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

Percentage Accurate: 99.3% → 99.8%

Time: 17.2s

Alternatives: 17

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: 99.8% 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 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Final simplification 99.8%

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

Alternative 2: 72.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -2e+53)
     (* a 120.0)
     (if (<= (* a 120.0) -1e-100)
       (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
       (if (<= (* a 120.0) 2e-148)
         t_1
         (if (<= (* a 120.0) 5e-125)
           (+ (* a 120.0) (/ -60.0 (/ t x)))
           (if (<= (* a 120.0) 1000000.0) t_1 (* a 120.0))))))))

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 ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	} else if ((a * 120.0) <= 1000000.0) {
		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 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-2d+53)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-100)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if ((a * 120.0d0) <= 2d-148) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-125) then
        tmp = (a * 120.0d0) + ((-60.0d0) / (t / x))
    else if ((a * 120.0d0) <= 1000000.0d0) 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 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -2e+53:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-100:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif (a * 120.0) <= 2e-148:
		tmp = t_1
	elif (a * 120.0) <= 5e-125:
		tmp = (a * 120.0) + (-60.0 / (t / x))
	elif (a * 120.0) <= 1000000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+53)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-100)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (Float64(a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-125)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(t / x)));
	elseif (Float64(a * 120.0) <= 1000000.0)
		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 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+53)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-100)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif ((a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-125)
		tmp = (a * 120.0) + (-60.0 / (t / x));
	elseif ((a * 120.0) <= 1000000.0)
		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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-100], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-148], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2e53 or 1e6 < (*.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. Taylor expanded in z around inf 84.2%

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

   if -2e53 < (*.f64 a 120) < -1e-100

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 75.5%

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

      1. associate-*r/ 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-/l* 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in z around inf 69.3%

      \[\leadsto \frac{x}{\color{blue}{0.016666666666666666 \cdot z}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   9. Simplified 69.3%

      \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   if -1e-100 < (*.f64 a 120) < 1.99999999999999987e-148 or 4.99999999999999967e-125 < (*.f64 a 120) < 1e6

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 83.0%

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

   if 1.99999999999999987e-148 < (*.f64 a 120) < 4.99999999999999967e-125

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 88.6%

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

      1. associate-*r/ 88.6%

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

      2. associate-/l* 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in x around inf 88.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -2e+53)
     (* a 120.0)
     (if (<= (* a 120.0) -1e-100)
       (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
       (if (<= (* a 120.0) 2e-148)
         t_1
         (if (<= (* a 120.0) 5e-125)
           (+ (* a 120.0) (/ (* 60.0 y) t))
           (if (<= (* a 120.0) 1000000.0) t_1 (* a 120.0))))))))

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 ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= 1000000.0) {
		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 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-2d+53)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-100)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if ((a * 120.0d0) <= 2d-148) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-125) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else if ((a * 120.0d0) <= 1000000.0d0) 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 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -2e+53:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-100:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif (a * 120.0) <= 2e-148:
		tmp = t_1
	elif (a * 120.0) <= 5e-125:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	elif (a * 120.0) <= 1000000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+53)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-100)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (Float64(a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-125)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	elseif (Float64(a * 120.0) <= 1000000.0)
		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 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+53)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-100)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif ((a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-125)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	elseif ((a * 120.0) <= 1000000.0)
		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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-100], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-148], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2e53 or 1e6 < (*.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. Taylor expanded in z around inf 84.2%

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

   if -2e53 < (*.f64 a 120) < -1e-100

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 75.5%

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

      1. associate-*r/ 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-/l* 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in z around inf 69.3%

      \[\leadsto \frac{x}{\color{blue}{0.016666666666666666 \cdot z}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   9. Simplified 69.3%

      \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   if -1e-100 < (*.f64 a 120) < 1.99999999999999987e-148 or 4.99999999999999967e-125 < (*.f64 a 120) < 1e6

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 83.0%

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

   if 1.99999999999999987e-148 < (*.f64 a 120) < 4.99999999999999967e-125

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 88.6%

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

      1. associate-*r/ 88.6%

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

      2. associate-/l* 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in x around 0 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*l/ 92.6%

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

   9. Simplified 92.6%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-152}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+53)
   (* a 120.0)
   (if (<= (* a 120.0) -1e-100)
     (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
     (if (<= (* a 120.0) 2e-152)
       (/ (- x y) (/ (- z t) 60.0))
       (if (<= (* a 120.0) 5e-125)
         (+ (* a 120.0) (/ (* 60.0 y) t))
         (if (<= (* a 120.0) 1000000.0)
           (* 60.0 (/ (- x y) (- z t)))
           (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((a * 120.0) <= 2e-152) {
		tmp = (x - y) / ((z - t) / 60.0);
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = 60.0 * ((x - 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 * 120.0d0) <= (-2d+53)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-100)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if ((a * 120.0d0) <= 2d-152) then
        tmp = (x - y) / ((z - t) / 60.0d0)
    else if ((a * 120.0d0) <= 5d-125) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else if ((a * 120.0d0) <= 1000000.0d0) then
        tmp = 60.0d0 * ((x - 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 * 120.0) <= -2e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-100) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((a * 120.0) <= 2e-152) {
		tmp = (x - y) / ((z - t) / 60.0);
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+53:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-100:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif (a * 120.0) <= 2e-152:
		tmp = (x - y) / ((z - t) / 60.0)
	elif (a * 120.0) <= 5e-125:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	elif (a * 120.0) <= 1000000.0:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+53)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-100)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (Float64(a * 120.0) <= 2e-152)
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) / 60.0));
	elseif (Float64(a * 120.0) <= 5e-125)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	elseif (Float64(a * 120.0) <= 1000000.0)
		tmp = Float64(60.0 * Float64(Float64(x - 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 * 120.0) <= -2e+53)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-100)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif ((a * 120.0) <= 2e-152)
		tmp = (x - y) / ((z - t) / 60.0);
	elseif ((a * 120.0) <= 5e-125)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	elseif ((a * 120.0) <= 1000000.0)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-100], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-152], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -2e53 or 1e6 < (*.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. Taylor expanded in z around inf 84.2%

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

   if -2e53 < (*.f64 a 120) < -1e-100

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 75.5%

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

      1. associate-*r/ 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-/l* 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in z around inf 69.3%

      \[\leadsto \frac{x}{\color{blue}{0.016666666666666666 \cdot z}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   9. Simplified 69.3%

      \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   if -1e-100 < (*.f64 a 120) < 2.00000000000000013e-152

   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. Taylor expanded in a around 0 88.4%

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

      1. expm1-log1p-u 56.0%

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

      2. expm1-udef 26.4%

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

      3. associate-*r/ 26.4%

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

      4. *-commutative 26.4%

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

   6. Applied egg-rr 26.4%

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

      1. expm1-def 56.1%

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

      2. expm1-log1p 88.5%

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

      3. associate-/l* 88.5%

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

   8. Simplified 88.5%

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

   if 2.00000000000000013e-152 < (*.f64 a 120) < 4.99999999999999967e-125

   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. Taylor expanded in z around 0 90.8%

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

      1. associate-*r/ 90.7%

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

      2. associate-/l* 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in x around 0 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-*l/ 93.9%

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

   9. Simplified 93.9%

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

   if 4.99999999999999967e-125 < (*.f64 a 120) < 1e6

   1. Initial program 97.2%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 72.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-152}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 75.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+78}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 195000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* (- x y) (/ -60.0 t))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= z -5.8e+78)
     (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
     (if (<= z -1e+23)
       (/ (- x y) (/ (- z t) 60.0))
       (if (<= z -4.6e-23)
         t_2
         (if (<= z 1.5e-58)
           t_1
           (if (<= z 195000000.0)
             (* 60.0 (/ (- x y) (- z t)))
             (if (<= z 5e+93) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((x - y) * (-60.0 / t));
	double t_2 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -5.8e+78) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= -1e+23) {
		tmp = (x - y) / ((z - t) / 60.0);
	} else if (z <= -4.6e-23) {
		tmp = t_2;
	} else if (z <= 1.5e-58) {
		tmp = t_1;
	} else if (z <= 195000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 5e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if (z <= (-5.8d+78)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if (z <= (-1d+23)) then
        tmp = (x - y) / ((z - t) / 60.0d0)
    else if (z <= (-4.6d-23)) then
        tmp = t_2
    else if (z <= 1.5d-58) then
        tmp = t_1
    else if (z <= 195000000.0d0) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (z <= 5d+93) then
        tmp = t_1
    else
        tmp = t_2
    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) + ((x - y) * (-60.0 / t));
	double t_2 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -5.8e+78) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= -1e+23) {
		tmp = (x - y) / ((z - t) / 60.0);
	} else if (z <= -4.6e-23) {
		tmp = t_2;
	} else if (z <= 1.5e-58) {
		tmp = t_1;
	} else if (z <= 195000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 5e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((x - y) * (-60.0 / t))
	t_2 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if z <= -5.8e+78:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif z <= -1e+23:
		tmp = (x - y) / ((z - t) / 60.0)
	elif z <= -4.6e-23:
		tmp = t_2
	elif z <= 1.5e-58:
		tmp = t_1
	elif z <= 195000000.0:
		tmp = 60.0 * ((x - y) / (z - t))
	elif z <= 5e+93:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (z <= -5.8e+78)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (z <= -1e+23)
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) / 60.0));
	elseif (z <= -4.6e-23)
		tmp = t_2;
	elseif (z <= 1.5e-58)
		tmp = t_1;
	elseif (z <= 195000000.0)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (z <= 5e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((x - y) * (-60.0 / t));
	t_2 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if (z <= -5.8e+78)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif (z <= -1e+23)
		tmp = (x - y) / ((z - t) / 60.0);
	elseif (z <= -4.6e-23)
		tmp = t_2;
	elseif (z <= 1.5e-58)
		tmp = t_1;
	elseif (z <= 195000000.0)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (z <= 5e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+78], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e+23], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-23], t$95$2, If[LessEqual[z, 1.5e-58], t$95$1, If[LessEqual[z, 195000000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+93], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.80000000000000034e78

   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. Taylor expanded in x around inf 88.0%

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

      1. associate-*r/ 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-/l* 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in z around inf 88.0%

      \[\leadsto \frac{x}{\color{blue}{0.016666666666666666 \cdot z}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. *-commutative 88.0%

         \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   9. Simplified 88.0%

      \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]

   if -5.80000000000000034e78 < z < -9.9999999999999992e22

   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. Taylor expanded in a around 0 77.3%

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

      1. expm1-log1p-u 27.5%

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

      2. expm1-udef 14.0%

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

      3. associate-*r/ 14.0%

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

      4. *-commutative 14.0%

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

   6. Applied egg-rr 14.0%

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

      1. expm1-def 27.5%

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

      2. expm1-log1p 77.5%

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

      3. associate-/l* 77.5%

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

   8. Simplified 77.5%

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

   if -9.9999999999999992e22 < z < -4.6000000000000002e-23 or 5.0000000000000001e93 < z

   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. Taylor expanded in z around inf 96.4%

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

      1. associate-*r/ 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-/l* 96.5%

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

   6. Simplified 96.5%

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

   7. Taylor expanded in x around 0 87.2%

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

   if -4.6000000000000002e-23 < z < 1.50000000000000004e-58 or 1.95e8 < z < 5.0000000000000001e93

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 87.6%

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

      1. associate-*r/ 86.9%

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

      2. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

      1. associate-/r/ 87.6%

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

   8. Applied egg-rr 87.6%

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

   if 1.50000000000000004e-58 < z < 1.95e8

   1. Initial program 100.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 89.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+78}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;z \leq 195000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+93}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 6: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -1e-10)
     (* a 120.0)
     (if (<= (* a 120.0) 2e-148)
       t_1
       (if (<= (* a 120.0) 5e-125)
         (+ (* a 120.0) (/ -60.0 (/ t x)))
         (if (<= (* a 120.0) 1000000.0) t_1 (* a 120.0)))))))

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 ((a * 120.0) <= -1e-10) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	} else if ((a * 120.0) <= 1000000.0) {
		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 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-1d-10)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-148) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-125) then
        tmp = (a * 120.0d0) + ((-60.0d0) / (t / x))
    else if ((a * 120.0d0) <= 1000000.0d0) 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 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -1e-10) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-148) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-125) {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	} else if ((a * 120.0) <= 1000000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -1e-10:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-148:
		tmp = t_1
	elif (a * 120.0) <= 5e-125:
		tmp = (a * 120.0) + (-60.0 / (t / x))
	elif (a * 120.0) <= 1000000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-10)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-125)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(t / x)));
	elseif (Float64(a * 120.0) <= 1000000.0)
		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 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -1e-10)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-148)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-125)
		tmp = (a * 120.0) + (-60.0 / (t / x));
	elseif ((a * 120.0) <= 1000000.0)
		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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-10], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-148], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -1.00000000000000004e-10 or 1e6 < (*.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. Taylor expanded in z around inf 80.7%

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

   if -1.00000000000000004e-10 < (*.f64 a 120) < 1.99999999999999987e-148 or 4.99999999999999967e-125 < (*.f64 a 120) < 1e6

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 79.6%

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

   if 1.99999999999999987e-148 < (*.f64 a 120) < 4.99999999999999967e-125

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 88.6%

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

      1. associate-*r/ 88.6%

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

      2. associate-/l* 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in x around inf 88.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-148}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 1000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 57.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-116} \lor \neg \left(a \leq 1.25 \cdot 10^{-149} \lor \neg \left(a \leq 1.9 \cdot 10^{-132}\right) \land a \leq 2.2 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e-116)
         (not
          (or (<= a 1.25e-149) (and (not (<= a 1.9e-132)) (<= a 2.2e-41)))))
   (* 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 <= -7e-116) || !((a <= 1.25e-149) || (!(a <= 1.9e-132) && (a <= 2.2e-41)))) {
		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 <= (-7d-116)) .or. (.not. (a <= 1.25d-149) .or. (.not. (a <= 1.9d-132)) .and. (a <= 2.2d-41))) 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 <= -7e-116) || !((a <= 1.25e-149) || (!(a <= 1.9e-132) && (a <= 2.2e-41)))) {
		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 <= -7e-116) or not ((a <= 1.25e-149) or (not (a <= 1.9e-132) and (a <= 2.2e-41))):
		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 <= -7e-116) || !((a <= 1.25e-149) || (!(a <= 1.9e-132) && (a <= 2.2e-41))))
		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 <= -7e-116) || ~(((a <= 1.25e-149) || (~((a <= 1.9e-132)) && (a <= 2.2e-41)))))
		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, -7e-116], N[Not[Or[LessEqual[a, 1.25e-149], And[N[Not[LessEqual[a, 1.9e-132]], $MachinePrecision], LessEqual[a, 2.2e-41]]]], $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 < -6.99999999999999968e-116 or 1.24999999999999992e-149 < a < 1.8999999999999998e-132 or 2.2e-41 < a

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in z around inf 74.2%

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

   if -6.99999999999999968e-116 < a < 1.24999999999999992e-149 or 1.8999999999999998e-132 < a < 2.2e-41

   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. Step-by-step derivation

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 54.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-116} \lor \neg \left(a \leq 1.25 \cdot 10^{-149} \lor \neg \left(a \leq 1.9 \cdot 10^{-132}\right) \land a \leq 2.2 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 8: 57.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-131} \lor \neg \left(a \leq 2.75 \cdot 10^{-39}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e-118)
   (* a 120.0)
   (if (<= a 1.3e-149)
     (* -60.0 (/ y (- z t)))
     (if (or (<= a 5e-131) (not (<= a 2.75e-39)))
       (* a 120.0)
       (* -60.0 (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e-118) {
		tmp = a * 120.0;
	} else if (a <= 1.3e-149) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= 5e-131) || !(a <= 2.75e-39)) {
		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 (a <= (-2.6d-118)) then
        tmp = a * 120.0d0
    else if (a <= 1.3d-149) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((a <= 5d-131) .or. (.not. (a <= 2.75d-39))) 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 (a <= -2.6e-118) {
		tmp = a * 120.0;
	} else if (a <= 1.3e-149) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= 5e-131) || !(a <= 2.75e-39)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e-118:
		tmp = a * 120.0
	elif a <= 1.3e-149:
		tmp = -60.0 * (y / (z - t))
	elif (a <= 5e-131) or not (a <= 2.75e-39):
		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 (a <= -2.6e-118)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.3e-149)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif ((a <= 5e-131) || !(a <= 2.75e-39))
		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 (a <= -2.6e-118)
		tmp = a * 120.0;
	elseif (a <= 1.3e-149)
		tmp = -60.0 * (y / (z - t));
	elseif ((a <= 5e-131) || ~((a <= 2.75e-39)))
		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[a, -2.6e-118], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.3e-149], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5e-131], N[Not[LessEqual[a, 2.75e-39]], $MachinePrecision]], 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 a < -2.6e-118 or 1.29999999999999999e-149 < a < 5.0000000000000004e-131 or 2.75000000000000009e-39 < a

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in z around inf 74.2%

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

   if -2.6e-118 < a < 1.29999999999999999e-149

   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. Step-by-step derivation

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 58.1%

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

   if 5.0000000000000004e-131 < a < 2.75000000000000009e-39

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 84.6%

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

      1. expm1-log1p-u 38.6%

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

      2. expm1-udef 25.2%

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

      3. associate-*r/ 25.2%

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

      4. *-commutative 25.2%

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

   6. Applied egg-rr 25.2%

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

      1. expm1-def 38.6%

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

      2. expm1-log1p 84.5%

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

      3. associate-/l* 84.5%

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

   8. Simplified 84.5%

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

   9. Taylor expanded in z around 0 54.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-131} \lor \neg \left(a \leq 2.75 \cdot 10^{-39}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 9: 57.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 10^{-132} \lor \neg \left(a \leq 2.1 \cdot 10^{-40}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e-112)
   (* a 120.0)
   (if (<= a 1.3e-149)
     (/ -60.0 (/ (- z t) y))
     (if (or (<= a 1e-132) (not (<= a 2.1e-40)))
       (* a 120.0)
       (* -60.0 (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-112) {
		tmp = a * 120.0;
	} else if (a <= 1.3e-149) {
		tmp = -60.0 / ((z - t) / y);
	} else if ((a <= 1e-132) || !(a <= 2.1e-40)) {
		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 (a <= (-3.9d-112)) then
        tmp = a * 120.0d0
    else if (a <= 1.3d-149) then
        tmp = (-60.0d0) / ((z - t) / y)
    else if ((a <= 1d-132) .or. (.not. (a <= 2.1d-40))) 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 (a <= -3.9e-112) {
		tmp = a * 120.0;
	} else if (a <= 1.3e-149) {
		tmp = -60.0 / ((z - t) / y);
	} else if ((a <= 1e-132) || !(a <= 2.1e-40)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e-112:
		tmp = a * 120.0
	elif a <= 1.3e-149:
		tmp = -60.0 / ((z - t) / y)
	elif (a <= 1e-132) or not (a <= 2.1e-40):
		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 (a <= -3.9e-112)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.3e-149)
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	elseif ((a <= 1e-132) || !(a <= 2.1e-40))
		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 (a <= -3.9e-112)
		tmp = a * 120.0;
	elseif (a <= 1.3e-149)
		tmp = -60.0 / ((z - t) / y);
	elseif ((a <= 1e-132) || ~((a <= 2.1e-40)))
		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[a, -3.9e-112], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.3e-149], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1e-132], N[Not[LessEqual[a, 2.1e-40]], $MachinePrecision]], 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 a < -3.9000000000000001e-112 or 1.29999999999999999e-149 < a < 9.9999999999999999e-133 or 2.10000000000000018e-40 < a

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in z around inf 74.2%

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

   if -3.9000000000000001e-112 < a < 1.29999999999999999e-149

   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. Step-by-step derivation

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 58.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

   if 9.9999999999999999e-133 < a < 2.10000000000000018e-40

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 84.6%

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

      1. expm1-log1p-u 38.6%

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

      2. expm1-udef 25.2%

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

      3. associate-*r/ 25.2%

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

      4. *-commutative 25.2%

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

   6. Applied egg-rr 25.2%

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

      1. expm1-def 38.6%

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

      2. expm1-log1p 84.5%

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

      3. associate-/l* 84.5%

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

   8. Simplified 84.5%

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

   9. Taylor expanded in z around 0 54.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 10^{-132} \lor \neg \left(a \leq 2.1 \cdot 10^{-40}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 10: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-29} \lor \neg \left(t \leq 8.6 \cdot 10^{-56}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.3e-29) (not (<= t 8.6e-56)))
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
   (+ (* a 120.0) (* (- x y) (/ 60.0 z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.3e-29) || !(t <= 8.6e-56)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + ((x - y) * (60.0 / 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 <= (-4.3d-29)) .or. (.not. (t <= 8.6d-56))) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / 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 <= -4.3e-29) || !(t <= 8.6e-56)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.3e-29) or not (t <= 8.6e-56):
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.3e-29) || !(t <= 8.6e-56))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.3e-29) || ~((t <= 8.6e-56)))
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.3e-29], N[Not[LessEqual[t, 8.6e-56]], $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[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2999999999999998e-29 or 8.6000000000000002e-56 < t

   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. Taylor expanded in z around 0 89.0%

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

      1. associate-*r/ 88.4%

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

      2. associate-/l* 89.0%

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

   6. Simplified 89.0%

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

      1. associate-/r/ 89.0%

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

   8. Applied egg-rr 89.0%

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

   if -4.2999999999999998e-29 < t < 8.6000000000000002e-56

   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. Taylor expanded in z around inf 85.4%

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

      1. associate-*r/ 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

      1. div-inv 85.5%

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

      2. *-commutative 85.5%

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

      3. clear-num 85.5%

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

   8. Applied egg-rr 85.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-29} \lor \neg \left(t \leq 8.6 \cdot 10^{-56}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \]

Alternative 11: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+75} \lor \neg \left(x \leq 2.5 \cdot 10^{+175}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.7e+75) (not (<= x 2.5e+175)))
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
   (+ (* 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 <= -4.7e+75) || !(x <= 2.5e+175)) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} 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 <= (-4.7d+75)) .or. (.not. (x <= 2.5d+175))) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    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 <= -4.7e+75) || !(x <= 2.5e+175)) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.7e+75) or not (x <= 2.5e+175):
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	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 <= -4.7e+75) || !(x <= 2.5e+175))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	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 <= -4.7e+75) || ~((x <= 2.5e+175)))
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	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, -4.7e+75], N[Not[LessEqual[x, 2.5e+175]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $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 < -4.69999999999999984e75 or 2.5e175 < x

   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. Taylor expanded in x around inf 93.4%

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

   if -4.69999999999999984e75 < x < 2.5e175

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 92.3%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+75} \lor \neg \left(x \leq 2.5 \cdot 10^{+175}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]

Alternative 12: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-56}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.7e-30)
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
   (if (<= t 2.85e-56)
     (+ (* a 120.0) (* (- x y) (/ 60.0 z)))
     (+ (* a 120.0) (/ -60.0 (/ t (- x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e-30) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else if (t <= 2.85e-56) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + (-60.0 / (t / (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 (t <= (-3.7d-30)) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else if (t <= 2.85d-56) then
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) / (t / (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 (t <= -3.7e-30) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else if (t <= 2.85e-56) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + (-60.0 / (t / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.7e-30:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	elif t <= 2.85e-56:
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	else:
		tmp = (a * 120.0) + (-60.0 / (t / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.7e-30)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	elseif (t <= 2.85e-56)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(t / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.7e-30)
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	elseif (t <= 2.85e-56)
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	else
		tmp = (a * 120.0) + (-60.0 / (t / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.7e-30], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.85e-56], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000003e-30

   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. Taylor expanded in z around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. associate-/l* 89.9%

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

   6. Simplified 89.9%

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

      1. associate-/r/ 90.0%

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

   8. Applied egg-rr 90.0%

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

   if -3.7000000000000003e-30 < t < 2.8499999999999999e-56

   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. Taylor expanded in z around inf 85.4%

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

      1. associate-*r/ 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

      1. div-inv 85.5%

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

      2. *-commutative 85.5%

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

      3. clear-num 85.5%

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

   8. Applied egg-rr 85.5%

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

   if 2.8499999999999999e-56 < t

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in z around 0 88.3%

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

      1. associate-*r/ 87.0%

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

      2. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-56}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x - y}}\\ \end{array} \]

Alternative 13: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-19} \lor \neg \left(a \leq 2700000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.8e-19) (not (<= a 2700000.0)))
   (* 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 <= -6.8e-19) || !(a <= 2700000.0)) {
		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 <= (-6.8d-19)) .or. (.not. (a <= 2700000.0d0))) 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 <= -6.8e-19) || !(a <= 2700000.0)) {
		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 <= -6.8e-19) or not (a <= 2700000.0):
		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 ((a <= -6.8e-19) || !(a <= 2700000.0))
		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 <= -6.8e-19) || ~((a <= 2700000.0)))
		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[a, -6.8e-19], N[Not[LessEqual[a, 2700000.0]], $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 a < -6.8000000000000004e-19 or 2.7e6 < a

   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. Taylor expanded in z around inf 80.7%

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

   if -6.8000000000000004e-19 < a < 2.7e6

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 76.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-19} \lor \neg \left(a \leq 2700000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 14: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-141} \lor \neg \left(a \leq 7.8 \cdot 10^{-108}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.6e-141) (not (<= a 7.8e-108))) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e-141) || !(a <= 7.8e-108)) {
		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 ((a <= (-5.6d-141)) .or. (.not. (a <= 7.8d-108))) 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 ((a <= -5.6e-141) || !(a <= 7.8e-108)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.6e-141) or not (a <= 7.8e-108):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.6e-141) || !(a <= 7.8e-108))
		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 ((a <= -5.6e-141) || ~((a <= 7.8e-108)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.6e-141], N[Not[LessEqual[a, 7.8e-108]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.60000000000000023e-141 or 7.79999999999999989e-108 < a

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in z around inf 67.9%

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

   if -5.60000000000000023e-141 < a < 7.79999999999999989e-108

   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. Taylor expanded in z around 0 61.3%

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

      1. associate-*r/ 61.3%

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

      2. associate-/l* 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in x around 0 48.1%

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

      1. *-commutative 48.1%

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

      2. associate-*l/ 48.1%

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

   9. Simplified 48.1%

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

       1. +-commutative 48.1%

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

       2. fma-def 48.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t}\right)} \]

       3. *-commutative 48.1%

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{60 \cdot y}}{t}\right) \]

       4. *-un-lft-identity 48.1%

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{60 \cdot y}{\color{blue}{1 \cdot t}}\right) \]

       5. times-frac 48.1%

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{1} \cdot \frac{y}{t}}\right) \]

       6. metadata-eval 48.1%

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{60} \cdot \frac{y}{t}\right) \]

   11. Applied egg-rr 48.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{y}{t}\right)} \]

   12. Taylor expanded in a around 0 39.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-141} \lor \neg \left(a \leq 7.8 \cdot 10^{-108}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 15: 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 99.4%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 16: 51.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+195}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 5.2e+195) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.2e+195) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (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 (y <= 5.2d+195) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (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 (y <= 5.2e+195) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 5.2e+195:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 5.2e+195)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 5.2e+195)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 5.2e+195], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.20000000000000004e195

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in z around inf 57.6%

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

   if 5.20000000000000004e195 < y

   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. Taylor expanded in z around inf 54.2%

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

      1. associate-*r/ 54.1%

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

      2. *-commutative 54.1%

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

      3. associate-/l* 54.3%

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

   6. Simplified 54.3%

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

   7. Taylor expanded in y around inf 41.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+195}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 17: 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 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Taylor expanded in z around inf 52.8%

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

5. Final simplification 52.8%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% 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 2023336 
(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)))