Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.4% → 99.4%

Time: 17.5s

Alternatives: 15

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
4. Add Preprocessing

Alternative 2: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-82}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= z -1.42e-30)
     t_1
     (if (<= z 2.1e-163)
       (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
       (if (<= z 3.8e-82)
         (* 60.0 (/ (- x y) (- z t)))
         (if (<= z 5.8e-47) (+ (* a 120.0) (/ (* 60.0 y) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -1.42e-30) {
		tmp = t_1;
	} else if (z <= 2.1e-163) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 3.8e-82) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 5.8e-47) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if (z <= (-1.42d-30)) then
        tmp = t_1
    else if (z <= 2.1d-163) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else if (z <= 3.8d-82) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (z <= 5.8d-47) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -1.42e-30) {
		tmp = t_1;
	} else if (z <= 2.1e-163) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 3.8e-82) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 5.8e-47) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if z <= -1.42e-30:
		tmp = t_1
	elif z <= 2.1e-163:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	elif z <= 3.8e-82:
		tmp = 60.0 * ((x - y) / (z - t))
	elif z <= 5.8e-47:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (z <= -1.42e-30)
		tmp = t_1;
	elseif (z <= 2.1e-163)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	elseif (z <= 3.8e-82)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (z <= 5.8e-47)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if (z <= -1.42e-30)
		tmp = t_1;
	elseif (z <= 2.1e-163)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	elseif (z <= 3.8e-82)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (z <= 5.8e-47)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.42e-30], t$95$1, If[LessEqual[z, 2.1e-163], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-82], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-47], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.42e-30 or 5.8000000000000001e-47 < z

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z}} + a \cdot 120 \]

   4. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} + a \cdot 120 \]

   if -1.42e-30 < z < 2.09999999999999998e-163

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} + a \cdot 120 \]

   if 2.09999999999999998e-163 < z < 3.8000000000000002e-82

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.7%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.7%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.8%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.8%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.8%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in a around 0 93.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if 3.8000000000000002e-82 < z < 5.8000000000000001e-47

   1. Initial program 100.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   4. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

   6. Taylor expanded in z around 0 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{60 \cdot y}{t}} + a \cdot 120 \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{60 \cdot y}{t}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-82}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-278}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= a -1.95e-53)
     (* a 120.0)
     (if (<= a -1.8e-295)
       t_1
       (if (<= a 4.6e-278)
         (* 60.0 (/ x (- z t)))
         (if (<= a 3.4e-43) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.95e-53) {
		tmp = a * 120.0;
	} else if (a <= -1.8e-295) {
		tmp = t_1;
	} else if (a <= 4.6e-278) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 3.4e-43) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (a <= (-1.95d-53)) then
        tmp = a * 120.0d0
    else if (a <= (-1.8d-295)) then
        tmp = t_1
    else if (a <= 4.6d-278) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 3.4d-43) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.95e-53) {
		tmp = a * 120.0;
	} else if (a <= -1.8e-295) {
		tmp = t_1;
	} else if (a <= 4.6e-278) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 3.4e-43) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -1.95e-53:
		tmp = a * 120.0
	elif a <= -1.8e-295:
		tmp = t_1
	elif a <= 4.6e-278:
		tmp = 60.0 * (x / (z - t))
	elif a <= 3.4e-43:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.95e-53)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.8e-295)
		tmp = t_1;
	elseif (a <= 4.6e-278)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 3.4e-43)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -1.95e-53)
		tmp = a * 120.0;
	elseif (a <= -1.8e-295)
		tmp = t_1;
	elseif (a <= 4.6e-278)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 3.4e-43)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e-53], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.8e-295], t$95$1, If[LessEqual[a, 4.6e-278], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-43], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9500000000000001e-53 or 3.4000000000000001e-43 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.9500000000000001e-53 < a < -1.8000000000000001e-295 or 4.60000000000000006e-278 < a < 3.4000000000000001e-43

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.8%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.8%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.7%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -1.8000000000000001e-295 < a < 4.60000000000000006e-278

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.3%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.3%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.3%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.3%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.3%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.3%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.3%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in x around inf 85.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-295}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-278}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-43}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= a -1.5e-53)
     (* a 120.0)
     (if (<= a -5.4e-296)
       t_1
       (if (<= a 1.9e-277)
         (* x (/ 60.0 (- z t)))
         (if (<= a 3.3e-43) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.5e-53) {
		tmp = a * 120.0;
	} else if (a <= -5.4e-296) {
		tmp = t_1;
	} else if (a <= 1.9e-277) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 3.3e-43) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (a <= (-1.5d-53)) then
        tmp = a * 120.0d0
    else if (a <= (-5.4d-296)) then
        tmp = t_1
    else if (a <= 1.9d-277) then
        tmp = x * (60.0d0 / (z - t))
    else if (a <= 3.3d-43) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.5e-53) {
		tmp = a * 120.0;
	} else if (a <= -5.4e-296) {
		tmp = t_1;
	} else if (a <= 1.9e-277) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 3.3e-43) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -1.5e-53:
		tmp = a * 120.0
	elif a <= -5.4e-296:
		tmp = t_1
	elif a <= 1.9e-277:
		tmp = x * (60.0 / (z - t))
	elif a <= 3.3e-43:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.5e-53)
		tmp = Float64(a * 120.0);
	elseif (a <= -5.4e-296)
		tmp = t_1;
	elseif (a <= 1.9e-277)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (a <= 3.3e-43)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -1.5e-53)
		tmp = a * 120.0;
	elseif (a <= -5.4e-296)
		tmp = t_1;
	elseif (a <= 1.9e-277)
		tmp = x * (60.0 / (z - t));
	elseif (a <= 3.3e-43)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e-53], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -5.4e-296], t$95$1, If[LessEqual[a, 1.9e-277], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-43], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5000000000000001e-53 or 3.30000000000000016e-43 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.5000000000000001e-53 < a < -5.39999999999999998e-296 or 1.89999999999999993e-277 < a < 3.30000000000000016e-43

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.8%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.8%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.7%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -5.39999999999999998e-296 < a < 1.89999999999999993e-277

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.3%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.3%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.3%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.3%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.3%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.3%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.3%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in x around inf 85.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 85.4%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. associate-*l/ 85.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} \]

      3. *-commutative 85.6%

         \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} \]

   7. Simplified 85.6%

      \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-296}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-43}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-47}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 0.057:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 55000:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e-10)
   (* a 120.0)
   (if (<= a 3.9e-47)
     (* (- x y) (/ -60.0 t))
     (if (<= a 0.057)
       (* x (/ 60.0 (- z t)))
       (if (<= a 55000.0) (* -60.0 (/ y (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-10) {
		tmp = a * 120.0;
	} else if (a <= 3.9e-47) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 0.057) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 55000.0) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.8d-10)) then
        tmp = a * 120.0d0
    else if (a <= 3.9d-47) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 0.057d0) then
        tmp = x * (60.0d0 / (z - t))
    else if (a <= 55000.0d0) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-10) {
		tmp = a * 120.0;
	} else if (a <= 3.9e-47) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 0.057) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 55000.0) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e-10:
		tmp = a * 120.0
	elif a <= 3.9e-47:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 0.057:
		tmp = x * (60.0 / (z - t))
	elif a <= 55000.0:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e-10)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.9e-47)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 0.057)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (a <= 55000.0)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e-10)
		tmp = a * 120.0;
	elseif (a <= 3.9e-47)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 0.057)
		tmp = x * (60.0 / (z - t));
	elseif (a <= 55000.0)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e-10], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.9e-47], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.057], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 55000.0], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.79999999999999962e-10 or 55000 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -5.79999999999999962e-10 < a < 3.89999999999999978e-47

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.7%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.7%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.7%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in z around 0 64.7%

      \[\leadsto \left(-\frac{x - y}{\color{blue}{0.016666666666666666 \cdot t}}\right) + a \cdot 120 \]
   6. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{t \cdot 0.016666666666666666}}\right) + a \cdot 120 \]

   7. Simplified 64.7%

      \[\leadsto \left(-\frac{x - y}{\color{blue}{t \cdot 0.016666666666666666}}\right) + a \cdot 120 \]

   8. Taylor expanded in t around 0 55.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
   9. Step-by-step derivation

      1. metadata-eval 55.1%

         \[\leadsto \color{blue}{\left(-60\right)} \cdot \frac{x - y}{t} \]

      2. distribute-lft-neg-in 55.1%

         \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]

      3. *-commutative 55.1%

         \[\leadsto -\color{blue}{\frac{x - y}{t} \cdot 60} \]

      4. associate-*l/ 55.2%

         \[\leadsto -\color{blue}{\frac{\left(x - y\right) \cdot 60}{t}} \]

      5. associate-*r/ 55.1%

         \[\leadsto -\color{blue}{\left(x - y\right) \cdot \frac{60}{t}} \]

      6. distribute-rgt-neg-out 55.1%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(-\frac{60}{t}\right)} \]

      7. distribute-neg-frac 55.1%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{-60}{t}} \]

      8. metadata-eval 55.1%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{-60}}{t} \]

   10. Simplified 55.1%

       \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{-60}{t}} \]

   if 3.89999999999999978e-47 < a < 0.0570000000000000021

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.8%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.8%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.9%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.9%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.9%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in x around inf 56.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 56.8%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. associate-*l/ 56.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} \]

      3. *-commutative 56.7%

         \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} \]

   7. Simplified 56.7%

      \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} \]

   if 0.0570000000000000021 < a < 55000

   1. Initial program 100.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 100.0%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 100.0%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 100.0%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 100.0%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 100.0%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-47}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 0.057:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 55000:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-6} \lor \neg \left(a \cdot 120 \leq 10000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-6) (not (<= (* a 120.0) 10000000.0)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-6) || !((a * 120.0) <= 10000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-6)) .or. (.not. ((a * 120.0d0) <= 10000000.0d0))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-6) || !((a * 120.0) <= 10000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-6) or not ((a * 120.0) <= 10000000.0):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-6) || !(Float64(a * 120.0) <= 10000000.0))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-6) || ~(((a * 120.0) <= 10000000.0)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-6], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 10000000.0]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -1.99999999999999991e-6 or 1e7 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.99999999999999991e-6 < (*.f64 a 120) < 1e7

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.7%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.7%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.7%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in a around 0 80.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-6} \lor \neg \left(a \cdot 120 \leq 10000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-6}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-6)
   (* a 120.0)
   (if (<= (* a 120.0) 10000000.0)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* 60.0 (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-6) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 10000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-6)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 10000000.0d0) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-6) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 10000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-6:
		tmp = a * 120.0
	elif (a * 120.0) <= 10000000.0:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-6)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 10000000.0)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-6)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 10000000.0)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-6], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 10000000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -1.99999999999999991e-6

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.99999999999999991e-6 < (*.f64 a 120) < 1e7

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.7%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.7%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.7%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in a around 0 80.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if 1e7 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z}} + a \cdot 120 \]

   4. Taylor expanded in x around inf 82.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-6}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+78} \lor \neg \left(t \leq 1.05 \cdot 10^{-24}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.6e+78) (not (<= t 1.05e-24)))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+78) || !(t <= 1.05e-24)) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.6d+78)) .or. (.not. (t <= 1.05d-24))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+78) || !(t <= 1.05e-24)) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.6e+78) or not (t <= 1.05e-24):
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	else:
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.6e+78) || !(t <= 1.05e-24))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.6e+78) || ~((t <= 1.05e-24)))
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	else
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.6e+78], N[Not[LessEqual[t, 1.05e-24]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6e78 or 1.05e-24 < t

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 95.5%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} + a \cdot 120 \]

   if -6.6e78 < t < 1.05e-24

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+78} \lor \neg \left(t \leq 1.05 \cdot 10^{-24}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+78} \lor \neg \left(t \leq 4.1 \cdot 10^{-22}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.6e+78) (not (<= t 4.1e-22)))
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+78) || !(t <= 4.1e-22)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.6d+78)) .or. (.not. (t <= 4.1d-22))) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+78) || !(t <= 4.1e-22)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.6e+78) or not (t <= 4.1e-22):
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.6e+78) || !(t <= 4.1e-22))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.6e+78) || ~((t <= 4.1e-22)))
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.6e+78], N[Not[LessEqual[t, 4.1e-22]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6e78 or 4.0999999999999999e-22 < t

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Taylor expanded in z around 0 95.5%

      \[\leadsto \color{blue}{\frac{-60}{t}} \cdot \left(x - y\right) + a \cdot 120 \]

   if -6.6e78 < t < 4.0999999999999999e-22

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+78} \lor \neg \left(t \leq 4.1 \cdot 10^{-22}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7800000000 \lor \neg \left(x \leq 2.1 \cdot 10^{+75}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7800000000.0) (not (<= x 2.1e+75)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7800000000.0) || !(x <= 2.1e+75)) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-7800000000.0d0)) .or. (.not. (x <= 2.1d+75))) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7800000000.0) || !(x <= 2.1e+75)) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7800000000.0) or not (x <= 2.1e+75):
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7800000000.0) || !(x <= 2.1e+75))
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7800000000.0) || ~((x <= 2.1e+75)))
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7800000000.0], N[Not[LessEqual[x, 2.1e+75]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8e9 or 2.09999999999999999e75 < x

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   4. Step-by-step derivation

      1. associate-*r/ 87.2%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} + a \cdot 120 \]

      2. *-commutative 87.2%

         \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} + a \cdot 120 \]

      3. associate-*r/ 87.3%

         \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} + a \cdot 120 \]

   5. Simplified 87.3%

      \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} + a \cdot 120 \]

   if -7.8e9 < x < 2.09999999999999999e75

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.9%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   4. Step-by-step derivation

      1. associate-*r/ 94.9%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

   5. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7800000000 \lor \neg \left(x \leq 2.1 \cdot 10^{+75}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-55} \lor \neg \left(a \leq 3.2 \cdot 10^{-43}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5e-55) (not (<= a 3.2e-43)))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5e-55) || !(a <= 3.2e-43)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5d-55)) .or. (.not. (a <= 3.2d-43))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5e-55) || !(a <= 3.2e-43)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5e-55) or not (a <= 3.2e-43):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5e-55) || !(a <= 3.2e-43))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5e-55) || ~((a <= 3.2e-43)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5e-55], N[Not[LessEqual[a, 3.2e-43]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.0000000000000002e-55 or 3.19999999999999985e-43 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -5.0000000000000002e-55 < a < 3.19999999999999985e-43

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.7%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.7%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.7%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.7%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in y around inf 54.7%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-55} \lor \neg \left(a \leq 3.2 \cdot 10^{-43}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z - t} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* a 120.0) (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((x - y) * (60.0 / (z - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (a * 120.0d0) + ((x - y) * (60.0d0 / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((x - y) * (60.0 / (z - t)));
}

Python

def code(x, y, z, t, a):
	return (a * 120.0) + ((x - y) * (60.0 / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (a * 120.0) + ((x - y) * (60.0 / (z - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   2. associate-/r/ 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

5. Final simplification 99.8%

   \[\leadsto a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z - t} \]
6. Add Preprocessing

Alternative 13: 51.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.7e+200) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.7e+200) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 1.7d+200) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.7e+200) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.7e+200:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.7e+200)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.7e+200)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.7e+200], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.69999999999999985e200

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 55.4%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 1.69999999999999985e200 < y

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.4%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.4%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.4%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.4%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.4%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.4%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.4%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 75.6%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]

      2. *-commutative 75.6%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} \]

   7. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{y \cdot -60}{z - t}} \]

   8. Taylor expanded in z around 0 57.0%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{+200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 2.75e+200) (* a 120.0) (* y (/ 60.0 t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.75e+200) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 2.75d+200) then
        tmp = a * 120.0d0
    else
        tmp = y * (60.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.75e+200) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.75e+200:
		tmp = a * 120.0
	else:
		tmp = y * (60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.75e+200)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y * Float64(60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.75e+200)
		tmp = a * 120.0;
	else
		tmp = y * (60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.75e+200], N[(a * 120.0), $MachinePrecision], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.75e200

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 55.4%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 2.75e200 < y

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.4%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120 \]

      3. frac-2neg 99.4%

         \[\leadsto \color{blue}{\frac{-\left(x - y\right)}{-\frac{z - t}{60}}} + a \cdot 120 \]

      4. distribute-frac-neg 99.4%

         \[\leadsto \color{blue}{\left(-\frac{x - y}{-\frac{z - t}{60}}\right)} + a \cdot 120 \]

      5. div-inv 99.4%

         \[\leadsto \left(-\frac{x - y}{-\color{blue}{\left(z - t\right) \cdot \frac{1}{60}}}\right) + a \cdot 120 \]

      6. distribute-rgt-neg-in 99.4%

         \[\leadsto \left(-\frac{x - y}{\color{blue}{\left(z - t\right) \cdot \left(-\frac{1}{60}\right)}}\right) + a \cdot 120 \]

      7. metadata-eval 99.4%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \left(-\color{blue}{0.016666666666666666}\right)}\right) + a \cdot 120 \]

      8. metadata-eval 99.4%

         \[\leadsto \left(-\frac{x - y}{\left(z - t\right) \cdot \color{blue}{-0.016666666666666666}}\right) + a \cdot 120 \]

   4. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\left(-\frac{x - y}{\left(z - t\right) \cdot -0.016666666666666666}\right)} + a \cdot 120 \]

   5. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 75.6%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]

      2. *-commutative 75.6%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} \]

   7. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{y \cdot -60}{z - t}} \]

   8. Taylor expanded in z around 0 57.0%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 56.9%

         \[\leadsto \color{blue}{\frac{60 \cdot y}{t}} \]

      2. associate-*l/ 57.1%

         \[\leadsto \color{blue}{\frac{60}{t} \cdot y} \]

      3. *-commutative 57.1%

         \[\leadsto \color{blue}{y \cdot \frac{60}{t}} \]

   10. Simplified 57.1%

       \[\leadsto \color{blue}{y \cdot \frac{60}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{+200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = a * 120.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = a * 120.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Add Preprocessing

3. Taylor expanded in z around inf 53.1%

   \[\leadsto \color{blue}{120 \cdot a} \]

4. Final simplification 53.1%

   \[\leadsto a \cdot 120 \]
5. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))