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

Percentage Accurate: 99.5% → 99.8%

Time: 14.0s

Alternatives: 21

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: 99.5% 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 99.8%

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

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

Alternative 2: 82.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-108}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+21}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* x (/ 60.0 (- z t))))))
   (if (<= (* a 120.0) -4e-38)
     t_1
     (if (<= (* a 120.0) 1e-108)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (<= (* a 120.0) 5e-89)
         t_1
         (if (<= (* a 120.0) 1e-12)
           (* 60.0 (/ (- x y) (- z t)))
           (if (<= (* a 120.0) 1e+21)
             (+ (* a 120.0) (/ 60.0 (/ (- z) y)))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (60.0 / (z - t)));
	double tmp;
	if ((a * 120.0) <= -4e-38) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-108) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= 5e-89) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-12) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+21) {
		tmp = (a * 120.0) + (60.0 / (-z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    if ((a * 120.0d0) <= (-4d-38)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 1d-108) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if ((a * 120.0d0) <= 5d-89) then
        tmp = t_1
    else if ((a * 120.0d0) <= 1d-12) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 1d+21) then
        tmp = (a * 120.0d0) + (60.0d0 / (-z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (60.0 / (z - t)));
	double tmp;
	if ((a * 120.0) <= -4e-38) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-108) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= 5e-89) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-12) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+21) {
		tmp = (a * 120.0) + (60.0 / (-z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x * (60.0 / (z - t)))
	tmp = 0
	if (a * 120.0) <= -4e-38:
		tmp = t_1
	elif (a * 120.0) <= 1e-108:
		tmp = 60.0 / ((z - t) / (x - y))
	elif (a * 120.0) <= 5e-89:
		tmp = t_1
	elif (a * 120.0) <= 1e-12:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 1e+21:
		tmp = (a * 120.0) + (60.0 / (-z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-38)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 1e-108)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (Float64(a * 120.0) <= 5e-89)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 1e-12)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e+21)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(-z) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x * (60.0 / (z - t)));
	tmp = 0.0;
	if ((a * 120.0) <= -4e-38)
		tmp = t_1;
	elseif ((a * 120.0) <= 1e-108)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif ((a * 120.0) <= 5e-89)
		tmp = t_1;
	elseif ((a * 120.0) <= 1e-12)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 1e+21)
		tmp = (a * 120.0) + (60.0 / (-z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-38], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-108], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-89], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-12], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+21], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[((-z) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -3.9999999999999998e-38 or 1.00000000000000004e-108 < (*.f64 a 120) < 4.99999999999999967e-89 or 1e21 < (*.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 x around inf 90.8%

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

      1. associate-*r/ 90.8%

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

      2. associate-*l/ 90.8%

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

      3. *-commutative 90.8%

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

   6. Simplified 90.8%

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

   if -3.9999999999999998e-38 < (*.f64 a 120) < 1.00000000000000004e-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* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/l* 99.7%

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

      2. clear-num 99.5%

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

      3. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 88.5%

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

      1. associate-*r/ 88.5%

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

      2. associate-/l* 88.6%

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

   8. Simplified 88.6%

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

   if 4.99999999999999967e-89 < (*.f64 a 120) < 9.9999999999999998e-13

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 77.1%

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

   if 9.9999999999999998e-13 < (*.f64 a 120) < 1e21

   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* 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 inf 90.4%

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

   5. Taylor expanded in x around 0 90.4%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{z}{y}}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. mul-1-neg 90.4%

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

   7. Simplified 90.4%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-108}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-89}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+21}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+70}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-38)
   (+ (* a 120.0) (/ (* 60.0 x) z))
   (if (<= (* a 120.0) 1e-12)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 1e+70)
       (+ (* a 120.0) (/ 60.0 (/ z x)))
       (if (<= (* a 120.0) 5e+165)
         (+ (* a 120.0) (/ (* 60.0 y) t))
         (+ (* a 120.0) (* -60.0 (/ y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-38) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 1e-12) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+70) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 5e+165) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else {
		tmp = (a * 120.0) + (-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 ((a * 120.0d0) <= (-4d-38)) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else if ((a * 120.0d0) <= 1d-12) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 1d+70) then
        tmp = (a * 120.0d0) + (60.0d0 / (z / x))
    else if ((a * 120.0d0) <= 5d+165) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else
        tmp = (a * 120.0d0) + ((-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 ((a * 120.0) <= -4e-38) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 1e-12) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+70) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 5e+165) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e-38:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	elif (a * 120.0) <= 1e-12:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 1e+70:
		tmp = (a * 120.0) + (60.0 / (z / x))
	elif (a * 120.0) <= 5e+165:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-38)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	elseif (Float64(a * 120.0) <= 1e-12)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e+70)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / x)));
	elseif (Float64(a * 120.0) <= 5e+165)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e-38)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	elseif ((a * 120.0) <= 1e-12)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 1e+70)
		tmp = (a * 120.0) + (60.0 / (z / x));
	elseif ((a * 120.0) <= 5e+165)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-38], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-12], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+70], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+165], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -3.9999999999999998e-38

   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* 99.9%

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

   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%

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

      1. associate-/r/ 80.7%

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

   6. Applied egg-rr 80.7%

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

   7. Taylor expanded in x around inf 81.3%

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

      1. associate-*r/ 81.3%

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

   9. Simplified 81.3%

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

   if -3.9999999999999998e-38 < (*.f64 a 120) < 9.9999999999999998e-13

   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 a around 0 83.1%

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

   if 9.9999999999999998e-13 < (*.f64 a 120) < 1.00000000000000007e70

   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 78.3%

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

   5. Taylor expanded in x around inf 73.8%

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

   if 1.00000000000000007e70 < (*.f64 a 120) < 4.9999999999999997e165

   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 z around 0 81.4%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{t}{x - y}}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. neg-mul-1 81.4%

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

      2. distribute-neg-frac 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in x around 0 99.1%

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

      1. associate-*r/ 99.2%

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

   9. Simplified 99.2%

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

   if 4.9999999999999997e165 < (*.f64 a 120)

   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 83.2%

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

   5. Taylor expanded in x around 0 85.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+70}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 4: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+70}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-38)
   (+ (* a 120.0) (/ (* 60.0 x) z))
   (if (<= (* a 120.0) 1e-12)
     (/ 60.0 (/ (- z t) (- x y)))
     (if (<= (* a 120.0) 1e+70)
       (+ (* a 120.0) (/ 60.0 (/ z x)))
       (if (<= (* a 120.0) 5e+165)
         (+ (* a 120.0) (/ (* 60.0 y) t))
         (+ (* a 120.0) (* -60.0 (/ y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-38) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 1e-12) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= 1e+70) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 5e+165) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else {
		tmp = (a * 120.0) + (-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 ((a * 120.0d0) <= (-4d-38)) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else if ((a * 120.0d0) <= 1d-12) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if ((a * 120.0d0) <= 1d+70) then
        tmp = (a * 120.0d0) + (60.0d0 / (z / x))
    else if ((a * 120.0d0) <= 5d+165) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else
        tmp = (a * 120.0d0) + ((-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 ((a * 120.0) <= -4e-38) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 1e-12) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= 1e+70) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 5e+165) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e-38:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	elif (a * 120.0) <= 1e-12:
		tmp = 60.0 / ((z - t) / (x - y))
	elif (a * 120.0) <= 1e+70:
		tmp = (a * 120.0) + (60.0 / (z / x))
	elif (a * 120.0) <= 5e+165:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-38)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	elseif (Float64(a * 120.0) <= 1e-12)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (Float64(a * 120.0) <= 1e+70)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / x)));
	elseif (Float64(a * 120.0) <= 5e+165)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e-38)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	elseif ((a * 120.0) <= 1e-12)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif ((a * 120.0) <= 1e+70)
		tmp = (a * 120.0) + (60.0 / (z / x));
	elseif ((a * 120.0) <= 5e+165)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-38], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-12], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+70], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+165], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -3.9999999999999998e-38

   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* 99.9%

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

   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%

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

      1. associate-/r/ 80.7%

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

   6. Applied egg-rr 80.7%

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

   7. Taylor expanded in x around inf 81.3%

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

      1. associate-*r/ 81.3%

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

   9. Simplified 81.3%

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

   if -3.9999999999999998e-38 < (*.f64 a 120) < 9.9999999999999998e-13

   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. Step-by-step derivation

      1. associate-/l* 99.7%

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

      2. clear-num 99.5%

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

      3. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.1%

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

      1. associate-*r/ 83.2%

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

      2. associate-/l* 83.2%

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

   8. Simplified 83.2%

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

   if 9.9999999999999998e-13 < (*.f64 a 120) < 1.00000000000000007e70

   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 78.3%

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

   5. Taylor expanded in x around inf 73.8%

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

   if 1.00000000000000007e70 < (*.f64 a 120) < 4.9999999999999997e165

   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 z around 0 81.4%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{t}{x - y}}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. neg-mul-1 81.4%

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

      2. distribute-neg-frac 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in x around 0 99.1%

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

      1. associate-*r/ 99.2%

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

   9. Simplified 99.2%

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

   if 4.9999999999999997e165 < (*.f64 a 120)

   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 83.2%

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

   5. Taylor expanded in x around 0 85.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+70}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+165}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 5: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38} \lor \neg \left(a \cdot 120 \leq 10^{-12}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e-38) (not (<= (* a 120.0) 1e-12)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e-38) || !((a * 120.0) <= 1e-12)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-4d-38)) .or. (.not. ((a * 120.0d0) <= 1d-12))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e-38) || !((a * 120.0) <= 1e-12)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -4e-38) or not ((a * 120.0) <= 1e-12):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -4e-38) || !(Float64(a * 120.0) <= 1e-12))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -4e-38) || ~(((a * 120.0) <= 1e-12)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-38], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-12]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -3.9999999999999998e-38 or 9.9999999999999998e-13 < (*.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 79.4%

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

   if -3.9999999999999998e-38 < (*.f64 a 120) < 9.9999999999999998e-13

   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 a around 0 83.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38} \lor \neg \left(a \cdot 120 \leq 10^{-12}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 6: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-38)
   (+ (* a 120.0) (/ 60.0 (/ z x)))
   (if (<= (* a 120.0) 1e-12) (* 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) <= -4e-38) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 1e-12) {
		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) <= (-4d-38)) then
        tmp = (a * 120.0d0) + (60.0d0 / (z / x))
    else if ((a * 120.0d0) <= 1d-12) 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) <= -4e-38) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if ((a * 120.0) <= 1e-12) {
		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) <= -4e-38:
		tmp = (a * 120.0) + (60.0 / (z / x))
	elif (a * 120.0) <= 1e-12:
		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) <= -4e-38)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / x)));
	elseif (Float64(a * 120.0) <= 1e-12)
		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) <= -4e-38)
		tmp = (a * 120.0) + (60.0 / (z / x));
	elseif ((a * 120.0) <= 1e-12)
		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], -4e-38], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-12], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -3.9999999999999998e-38

   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* 99.9%

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

   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%

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

   5. Taylor expanded in x around inf 81.3%

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

   if -3.9999999999999998e-38 < (*.f64 a 120) < 9.9999999999999998e-13

   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 a around 0 83.1%

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

   if 9.9999999999999998e-13 < (*.f64 a 120)

   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 78.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-38)
   (+ (* a 120.0) (/ (* 60.0 x) z))
   (if (<= (* a 120.0) 1e-12) (* 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) <= -4e-38) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 1e-12) {
		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) <= (-4d-38)) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else if ((a * 120.0d0) <= 1d-12) 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) <= -4e-38) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 1e-12) {
		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) <= -4e-38:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	elif (a * 120.0) <= 1e-12:
		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) <= -4e-38)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	elseif (Float64(a * 120.0) <= 1e-12)
		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) <= -4e-38)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	elseif ((a * 120.0) <= 1e-12)
		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], -4e-38], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-12], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -3.9999999999999998e-38

   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* 99.9%

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

   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%

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

      1. associate-/r/ 80.7%

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

   6. Applied egg-rr 80.7%

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

   7. Taylor expanded in x around inf 81.3%

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

      1. associate-*r/ 81.3%

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

   9. Simplified 81.3%

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

   if -3.9999999999999998e-38 < (*.f64 a 120) < 9.9999999999999998e-13

   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 a around 0 83.1%

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

   if 9.9999999999999998e-13 < (*.f64 a 120)

   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 78.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-12}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-140}:\\ \;\;\;\;60 \cdot \frac{-y}{z - t}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-188}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e-41)
   (* a 120.0)
   (if (<= a -2.05e-140)
     (* 60.0 (/ (- y) (- z t)))
     (if (<= a -2.55e-188)
       (* 60.0 (/ (- y x) t))
       (if (<= a 3.4e-15) (* 60.0 (/ (- x y) z)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e-41) {
		tmp = a * 120.0;
	} else if (a <= -2.05e-140) {
		tmp = 60.0 * (-y / (z - t));
	} else if (a <= -2.55e-188) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 3.4e-15) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.4d-41)) then
        tmp = a * 120.0d0
    else if (a <= (-2.05d-140)) then
        tmp = 60.0d0 * (-y / (z - t))
    else if (a <= (-2.55d-188)) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 3.4d-15) then
        tmp = 60.0d0 * ((x - y) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e-41) {
		tmp = a * 120.0;
	} else if (a <= -2.05e-140) {
		tmp = 60.0 * (-y / (z - t));
	} else if (a <= -2.55e-188) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 3.4e-15) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e-41:
		tmp = a * 120.0
	elif a <= -2.05e-140:
		tmp = 60.0 * (-y / (z - t))
	elif a <= -2.55e-188:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 3.4e-15:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e-41)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.05e-140)
		tmp = Float64(60.0 * Float64(Float64(-y) / Float64(z - t)));
	elseif (a <= -2.55e-188)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 3.4e-15)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e-41)
		tmp = a * 120.0;
	elseif (a <= -2.05e-140)
		tmp = 60.0 * (-y / (z - t));
	elseif (a <= -2.55e-188)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 3.4e-15)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e-41], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.05e-140], N[(60.0 * N[((-y) / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-188], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-15], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3999999999999998e-41 or 3.4e-15 < 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 78.9%

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

   if -3.3999999999999998e-41 < a < -2.0500000000000001e-140

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 94.6%

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

   5. Taylor expanded in x around 0 65.7%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{y}{z - t}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 65.7%

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

      2. distribute-neg-frac 65.7%

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

   7. Simplified 65.7%

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

   if -2.0500000000000001e-140 < a < -2.55000000000000005e-188

   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 99.4%

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

   5. Taylor expanded in z around 0 73.6%

      \[\leadsto 60 \cdot \color{blue}{\left(-1 \cdot \frac{x - y}{t}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 73.6%

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

      2. distribute-neg-frac 73.6%

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

   7. Simplified 73.6%

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

   8. Taylor expanded in t around 0 73.6%

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

   if -2.55000000000000005e-188 < a < 3.4e-15

   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 a around 0 77.7%

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

   5. Taylor expanded in z around inf 53.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-140}:\\ \;\;\;\;60 \cdot \frac{-y}{z - t}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-188}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 85.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00062 \lor \neg \left(t \leq 2.8 \cdot 10^{-8}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.00062) (not (<= t 2.8e-8)))
   (+ (* 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 <= -0.00062) || !(t <= 2.8e-8)) {
		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 <= (-0.00062d0)) .or. (.not. (t <= 2.8d-8))) 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 <= -0.00062) || !(t <= 2.8e-8)) {
		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 <= -0.00062) or not (t <= 2.8e-8):
		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 <= -0.00062) || !(t <= 2.8e-8))
		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 <= -0.00062) || ~((t <= 2.8e-8)))
		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, -0.00062], N[Not[LessEqual[t, 2.8e-8]], $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 < -6.2e-4 or 2.7999999999999999e-8 < t

   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. 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. Taylor expanded in z around 0 83.0%

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

   if -6.2e-4 < t < 2.7999999999999999e-8

   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 90.8%

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

      1. associate-/r/ 90.7%

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

   6. Applied egg-rr 90.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00062 \lor \neg \left(t \leq 2.8 \cdot 10^{-8}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \]

Alternative 10: 85.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-5} \lor \neg \left(t \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e-5) (not (<= t 1.35e-8)))
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
   (+ (* a 120.0) (/ 60.0 (/ z (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-5) || !(t <= 1.35e-8)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.3d-5)) .or. (.not. (t <= 1.35d-8))) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-5) || !(t <= 1.35e-8)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e-5) or not (t <= 1.35e-8):
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = (a * 120.0) + (60.0 / (z / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e-5) || !(t <= 1.35e-8))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e-5) || ~((t <= 1.35e-8)))
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e-5], N[Not[LessEqual[t, 1.35e-8]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999992e-5 or 1.35000000000000001e-8 < t

   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. 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. Taylor expanded in z around 0 83.0%

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

   if -1.29999999999999992e-5 < t < 1.35000000000000001e-8

   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 90.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-5} \lor \neg \left(t \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 11: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+75} \lor \neg \left(y \leq 4.3 \cdot 10^{+117}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4e+75) (not (<= y 4.3e+117)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4e+75) || !(y <= 4.3e+117)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4d+75)) .or. (.not. (y <= 4.3d+117))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4e+75) || !(y <= 4.3e+117)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4e+75) or not (y <= 4.3e+117):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4e+75) || !(y <= 4.3e+117))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4e+75) || ~((y <= 4.3e+117)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4e+75], N[Not[LessEqual[y, 4.3e+117]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999971e75 or 4.29999999999999998e117 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 90.9%

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

   if -3.99999999999999971e75 < y < 4.29999999999999998e117

   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 x around inf 92.6%

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

      1. associate-*r/ 92.6%

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

      2. associate-*l/ 92.5%

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

      3. *-commutative 92.5%

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

   6. Simplified 92.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+75} \lor \neg \left(y \leq 4.3 \cdot 10^{+117}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]

Alternative 12: 88.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+76} \lor \neg \left(y \leq 1.1 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.4e+76) (not (<= y 1.1e+118)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+76) || !(y <= 1.1e+118)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.4d+76)) .or. (.not. (y <= 1.1d+118))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+76) || !(y <= 1.1e+118)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.4e+76) or not (y <= 1.1e+118):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.4e+76) || !(y <= 1.1e+118))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.4e+76) || ~((y <= 1.1e+118)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.4e+76], N[Not[LessEqual[y, 1.1e+118]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3999999999999999e76 or 1.09999999999999993e118 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 90.9%

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

   if -1.3999999999999999e76 < y < 1.09999999999999993e118

   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 x around inf 92.6%

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

      1. associate-*r/ 92.6%

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

      2. *-commutative 92.6%

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

   6. Simplified 92.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+76} \lor \neg \left(y \leq 1.1 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]

Alternative 13: 88.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120 + \frac{1}{z - t} \cdot \left(y \cdot -60\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+117}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.5e+75)
   (+ (* a 120.0) (* (/ 1.0 (- z t)) (* y -60.0)))
   (if (<= y 4.3e+117)
     (+ (* a 120.0) (/ (* 60.0 x) (- z t)))
     (+ (* a 120.0) (/ (* y -60.0) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.5e+75) {
		tmp = (a * 120.0) + ((1.0 / (z - t)) * (y * -60.0));
	} else if (y <= 4.3e+117) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.5d+75)) then
        tmp = (a * 120.0d0) + ((1.0d0 / (z - t)) * (y * (-60.0d0)))
    else if (y <= 4.3d+117) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - t))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.5e+75) {
		tmp = (a * 120.0) + ((1.0 / (z - t)) * (y * -60.0));
	} else if (y <= 4.3e+117) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.5e+75:
		tmp = (a * 120.0) + ((1.0 / (z - t)) * (y * -60.0))
	elif y <= 4.3e+117:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.5e+75)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(1.0 / Float64(z - t)) * Float64(y * -60.0)));
	elseif (y <= 4.3e+117)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.5e+75)
		tmp = (a * 120.0) + ((1.0 / (z - t)) * (y * -60.0));
	elseif (y <= 4.3e+117)
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.5e+75], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(y * -60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+117], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $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 3 regimes

2. if y < -4.5000000000000004e75

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/l* 99.9%

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

      2. clear-num 99.6%

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

      3. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 90.9%

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

   if -4.5000000000000004e75 < y < 4.29999999999999998e117

   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 x around inf 92.6%

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

      1. associate-*r/ 92.6%

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

      2. *-commutative 92.6%

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

   6. Simplified 92.6%

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

   if 4.29999999999999998e117 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 91.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120 + \frac{1}{z - t} \cdot \left(y \cdot -60\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+117}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]

Alternative 14: 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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. 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 15: 52.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-187}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-172}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e-61)
   (* a 120.0)
   (if (<= a -1.65e-187)
     (* -60.0 (/ x t))
     (if (<= a 1.6e-172) (* 60.0 (/ x z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e-61) {
		tmp = a * 120.0;
	} else if (a <= -1.65e-187) {
		tmp = -60.0 * (x / t);
	} else if (a <= 1.6e-172) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.7d-61)) then
        tmp = a * 120.0d0
    else if (a <= (-1.65d-187)) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 1.6d-172) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e-61) {
		tmp = a * 120.0;
	} else if (a <= -1.65e-187) {
		tmp = -60.0 * (x / t);
	} else if (a <= 1.6e-172) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e-61:
		tmp = a * 120.0
	elif a <= -1.65e-187:
		tmp = -60.0 * (x / t)
	elif a <= 1.6e-172:
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e-61)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.65e-187)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 1.6e-172)
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e-61)
		tmp = a * 120.0;
	elseif (a <= -1.65e-187)
		tmp = -60.0 * (x / t);
	elseif (a <= 1.6e-172)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.65e-187], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-172], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6999999999999999e-61 or 1.6000000000000001e-172 < a

   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 70.1%

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

   if -1.6999999999999999e-61 < a < -1.65e-187

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 96.3%

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

   5. Taylor expanded in x around inf 38.1%

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

   6. Taylor expanded in z around 0 30.6%

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

   if -1.65e-187 < a < 1.6000000000000001e-172

   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 a around 0 88.7%

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

   5. Taylor expanded in x around inf 46.1%

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

   6. Taylor expanded in z around inf 31.1%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-187}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-172}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16: 52.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-168}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e-61)
   (* a 120.0)
   (if (<= a -5.8e-191)
     (/ -60.0 (/ t x))
     (if (<= a 3.4e-168) (* 60.0 (/ x z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e-61) {
		tmp = a * 120.0;
	} else if (a <= -5.8e-191) {
		tmp = -60.0 / (t / x);
	} else if (a <= 3.4e-168) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.7d-61)) then
        tmp = a * 120.0d0
    else if (a <= (-5.8d-191)) then
        tmp = (-60.0d0) / (t / x)
    else if (a <= 3.4d-168) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e-61) {
		tmp = a * 120.0;
	} else if (a <= -5.8e-191) {
		tmp = -60.0 / (t / x);
	} else if (a <= 3.4e-168) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e-61:
		tmp = a * 120.0
	elif a <= -5.8e-191:
		tmp = -60.0 / (t / x)
	elif a <= 3.4e-168:
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e-61)
		tmp = Float64(a * 120.0);
	elseif (a <= -5.8e-191)
		tmp = Float64(-60.0 / Float64(t / x));
	elseif (a <= 3.4e-168)
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e-61)
		tmp = a * 120.0;
	elseif (a <= -5.8e-191)
		tmp = -60.0 / (t / x);
	elseif (a <= 3.4e-168)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -5.8e-191], N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-168], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6999999999999999e-61 or 3.40000000000000022e-168 < a

   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 70.1%

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

   if -1.6999999999999999e-61 < a < -5.7999999999999999e-191

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 96.3%

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

   5. Taylor expanded in x around inf 38.1%

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

   6. Taylor expanded in z around 0 30.6%

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

      1. associate-*r/ 30.6%

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

      2. associate-/l* 30.7%

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

   8. Simplified 30.7%

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

   if -5.7999999999999999e-191 < a < 3.40000000000000022e-168

   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 a around 0 88.7%

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

   5. Taylor expanded in x around inf 46.1%

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

   6. Taylor expanded in z around inf 31.1%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-168}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-171}:\\ \;\;\;\;\frac{60}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e-52)
   (* a 120.0)
   (if (<= a -1.6e-187)
     (/ -60.0 (/ t x))
     (if (<= a 1.1e-171) (/ 60.0 (/ z x)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-52) {
		tmp = a * 120.0;
	} else if (a <= -1.6e-187) {
		tmp = -60.0 / (t / x);
	} else if (a <= 1.1e-171) {
		tmp = 60.0 / (z / x);
	} 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 <= (-3.7d-52)) then
        tmp = a * 120.0d0
    else if (a <= (-1.6d-187)) then
        tmp = (-60.0d0) / (t / x)
    else if (a <= 1.1d-171) then
        tmp = 60.0d0 / (z / x)
    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 <= -3.7e-52) {
		tmp = a * 120.0;
	} else if (a <= -1.6e-187) {
		tmp = -60.0 / (t / x);
	} else if (a <= 1.1e-171) {
		tmp = 60.0 / (z / x);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e-52:
		tmp = a * 120.0
	elif a <= -1.6e-187:
		tmp = -60.0 / (t / x)
	elif a <= 1.1e-171:
		tmp = 60.0 / (z / x)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e-52)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.6e-187)
		tmp = Float64(-60.0 / Float64(t / x));
	elseif (a <= 1.1e-171)
		tmp = Float64(60.0 / Float64(z / x));
	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 <= -3.7e-52)
		tmp = a * 120.0;
	elseif (a <= -1.6e-187)
		tmp = -60.0 / (t / x);
	elseif (a <= 1.1e-171)
		tmp = 60.0 / (z / x);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e-52], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.6e-187], N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-171], N[(60.0 / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6999999999999997e-52 or 1.1000000000000001e-171 < a

   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 70.1%

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

   if -3.6999999999999997e-52 < a < -1.5999999999999999e-187

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 96.3%

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

   5. Taylor expanded in x around inf 38.1%

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

   6. Taylor expanded in z around 0 30.6%

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

      1. associate-*r/ 30.6%

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

      2. associate-/l* 30.7%

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

   8. Simplified 30.7%

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

   if -1.5999999999999999e-187 < a < 1.1000000000000001e-171

   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 a around 0 88.7%

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

   5. Taylor expanded in x around inf 46.1%

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

   6. Taylor expanded in z around inf 31.1%

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

      1. associate-*r/ 31.1%

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

      2. associate-/l* 31.1%

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

   8. Simplified 31.1%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-171}:\\ \;\;\;\;\frac{60}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 58.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-159}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e-64)
   (* a 120.0)
   (if (<= a 1.55e-159) (* 60.0 (/ x (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-64) {
		tmp = a * 120.0;
	} else if (a <= 1.55e-159) {
		tmp = 60.0 * (x / (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 <= (-3.7d-64)) then
        tmp = a * 120.0d0
    else if (a <= 1.55d-159) then
        tmp = 60.0d0 * (x / (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 <= -3.7e-64) {
		tmp = a * 120.0;
	} else if (a <= 1.55e-159) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e-64:
		tmp = a * 120.0
	elif a <= 1.55e-159:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e-64)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.55e-159)
		tmp = Float64(60.0 * Float64(x / 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 <= -3.7e-64)
		tmp = a * 120.0;
	elseif (a <= 1.55e-159)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e-64], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.55e-159], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.69999999999999999e-64 or 1.55e-159 < a

   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 70.1%

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

   if -3.69999999999999999e-64 < a < 1.55e-159

   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 a around 0 91.8%

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

   5. Taylor expanded in x around inf 42.9%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-159}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e-52)
   (* a 120.0)
   (if (<= a 3.6e-15) (* 60.0 (/ (- x y) z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-52) {
		tmp = a * 120.0;
	} else if (a <= 3.6e-15) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d-52)) then
        tmp = a * 120.0d0
    else if (a <= 3.6d-15) then
        tmp = 60.0d0 * ((x - y) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-52) {
		tmp = a * 120.0;
	} else if (a <= 3.6e-15) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e-52:
		tmp = a * 120.0
	elif a <= 3.6e-15:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e-52)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.6e-15)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e-52)
		tmp = a * 120.0;
	elseif (a <= 3.6e-15)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e-52], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.6e-15], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5e-52 or 3.6000000000000001e-15 < 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 78.4%

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

   if -5.5e-52 < a < 3.6000000000000001e-15

   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 a around 0 82.8%

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

   5. Taylor expanded in z around inf 52.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-15}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 20: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-179}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e-61)
   (* a 120.0)
   (if (<= a 2.6e-179) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e-61) {
		tmp = a * 120.0;
	} else if (a <= 2.6e-179) {
		tmp = -60.0 * (x / 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 <= (-1.7d-61)) then
        tmp = a * 120.0d0
    else if (a <= 2.6d-179) then
        tmp = (-60.0d0) * (x / 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 <= -1.7e-61) {
		tmp = a * 120.0;
	} else if (a <= 2.6e-179) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e-61:
		tmp = a * 120.0
	elif a <= 2.6e-179:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e-61)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.6e-179)
		tmp = Float64(-60.0 * Float64(x / 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 <= -1.7e-61)
		tmp = a * 120.0;
	elseif (a <= 2.6e-179)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.6e-179], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6999999999999999e-61 or 2.60000000000000005e-179 < a

   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 69.4%

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

   if -1.6999999999999999e-61 < a < 2.60000000000000005e-179

   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 91.6%

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

   5. Taylor expanded in x around inf 42.5%

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

   6. Taylor expanded in z around 0 23.9%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-179}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 21: 51.0% 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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 53.5%

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

5. Final simplification 53.5%

   \[\leadsto a \cdot 120 \]

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 2023271 
(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)))