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

Percentage Accurate: 99.3% → 99.7%

Time: 13.4s

Alternatives: 16

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: 99.3% 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: 99.7% 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]

Derivation

1. Initial program 99.1%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000 \lor \neg \left(a \cdot 120 \leq 10^{-100} \lor \neg \left(a \cdot 120 \leq 10^{+55}\right) \land a \cdot 120 \leq 5 \cdot 10^{+99}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -50000.0)
         (not
          (or (<= (* a 120.0) 1e-100)
              (and (not (<= (* a 120.0) 1e+55)) (<= (* a 120.0) 5e+99)))))
   (* 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) <= -50000.0) || !(((a * 120.0) <= 1e-100) || (!((a * 120.0) <= 1e+55) && ((a * 120.0) <= 5e+99)))) {
		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) <= (-50000.0d0)) .or. (.not. ((a * 120.0d0) <= 1d-100) .or. (.not. ((a * 120.0d0) <= 1d+55)) .and. ((a * 120.0d0) <= 5d+99))) 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) <= -50000.0) || !(((a * 120.0) <= 1e-100) || (!((a * 120.0) <= 1e+55) && ((a * 120.0) <= 5e+99)))) {
		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) <= -50000.0) or not (((a * 120.0) <= 1e-100) or (not ((a * 120.0) <= 1e+55) and ((a * 120.0) <= 5e+99))):
		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) <= -50000.0) || !((Float64(a * 120.0) <= 1e-100) || (!(Float64(a * 120.0) <= 1e+55) && (Float64(a * 120.0) <= 5e+99))))
		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) <= -50000.0) || ~((((a * 120.0) <= 1e-100) || (~(((a * 120.0) <= 1e+55)) && ((a * 120.0) <= 5e+99)))))
		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], -50000.0], N[Not[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-100], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+55]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 5e+99]]]], $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) < -5e4 or 1e-100 < (*.f64 a 120) < 1.00000000000000001e55 or 5.00000000000000008e99 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.6%

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

   if -5e4 < (*.f64 a 120) < 1e-100 or 1.00000000000000001e55 < (*.f64 a 120) < 5.00000000000000008e99

   1. Initial program 98.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 78.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000 \lor \neg \left(a \cdot 120 \leq 10^{-100} \lor \neg \left(a \cdot 120 \leq 10^{+55}\right) \land a \cdot 120 \leq 5 \cdot 10^{+99}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-100}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+212}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -50000.0)
   (+ (* a 120.0) (/ 60.0 (/ z x)))
   (if (<= (* a 120.0) 1e-100)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 1e+55)
       (* a 120.0)
       (if (<= (* a 120.0) 1e+212)
         (+ (* a 120.0) (* x (/ -60.0 t)))
         (+ (* a 120.0) (* 60.0 (/ y t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -50000.0) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 1e-100) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+55) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+212) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + (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 ((a * 120.0d0) <= (-50000.0d0)) then
        tmp = (a * 120.0d0) + (60.0d0 / (z / x))
    else if ((a * 120.0d0) <= 1d-100) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 1d+55) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+212) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else
        tmp = (a * 120.0d0) + (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 ((a * 120.0) <= -50000.0) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 1e-100) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+55) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+212) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -50000.0:
		tmp = (a * 120.0) + (60.0 / (z / x))
	elif (a * 120.0) <= 1e-100:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 1e+55:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+212:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	else:
		tmp = (a * 120.0) + (60.0 * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -50000.0)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / x)));
	elseif (Float64(a * 120.0) <= 1e-100)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e+55)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+212)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -50000.0)
		tmp = (a * 120.0) + (60.0 / (z / x));
	elseif ((a * 120.0) <= 1e-100)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 1e+55)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+212)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	else
		tmp = (a * 120.0) + (60.0 * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -50000.0], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-100], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+55], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+212], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -5e4

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 87.5%

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

   6. Taylor expanded in z around inf 78.6%

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

   if -5e4 < (*.f64 a 120) < 1e-100

   1. Initial program 98.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 78.7%

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

   if 1e-100 < (*.f64 a 120) < 1.00000000000000001e55

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 66.6%

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

   if 1.00000000000000001e55 < (*.f64 a 120) < 9.9999999999999991e211

   1. Initial program 96.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 85.6%

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

      1. associate-*r/ 22.7%

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

      2. associate-*l/ 22.7%

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

      3. *-commutative 22.7%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in z around 0 85.3%

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

   if 9.9999999999999991e211 < (*.f64 a 120)

   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 93.7%

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

   4. Taylor expanded in z around 0 93.4%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t}} + a \cdot 120 \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-100}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+212}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;t\_1 \leq 10^{+31}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+43)
     (/ 60.0 (/ (- z t) (- x y)))
     (if (<= t_1 1e+31) (* a 120.0) (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+43) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_1 <= 1e+31) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+43)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (t_1 <= 1d+31) 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 t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+43) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_1 <= 1e+31) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+43:
		tmp = 60.0 / ((z - t) / (x - y))
	elif t_1 <= 1e+31:
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+43)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (t_1 <= 1e+31)
		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)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+43)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (t_1 <= 1e+31)
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+43], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+31], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -1.00000000000000001e43

   1. Initial program 97.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 81.6%

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

      1. expm1-log1p-u 0.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 0.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   7. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 0.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 81.6%

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

      3. associate-*r/ 79.7%

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

      4. associate-/l* 81.7%

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

   9. Simplified 81.7%

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

   if -1.00000000000000001e43 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 9.9999999999999996e30

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.3%

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

   if 9.9999999999999996e30 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 81.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+31}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-100}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -50000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-100)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 1e+55)
       (* a 120.0)
       (+ (* a 120.0) (* x (/ -60.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -50000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-100) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+55) {
		tmp = a * 120.0;
	} else {
		tmp = (a * 120.0) + (x * (-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 ((a * 120.0d0) <= (-50000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-100) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 1d+55) then
        tmp = a * 120.0d0
    else
        tmp = (a * 120.0d0) + (x * ((-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 ((a * 120.0) <= -50000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-100) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+55) {
		tmp = a * 120.0;
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -50000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-100:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 1e+55:
		tmp = a * 120.0
	else:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -50000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-100)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e+55)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -50000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-100)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 1e+55)
		tmp = a * 120.0;
	else
		tmp = (a * 120.0) + (x * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -50000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-100], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+55], N[(a * 120.0), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -5e4 or 1e-100 < (*.f64 a 120) < 1.00000000000000001e55

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.6%

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

   if -5e4 < (*.f64 a 120) < 1e-100

   1. Initial program 98.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 78.7%

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

   if 1.00000000000000001e55 < (*.f64 a 120)

   1. Initial program 98.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 90.9%

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

      1. associate-*r/ 17.6%

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

      2. associate-*l/ 17.6%

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

      3. *-commutative 17.6%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in z around 0 84.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-100}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -3.05 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+192}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= x -3.05e+224)
     t_1
     (if (<= x -3.2e+164)
       (* a 120.0)
       (if (<= x -5.6e+79)
         (* 60.0 (/ (- x y) z))
         (if (<= x 1.5e+192) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -3.05e+224) {
		tmp = t_1;
	} else if (x <= -3.2e+164) {
		tmp = a * 120.0;
	} else if (x <= -5.6e+79) {
		tmp = 60.0 * ((x - y) / z);
	} else if (x <= 1.5e+192) {
		tmp = a * 120.0;
	} 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 = x * (60.0d0 / (z - t))
    if (x <= (-3.05d+224)) then
        tmp = t_1
    else if (x <= (-3.2d+164)) then
        tmp = a * 120.0d0
    else if (x <= (-5.6d+79)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (x <= 1.5d+192) then
        tmp = a * 120.0d0
    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 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -3.05e+224) {
		tmp = t_1;
	} else if (x <= -3.2e+164) {
		tmp = a * 120.0;
	} else if (x <= -5.6e+79) {
		tmp = 60.0 * ((x - y) / z);
	} else if (x <= 1.5e+192) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / (z - t))
	tmp = 0
	if x <= -3.05e+224:
		tmp = t_1
	elif x <= -3.2e+164:
		tmp = a * 120.0
	elif x <= -5.6e+79:
		tmp = 60.0 * ((x - y) / z)
	elif x <= 1.5e+192:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (x <= -3.05e+224)
		tmp = t_1;
	elseif (x <= -3.2e+164)
		tmp = Float64(a * 120.0);
	elseif (x <= -5.6e+79)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (x <= 1.5e+192)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (60.0 / (z - t));
	tmp = 0.0;
	if (x <= -3.05e+224)
		tmp = t_1;
	elseif (x <= -3.2e+164)
		tmp = a * 120.0;
	elseif (x <= -5.6e+79)
		tmp = 60.0 * ((x - y) / z);
	elseif (x <= 1.5e+192)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.05e+224], t$95$1, If[LessEqual[x, -3.2e+164], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -5.6e+79], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+192], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.05e224 or 1.5e192 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 90.3%

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

      1. expm1-log1p-u 60.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 48.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   7. Applied egg-rr 48.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 60.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 90.3%

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

      3. associate-*r/ 90.2%

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

      4. associate-/l* 90.2%

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

   9. Simplified 90.2%

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

   10. Taylor expanded in x around inf 83.7%

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

       1. associate-*r/ 83.7%

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

       2. associate-*l/ 83.7%

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

       3. *-commutative 83.7%

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

   12. Simplified 83.7%

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

   if -3.05e224 < x < -3.1999999999999998e164 or -5.6000000000000002e79 < x < 1.5e192

   1. Initial program 98.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.9%

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

   if -3.1999999999999998e164 < x < -5.6000000000000002e79

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 70.8%

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

   6. Taylor expanded in z around inf 60.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+192}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x}}\\ \mathbf{if}\;x \leq -3.05 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+164}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+192}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ (- z t) x))))
   (if (<= x -3.05e+224)
     t_1
     (if (<= x -3.5e+164)
       (* a 120.0)
       (if (<= x -5.6e+79)
         (* 60.0 (/ (- x y) z))
         (if (<= x 1.5e+192) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / x);
	double tmp;
	if (x <= -3.05e+224) {
		tmp = t_1;
	} else if (x <= -3.5e+164) {
		tmp = a * 120.0;
	} else if (x <= -5.6e+79) {
		tmp = 60.0 * ((x - y) / z);
	} else if (x <= 1.5e+192) {
		tmp = a * 120.0;
	} 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 = 60.0d0 / ((z - t) / x)
    if (x <= (-3.05d+224)) then
        tmp = t_1
    else if (x <= (-3.5d+164)) then
        tmp = a * 120.0d0
    else if (x <= (-5.6d+79)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (x <= 1.5d+192) then
        tmp = a * 120.0d0
    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 = 60.0 / ((z - t) / x);
	double tmp;
	if (x <= -3.05e+224) {
		tmp = t_1;
	} else if (x <= -3.5e+164) {
		tmp = a * 120.0;
	} else if (x <= -5.6e+79) {
		tmp = 60.0 * ((x - y) / z);
	} else if (x <= 1.5e+192) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / ((z - t) / x)
	tmp = 0
	if x <= -3.05e+224:
		tmp = t_1
	elif x <= -3.5e+164:
		tmp = a * 120.0
	elif x <= -5.6e+79:
		tmp = 60.0 * ((x - y) / z)
	elif x <= 1.5e+192:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(Float64(z - t) / x))
	tmp = 0.0
	if (x <= -3.05e+224)
		tmp = t_1;
	elseif (x <= -3.5e+164)
		tmp = Float64(a * 120.0);
	elseif (x <= -5.6e+79)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (x <= 1.5e+192)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / ((z - t) / x);
	tmp = 0.0;
	if (x <= -3.05e+224)
		tmp = t_1;
	elseif (x <= -3.5e+164)
		tmp = a * 120.0;
	elseif (x <= -5.6e+79)
		tmp = 60.0 * ((x - y) / z);
	elseif (x <= 1.5e+192)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.05e+224], t$95$1, If[LessEqual[x, -3.5e+164], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -5.6e+79], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+192], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.05e224 or 1.5e192 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 90.3%

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

      1. expm1-log1p-u 60.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 48.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   7. Applied egg-rr 48.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 60.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 90.3%

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

      3. associate-*r/ 90.2%

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

      4. associate-/l* 90.2%

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

   9. Simplified 90.2%

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

   10. Taylor expanded in x around inf 83.7%

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

   if -3.05e224 < x < -3.4999999999999998e164 or -5.6000000000000002e79 < x < 1.5e192

   1. Initial program 98.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.9%

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

   if -3.4999999999999998e164 < x < -5.6000000000000002e79

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 70.8%

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

   6. Taylor expanded in z around inf 60.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+224}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+164}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+192}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x}}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+164}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ (- z t) x))))
   (if (<= x -1.35e+225)
     t_1
     (if (<= x -3.6e+164)
       (* a 120.0)
       (if (<= x -2.5e+79)
         (/ (* 60.0 (- x y)) z)
         (if (<= x 3.1e+190) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / x);
	double tmp;
	if (x <= -1.35e+225) {
		tmp = t_1;
	} else if (x <= -3.6e+164) {
		tmp = a * 120.0;
	} else if (x <= -2.5e+79) {
		tmp = (60.0 * (x - y)) / z;
	} else if (x <= 3.1e+190) {
		tmp = a * 120.0;
	} 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 = 60.0d0 / ((z - t) / x)
    if (x <= (-1.35d+225)) then
        tmp = t_1
    else if (x <= (-3.6d+164)) then
        tmp = a * 120.0d0
    else if (x <= (-2.5d+79)) then
        tmp = (60.0d0 * (x - y)) / z
    else if (x <= 3.1d+190) then
        tmp = a * 120.0d0
    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 = 60.0 / ((z - t) / x);
	double tmp;
	if (x <= -1.35e+225) {
		tmp = t_1;
	} else if (x <= -3.6e+164) {
		tmp = a * 120.0;
	} else if (x <= -2.5e+79) {
		tmp = (60.0 * (x - y)) / z;
	} else if (x <= 3.1e+190) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / ((z - t) / x)
	tmp = 0
	if x <= -1.35e+225:
		tmp = t_1
	elif x <= -3.6e+164:
		tmp = a * 120.0
	elif x <= -2.5e+79:
		tmp = (60.0 * (x - y)) / z
	elif x <= 3.1e+190:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(Float64(z - t) / x))
	tmp = 0.0
	if (x <= -1.35e+225)
		tmp = t_1;
	elseif (x <= -3.6e+164)
		tmp = Float64(a * 120.0);
	elseif (x <= -2.5e+79)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / z);
	elseif (x <= 3.1e+190)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / ((z - t) / x);
	tmp = 0.0;
	if (x <= -1.35e+225)
		tmp = t_1;
	elseif (x <= -3.6e+164)
		tmp = a * 120.0;
	elseif (x <= -2.5e+79)
		tmp = (60.0 * (x - y)) / z;
	elseif (x <= 3.1e+190)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+225], t$95$1, If[LessEqual[x, -3.6e+164], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -2.5e+79], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 3.1e+190], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3499999999999999e225 or 3.1000000000000001e190 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 90.3%

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

      1. expm1-log1p-u 60.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 48.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   7. Applied egg-rr 48.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 60.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 90.3%

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

      3. associate-*r/ 90.2%

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

      4. associate-/l* 90.2%

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

   9. Simplified 90.2%

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

   10. Taylor expanded in x around inf 83.7%

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

   if -1.3499999999999999e225 < x < -3.5999999999999999e164 or -2.5e79 < x < 3.1000000000000001e190

   1. Initial program 98.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.9%

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

   if -3.5999999999999999e164 < x < -2.5e79

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 70.8%

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

      1. expm1-log1p-u 56.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 43.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   7. Applied egg-rr 43.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 56.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 70.8%

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

      3. associate-*r/ 71.0%

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

      4. associate-/l* 71.0%

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

   9. Simplified 71.0%

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

   10. Taylor expanded in z around inf 60.3%

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

       1. associate-*r/ 60.6%

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

       2. *-commutative 60.6%

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

   12. Simplified 60.6%

       \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+225}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+164}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+90} \lor \neg \left(y \leq 5.4 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.5e+90) (not (<= y 5.4e+87)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.5e+90) || !(y <= 5.4e+87)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (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 ((y <= (-6.5d+90)) .or. (.not. (y <= 5.4d+87))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * (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 ((y <= -6.5e+90) || !(y <= 5.4e+87)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.5e+90) or not (y <= 5.4e+87):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.5e+90) || !(y <= 5.4e+87))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.5e+90) || ~((y <= 5.4e+87)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.5e+90], N[Not[LessEqual[y, 5.4e+87]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000001e90 or 5.40000000000000013e87 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 88.5%

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

   if -6.5000000000000001e90 < y < 5.40000000000000013e87

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 96.0%

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

      1. associate-*r/ 38.8%

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

      2. associate-*l/ 38.9%

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

      3. *-commutative 38.9%

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

   7. Simplified 96.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+90} \lor \neg \left(y \leq 5.4 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+230}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- x y) -1e+230)
   (* -60.0 (/ y (- z t)))
   (if (<= (- x y) 2e+190) (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -1e+230) {
		tmp = -60.0 * (y / (z - t));
	} else if ((x - y) <= 2e+190) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - 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 ((x - y) <= (-1d+230)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((x - y) <= 2d+190) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - 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 ((x - y) <= -1e+230) {
		tmp = -60.0 * (y / (z - t));
	} else if ((x - y) <= 2e+190) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x - y) <= -1e+230:
		tmp = -60.0 * (y / (z - t))
	elif (x - y) <= 2e+190:
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x - y) <= -1e+230)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (Float64(x - y) <= 2e+190)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x - y) <= -1e+230)
		tmp = -60.0 * (y / (z - t));
	elseif ((x - y) <= 2e+190)
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x - y), $MachinePrecision], -1e+230], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 2e+190], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x y) < -1.0000000000000001e230

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 80.5%

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

   6. Taylor expanded in x around 0 44.6%

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

   if -1.0000000000000001e230 < (-.f64 x y) < 2.0000000000000001e190

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.8%

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

   if 2.0000000000000001e190 < (-.f64 x y)

   1. Initial program 96.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 85.3%

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

   6. Taylor expanded in z around 0 53.6%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+230}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+230}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- x y) -1e+230)
   (* 60.0 (/ (- x y) z))
   (if (<= (- x y) 2e+190) (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -1e+230) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((x - y) <= 2e+190) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - 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 ((x - y) <= (-1d+230)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if ((x - y) <= 2d+190) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - 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 ((x - y) <= -1e+230) {
		tmp = 60.0 * ((x - y) / z);
	} else if ((x - y) <= 2e+190) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x - y) <= -1e+230:
		tmp = 60.0 * ((x - y) / z)
	elif (x - y) <= 2e+190:
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x - y) <= -1e+230)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (Float64(x - y) <= 2e+190)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x - y) <= -1e+230)
		tmp = 60.0 * ((x - y) / z);
	elseif ((x - y) <= 2e+190)
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x - y), $MachinePrecision], -1e+230], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 2e+190], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x y) < -1.0000000000000001e230

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 80.5%

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

   6. Taylor expanded in z around inf 57.0%

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

   if -1.0000000000000001e230 < (-.f64 x y) < 2.0000000000000001e190

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.8%

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

   if 2.0000000000000001e190 < (-.f64 x y)

   1. Initial program 96.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 85.3%

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

   6. Taylor expanded in z around 0 53.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+230}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+175}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+146}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4e+175)
   (/ 60.0 (/ (- z t) (- x y)))
   (if (<= y 5.5e+146)
     (+ (* a 120.0) (* x (/ 60.0 (- z t))))
     (/ (* 60.0 (- x y)) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4e+175) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (y <= 5.5e+146) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} 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 (y <= (-4d+175)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (y <= 5.5d+146) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    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 (y <= -4e+175) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (y <= 5.5e+146) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (60.0 * (x - y)) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4e+175:
		tmp = 60.0 / ((z - t) / (x - y))
	elif y <= 5.5e+146:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	else:
		tmp = (60.0 * (x - y)) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4e+175)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (y <= 5.5e+146)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	else
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4e+175)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (y <= 5.5e+146)
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	else
		tmp = (60.0 * (x - y)) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4e+175], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+146], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999997e175

   1. Initial program 93.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 83.0%

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

      1. expm1-log1p-u 44.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 38.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   7. Applied egg-rr 38.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 44.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 83.0%

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

      3. associate-*r/ 76.4%

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

      4. associate-/l* 83.1%

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

   9. Simplified 83.1%

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

   if -3.9999999999999997e175 < y < 5.5000000000000004e146

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 92.8%

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

      1. associate-*r/ 35.8%

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

      2. associate-*l/ 35.8%

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

      3. *-commutative 35.8%

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

   7. Simplified 92.8%

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

   if 5.5000000000000004e146 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 66.0%

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

      1. associate-*r/ 66.2%

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

   7. Applied egg-rr 66.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+175}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+146}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.8e+166)
   (/ 60.0 (/ (- z t) (- x y)))
   (if (<= y 4.8e+92)
     (+ (* a 120.0) (* x (/ 60.0 (- z t))))
     (+ (* a 120.0) (/ 60.0 (/ z (- x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+166) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (y <= 4.8e+92) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	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 <= (-1.8d+166)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (y <= 4.8d+92) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    else
        tmp = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    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 <= -1.8e+166) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (y <= 4.8e+92) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.8e+166:
		tmp = 60.0 / ((z - t) / (x - y))
	elif y <= 4.8e+92:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	else:
		tmp = (a * 120.0) + (60.0 / (z / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.8e+166)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (y <= 4.8e+92)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.8e+166)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (y <= 4.8e+92)
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	else
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.8e+166], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+92], 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[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999999e166

   1. Initial program 93.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 83.0%

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

      1. expm1-log1p-u 44.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 38.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   7. Applied egg-rr 38.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 44.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 83.0%

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

      3. associate-*r/ 76.4%

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

      4. associate-/l* 83.1%

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

   9. Simplified 83.1%

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

   if -1.7999999999999999e166 < y < 4.80000000000000009e92

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 94.5%

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

      1. associate-*r/ 36.5%

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

      2. associate-*l/ 36.5%

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

      3. *-commutative 36.5%

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

   7. Simplified 94.6%

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

   if 4.80000000000000009e92 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 65.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+225} \lor \neg \left(x \leq 3.2 \cdot 10^{+193}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.7e+225) (not (<= x 3.2e+193))) (* 60.0 (/ x z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.7e+225) || !(x <= 3.2e+193)) {
		tmp = 60.0 * (x / z);
	} 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 ((x <= (-2.7d+225)) .or. (.not. (x <= 3.2d+193))) then
        tmp = 60.0d0 * (x / z)
    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 ((x <= -2.7e+225) || !(x <= 3.2e+193)) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.7e+225) or not (x <= 3.2e+193):
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.7e+225) || !(x <= 3.2e+193))
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.7e+225) || ~((x <= 3.2e+193)))
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.7e+225], N[Not[LessEqual[x, 3.2e+193]], $MachinePrecision]], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6999999999999999e225 or 3.20000000000000013e193 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 90.3%

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

   6. Taylor expanded in z around inf 55.0%

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

   7. Taylor expanded in x around inf 54.3%

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

   if -2.6999999999999999e225 < x < 3.20000000000000013e193

   1. Initial program 99.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 61.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+225} \lor \neg \left(x \leq 3.2 \cdot 10^{+193}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+177}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.5e+177) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.5e+177) {
		tmp = -60.0 * (y / z);
	} 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 (y <= (-6.5d+177)) then
        tmp = (-60.0d0) * (y / z)
    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 (y <= -6.5e+177) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.5e+177:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.5e+177)
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.5e+177)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.5e+177], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000002e177

   1. Initial program 93.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 83.0%

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

   6. Taylor expanded in x around 0 75.4%

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

   7. Taylor expanded in z around inf 41.4%

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

   if -6.5000000000000002e177 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+177}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.3% 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 99.1%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 52.2%

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

6. Final simplification 52.2%

   \[\leadsto a \cdot 120 \]
7. 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 2024026 
(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)))