((z <= -2.25e-76) || (!(z <= -2.45e-113) && (z <= 4.7e+16))))
		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 ((z <= -7.2e-14) || ~(((z <= -2.25e-76) || (~((z <= -2.45e-113)) && (z <= 4.7e+16)))))
		tmp = (z * -4.0) / y;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.2e-14], N[Not[Or[LessEqual[z, -2.25e-76], And[N[Not[LessEqual[z, -2.45e-113]], $MachinePrecision], LessEqual[z, 4.7e+16]]]], $MachinePrecision]], N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999996e-14 or -2.25e-76 < z < -2.4500000000000001e-113 or 4.7e16 < 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 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 78.8%

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

   7. Taylor expanded in z around inf 60.0%

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

      1. associate-*r/ 60.0%

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

   9. Simplified 60.0%

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

   if -7.1999999999999996e-14 < z < -2.25e-76 or -2.4500000000000001e-113 < z < 4.7e16

   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 52.8%

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

   7. Taylor expanded in z around 0 46.0%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-14} \lor \neg \left(z \leq -2.25 \cdot 10^{-76} \lor \neg \left(z \leq -2.45 \cdot 10^{-113}\right) \land z \leq 4.7 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-8} \lor \neg \left(z \leq -1.7 \cdot 10^{-76}\right) \land \left(z \leq -6.9 \cdot 10^{-110} \lor \neg \left(z \leq 26000000000000\right)\right):\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e-8)
         (and (not (<= z -1.7e-76))
              (or (<= z -6.9e-110) (not (<= z 26000000000000.0)))))
   (* z (/ -4.0 y))
   4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e-8) || (!(z <= -1.7e-76) && ((z <= -6.9e-110) || !(z <= 26000000000000.0)))) {
		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 ((z <= (-2.2d-8)) .or. (.not. (z <= (-1.7d-76))) .and. (z <= (-6.9d-110)) .or. (.not. (z <= 26000000000000.0d0))) 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 ((z <= -2.2e-8) || (!(z <= -1.7e-76) && ((z <= -6.9e-110) || !(z <= 26000000000000.0)))) {
		tmp = z * (-4.0 / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e-8) or (not (z <= -1.7e-76) and ((z <= -6.9e-110) or not (z <= 26000000000000.0))):
		tmp = z * (-4.0 / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e-8) || (!(z <= -1.7e-76) && ((z <= -6.9e-110) || !(z <= 26000000000000.0))))
		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 ((z <= -2.2e-8) || (~((z <= -1.7e-76)) && ((z <= -6.9e-110) || ~((z <= 26000000000000.0)))))
		tmp = z * (-4.0 / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e-8], And[N[Not[LessEqual[z, -1.7e-76]], $MachinePrecision], Or[LessEqual[z, -6.9e-110], N[Not[LessEqual[z, 26000000000000.0]], $MachinePrecision]]]], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999998e-8 or -1.7e-76 < z < -6.9000000000000004e-110 or 2.6e13 < 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 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 79.0%

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

   7. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-*l/ 59.6%

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

      3. associate-*r/ 59.4%

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

   9. Simplified 59.4%

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

   if -2.1999999999999998e-8 < z < -1.7e-76 or -6.9000000000000004e-110 < z < 2.6e13

   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 52.4%

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

   7. Taylor expanded in z around 0 45.5%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-8} \lor \neg \left(z \leq -1.7 \cdot 10^{-76}\right) \land \left(z \leq -6.9 \cdot 10^{-110} \lor \neg \left(z \leq 26000000000000\right)\right):\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-110} \lor \neg \left(z \leq 9 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.6e-9)
   (* z (/ -4.0 y))
   (if (<= z -1.55e-75)
     4.0
     (if (or (<= z -5.5e-110) (not (<= z 9e+14))) (/ -4.0 (/ y z)) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e-9) {
		tmp = z * (-4.0 / y);
	} else if (z <= -1.55e-75) {
		tmp = 4.0;
	} else if ((z <= -5.5e-110) || !(z <= 9e+14)) {
		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 (z <= (-7.6d-9)) then
        tmp = z * ((-4.0d0) / y)
    else if (z <= (-1.55d-75)) then
        tmp = 4.0d0
    else if ((z <= (-5.5d-110)) .or. (.not. (z <= 9d+14))) 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 (z <= -7.6e-9) {
		tmp = z * (-4.0 / y);
	} else if (z <= -1.55e-75) {
		tmp = 4.0;
	} else if ((z <= -5.5e-110) || !(z <= 9e+14)) {
		tmp = -4.0 / (y / z);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.6e-9:
		tmp = z * (-4.0 / y)
	elif z <= -1.55e-75:
		tmp = 4.0
	elif (z <= -5.5e-110) or not (z <= 9e+14):
		tmp = -4.0 / (y / z)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.6e-9)
		tmp = Float64(z * Float64(-4.0 / y));
	elseif (z <= -1.55e-75)
		tmp = 4.0;
	elseif ((z <= -5.5e-110) || !(z <= 9e+14))
		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 (z <= -7.6e-9)
		tmp = z * (-4.0 / y);
	elseif (z <= -1.55e-75)
		tmp = 4.0;
	elseif ((z <= -5.5e-110) || ~((z <= 9e+14)))
		tmp = -4.0 / (y / z);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.6e-9], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-75], 4.0, If[Or[LessEqual[z, -5.5e-110], N[Not[LessEqual[z, 9e+14]], $MachinePrecision]], N[(-4.0 / N[(y / z), $MachinePrecision]), $MachinePrecision], 4.0]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.60000000000000023e-9

   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 81.9%

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

   7. Taylor expanded in z around inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-*l/ 63.5%

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

      3. associate-*r/ 63.3%

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

   9. Simplified 63.3%

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

   if -7.60000000000000023e-9 < z < -1.55000000000000003e-75 or -5.4999999999999998e-110 < z < 9e14

   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 52.4%

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

   7. Taylor expanded in z around 0 45.5%

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

   if -1.55000000000000003e-75 < z < -5.4999999999999998e-110 or 9e14 < 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 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 76.4%

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

   7. Taylor expanded in z around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-*l/ 56.0%

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

      3. associate-*r/ 55.9%

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

   9. Simplified 55.9%

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

       1. associate-*r/ 56.0%

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

       2. *-commutative 56.0%

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

       3. associate-*r/ 56.0%

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

       4. clear-num 55.9%

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

       5. un-div-inv 55.9%

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

   11. Applied egg-rr 55.9%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-110} \lor \neg \left(z \leq 9 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+234} \lor \neg \left(x \leq 3 \cdot 10^{+87}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.02e+234) (not (<= x 3e+87)))
   (+ 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 <= -1.02e+234) || !(x <= 3e+87)) {
		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 <= (-1.02d+234)) .or. (.not. (x <= 3d+87))) 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 <= -1.02e+234) || !(x <= 3e+87)) {
		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 <= -1.02e+234) or not (x <= 3e+87):
		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 <= -1.02e+234) || !(x <= 3e+87))
		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 <= -1.02e+234) || ~((x <= 3e+87)))
		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, -1.02e+234], N[Not[LessEqual[x, 3e+87]], $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 < -1.02000000000000002e234 or 2.9999999999999999e87 < 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 82.7%

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

      1. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   if -1.02000000000000002e234 < x < 2.9999999999999999e87

   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 80.7%

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

   7. Taylor expanded in z around 0 80.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+234} \lor \neg \left(x \leq 3 \cdot 10^{+87}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1700000000000 \lor \neg \left(x \leq 5.7 \cdot 10^{-22}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1700000000000.0) (not (<= x 5.7e-22)))
   (+ 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 <= -1700000000000.0) || !(x <= 5.7e-22)) {
		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 <= (-1700000000000.0d0)) .or. (.not. (x <= 5.7d-22))) 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 <= -1700000000000.0) || !(x <= 5.7e-22)) {
		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 <= -1700000000000.0) or not (x <= 5.7e-22):
		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 <= -1700000000000.0) || !(x <= 5.7e-22))
		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 <= -1700000000000.0) || ~((x <= 5.7e-22)))
		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, -1700000000000.0], N[Not[LessEqual[x, 5.7e-22]], $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 < -1.7e12 or 5.6999999999999996e-22 < 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 61.8%

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

      1. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   if -1.7e12 < x < 5.6999999999999996e-22

   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 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*l/ 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1700000000000 \lor \neg \left(x \leq 5.7 \cdot 10^{-22}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1900000000000 \lor \neg \left(x \leq 1.12 \cdot 10^{-27}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1900000000000.0) (not (<= x 1.12e-27)))
   (+ 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 <= -1900000000000.0) || !(x <= 1.12e-27)) {
		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 <= (-1900000000000.0d0)) .or. (.not. (x <= 1.12d-27))) 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 <= -1900000000000.0) || !(x <= 1.12e-27)) {
		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 <= -1900000000000.0) or not (x <= 1.12e-27):
		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 <= -1900000000000.0) || !(x <= 1.12e-27))
		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 <= -1900000000000.0) || ~((x <= 1.12e-27)))
		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, -1900000000000.0], N[Not[LessEqual[x, 1.12e-27]], $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 < -1.9e12 or 1.1199999999999999e-27 < 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 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if -1.9e12 < x < 1.1199999999999999e-27

   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 58.4%

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

      1. metadata-eval 58.4%

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

      2. distribute-lft-neg-in 58.4%

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

      3. *-lft-identity 58.4%

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

      4. associate-*l/ 58.2%

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

      5. associate-*l* 58.2%

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

      6. *-commutative 58.2%

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

      7. distribute-rgt-neg-in 58.2%

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

      8. associate-*r/ 58.2%

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

      9. metadata-eval 58.2%

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

      10. distribute-neg-frac 58.2%

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

      11. metadata-eval 58.2%

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

   5. Simplified 58.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1900000000000 \lor \neg \left(x \leq 1.12 \cdot 10^{-27}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \end{array} \]
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)))