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

Percentage Accurate: 99.3% → 99.8%

Time: 10.9s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 3 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ x t)))))
   (if (<= (* a 120.0) -2e-48)
     t_1
     (if (<= (* a 120.0) 1e-54)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= (* a 120.0) 5e-29)
         (+ (* a 120.0) (* x (/ -60.0 t)))
         (if (<= (* a 120.0) 3e+61) (+ (* a 120.0) (/ (* 60.0 x) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -2e-48) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 5e-29) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= 3e+61) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (x / t))
    if ((a * 120.0d0) <= (-2d-48)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 1d-54) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 5d-29) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if ((a * 120.0d0) <= 3d+61) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -2e-48) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 5e-29) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= 3e+61) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (x / t))
	tmp = 0
	if (a * 120.0) <= -2e-48:
		tmp = t_1
	elif (a * 120.0) <= 1e-54:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 5e-29:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif (a * 120.0) <= 3e+61:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-48)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 1e-54)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 5e-29)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif (Float64(a * 120.0) <= 3e+61)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (x / t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e-48)
		tmp = t_1;
	elseif ((a * 120.0) <= 1e-54)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 5e-29)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif ((a * 120.0) <= 3e+61)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-48], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-54], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-29], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 3e+61], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -1.9999999999999999e-48 or 3e61 < (*.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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 90.5%

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

   5. Taylor expanded in z around 0 81.6%

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

   if -1.9999999999999999e-48 < (*.f64 a 120) < 1e-54

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.5%

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

   if 1e-54 < (*.f64 a 120) < 4.99999999999999986e-29

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 90.9%

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

   5. Taylor expanded in z around 0 90.9%

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

      1. associate-*r/ 90.8%

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

   7. Applied egg-rr 90.8%

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

      1. associate-/l* 90.9%

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

      2. associate-/r/ 91.1%

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

   9. Applied egg-rr 91.1%

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

   if 4.99999999999999986e-29 < (*.f64 a 120) < 3e61

   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* 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. 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 99.8%

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

      3. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 87.1%

      \[\leadsto \frac{1}{z - t} \cdot \color{blue}{\left(60 \cdot x\right)} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-commutative 87.1%

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

   8. Simplified 87.1%

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

   9. Taylor expanded in z around inf 73.1%

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

       1. associate-*r/ 73.3%

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

       2. *-commutative 73.3%

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

   11. Simplified 73.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 3 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + \frac{-1}{t} \cdot \left(60 \cdot x\right)\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 3 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-48)
   (+ (* a 120.0) (* (/ -1.0 t) (* 60.0 x)))
   (if (<= (* a 120.0) 1e-54)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 5e-29)
       (+ (* a 120.0) (* x (/ -60.0 t)))
       (if (<= (* a 120.0) 3e+61)
         (+ (* a 120.0) (/ (* 60.0 x) z))
         (+ (* a 120.0) (* -60.0 (/ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-48) {
		tmp = (a * 120.0) + ((-1.0 / t) * (60.0 * x));
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 5e-29) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= 3e+61) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-48)) then
        tmp = (a * 120.0d0) + (((-1.0d0) / t) * (60.0d0 * x))
    else if ((a * 120.0d0) <= 1d-54) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 5d-29) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if ((a * 120.0d0) <= 3d+61) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-48) {
		tmp = (a * 120.0) + ((-1.0 / t) * (60.0 * x));
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 5e-29) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= 3e+61) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-48:
		tmp = (a * 120.0) + ((-1.0 / t) * (60.0 * x))
	elif (a * 120.0) <= 1e-54:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 5e-29:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif (a * 120.0) <= 3e+61:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	else:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-48)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(-1.0 / t) * Float64(60.0 * x)));
	elseif (Float64(a * 120.0) <= 1e-54)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 5e-29)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif (Float64(a * 120.0) <= 3e+61)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-48)
		tmp = (a * 120.0) + ((-1.0 / t) * (60.0 * x));
	elseif ((a * 120.0) <= 1e-54)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 5e-29)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif ((a * 120.0) <= 3e+61)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	else
		tmp = (a * 120.0) + (-60.0 * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-48], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(-1.0 / t), $MachinePrecision] * N[(60.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-54], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-29], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 3e+61], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -1.9999999999999999e-48

   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. Step-by-step derivation

      1. associate-/l* 99.8%

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

      2. clear-num 99.8%

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

      3. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 87.5%

      \[\leadsto \frac{1}{z - t} \cdot \color{blue}{\left(60 \cdot x\right)} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-commutative 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in z around 0 78.4%

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

   if -1.9999999999999999e-48 < (*.f64 a 120) < 1e-54

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.5%

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

   if 1e-54 < (*.f64 a 120) < 4.99999999999999986e-29

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 90.9%

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

   5. Taylor expanded in z around 0 90.9%

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

      1. associate-*r/ 90.8%

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

   7. Applied egg-rr 90.8%

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

      1. associate-/l* 90.9%

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

      2. associate-/r/ 91.1%

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

   9. Applied egg-rr 91.1%

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

   if 4.99999999999999986e-29 < (*.f64 a 120) < 3e61

   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* 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. 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 99.8%

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

      3. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 87.1%

      \[\leadsto \frac{1}{z - t} \cdot \color{blue}{\left(60 \cdot x\right)} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-commutative 87.1%

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

   8. Simplified 87.1%

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

   9. Taylor expanded in z around inf 73.1%

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

       1. associate-*r/ 73.3%

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

       2. *-commutative 73.3%

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

   11. Simplified 73.3%

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

   if 3e61 < (*.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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 94.7%

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

   5. Taylor expanded in z around 0 86.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + \frac{-1}{t} \cdot \left(60 \cdot x\right)\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 3 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 4: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-48)
   (+ (* a 120.0) (* -60.0 (/ x t)))
   (if (<= (* a 120.0) 1e-54)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* x (/ -60.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-48) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-48)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a * 120.0d0) <= 1d-54) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-48) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-48:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a * 120.0) <= 1e-54:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-48)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 1e-54)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-48)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a * 120.0) <= 1e-54)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (x * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-48], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-54], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -1.9999999999999999e-48

   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 87.5%

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

   5. Taylor expanded in z around 0 78.4%

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

   if -1.9999999999999999e-48 < (*.f64 a 120) < 1e-54

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.5%

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

   if 1e-54 < (*.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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 92.9%

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

   5. Taylor expanded in z around 0 79.4%

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

      1. associate-*r/ 79.4%

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

   7. Applied egg-rr 79.4%

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

      1. associate-/l* 79.5%

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

      2. associate-/r/ 79.4%

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

   9. Applied egg-rr 79.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]

Alternative 5: 77.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-49)
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (if (<= (* a 120.0) 1e-54)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* x (/ -60.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-49) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-49)) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else if ((a * 120.0d0) <= 1d-54) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-49) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if ((a * 120.0) <= 1e-54) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-49:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	elif (a * 120.0) <= 1e-54:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-49)
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 1e-54)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-49)
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	elseif ((a * 120.0) <= 1e-54)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (x * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-49], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-54], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -1.99999999999999987e-49

   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 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. associate-/l* 84.1%

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

   6. Simplified 84.1%

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

   if -1.99999999999999987e-49 < (*.f64 a 120) < 1e-54

   1. Initial program 98.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 88.4%

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

   if 1e-54 < (*.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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 92.9%

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

   5. Taylor expanded in z around 0 79.4%

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

      1. associate-*r/ 79.4%

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

   7. Applied egg-rr 79.4%

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

      1. associate-/l* 79.5%

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

      2. associate-/r/ 79.4%

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

   9. Applied egg-rr 79.4%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-54}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]

Alternative 6: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+72} \lor \neg \left(y \leq 2.15 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.3e+72) (not (<= y 2.15e+46)))
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.3e+72) || !(y <= 2.15e+46)) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.3d+72)) .or. (.not. (y <= 2.15d+46))) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.3e+72) || !(y <= 2.15e+46)) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.3e+72) or not (y <= 2.15e+46):
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	else:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.3e+72) || !(y <= 2.15e+46))
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.3e+72) || ~((y <= 2.15e+46)))
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	else
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.3e+72], N[Not[LessEqual[y, 2.15e+46]], $MachinePrecision]], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999991e72 or 2.15000000000000002e46 < y

   1. Initial program 98.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 88.9%

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

      1. associate-*r/ 87.9%

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

      2. associate-/l* 88.9%

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

   6. Simplified 88.9%

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

   if -1.29999999999999991e72 < y < 2.15000000000000002e46

   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 x around inf 96.2%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+72} \lor \neg \left(y \leq 2.15 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 7: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-50} \lor \neg \left(a \leq 2.6 \cdot 10^{-54}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.3e-50) (not (<= a 2.6e-54)))
   (+ (* a 120.0) (* -60.0 (/ x t)))
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-50) || !(a <= 2.6e-54)) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.3d-50)) .or. (.not. (a <= 2.6d-54))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-50) || !(a <= 2.6e-54)) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.3e-50) or not (a <= 2.6e-54):
		tmp = (a * 120.0) + (-60.0 * (x / t))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.3e-50) || !(a <= 2.6e-54))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	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 <= -1.3e-50) || ~((a <= 2.6e-54)))
		tmp = (a * 120.0) + (-60.0 * (x / t));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.3e-50], N[Not[LessEqual[a, 2.6e-54]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3000000000000001e-50 or 2.60000000000000002e-54 < 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 x around inf 90.2%

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

   5. Taylor expanded in z around 0 78.9%

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

   if -1.3000000000000001e-50 < a < 2.60000000000000002e-54

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-50} \lor \neg \left(a \leq 2.6 \cdot 10^{-54}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 8: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-48}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e-20)
   (* a 120.0)
   (if (<= a 1.4e-48) (* 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 <= -3.5e-20) {
		tmp = a * 120.0;
	} else if (a <= 1.4e-48) {
		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 <= (-3.5d-20)) then
        tmp = a * 120.0d0
    else if (a <= 1.4d-48) 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 <= -3.5e-20) {
		tmp = a * 120.0;
	} else if (a <= 1.4e-48) {
		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 <= -3.5e-20:
		tmp = a * 120.0
	elif a <= 1.4e-48:
		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 (a <= -3.5e-20)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.4e-48)
		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 <= -3.5e-20)
		tmp = a * 120.0;
	elseif (a <= 1.4e-48)
		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[a, -3.5e-20], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.4e-48], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.50000000000000003e-20 or 1.40000000000000002e-48 < 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 74.5%

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

   if -3.50000000000000003e-20 < a < 1.40000000000000002e-48

   1. Initial program 98.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 84.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-48}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-113}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-67}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e-52)
   (* a 120.0)
   (if (<= a -8e-113)
     (* 60.0 (/ x z))
     (if (<= a 1.42e-67) (* 60.0 (/ y t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e-52) {
		tmp = a * 120.0;
	} else if (a <= -8e-113) {
		tmp = 60.0 * (x / z);
	} else if (a <= 1.42e-67) {
		tmp = 60.0 * (y / 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 <= (-1.35d-52)) then
        tmp = a * 120.0d0
    else if (a <= (-8d-113)) then
        tmp = 60.0d0 * (x / z)
    else if (a <= 1.42d-67) then
        tmp = 60.0d0 * (y / 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 <= -1.35e-52) {
		tmp = a * 120.0;
	} else if (a <= -8e-113) {
		tmp = 60.0 * (x / z);
	} else if (a <= 1.42e-67) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e-52:
		tmp = a * 120.0
	elif a <= -8e-113:
		tmp = 60.0 * (x / z)
	elif a <= 1.42e-67:
		tmp = 60.0 * (y / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e-52)
		tmp = Float64(a * 120.0);
	elseif (a <= -8e-113)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (a <= 1.42e-67)
		tmp = Float64(60.0 * Float64(y / 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 <= -1.35e-52)
		tmp = a * 120.0;
	elseif (a <= -8e-113)
		tmp = 60.0 * (x / z);
	elseif (a <= 1.42e-67)
		tmp = 60.0 * (y / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e-52], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8e-113], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e-67], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.35000000000000005e-52 or 1.42000000000000004e-67 < 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 71.0%

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

   if -1.35000000000000005e-52 < a < -7.99999999999999983e-113

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.6%

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

   5. Taylor expanded in x around inf 61.8%

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

   6. Taylor expanded in z around inf 38.0%

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

   if -7.99999999999999983e-113 < a < 1.42000000000000004e-67

   1. Initial program 98.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 62.1%

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

      2. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in z around 0 42.8%

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

   8. Taylor expanded in a around 0 36.3%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-113}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-67}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-112}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-67}:\\ \;\;\;\;\frac{60}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4e-52)
   (* a 120.0)
   (if (<= a -1.5e-112)
     (* 60.0 (/ x z))
     (if (<= a 1.42e-67) (/ 60.0 (/ t y)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4e-52) {
		tmp = a * 120.0;
	} else if (a <= -1.5e-112) {
		tmp = 60.0 * (x / z);
	} else if (a <= 1.42e-67) {
		tmp = 60.0 / (t / y);
	} 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 <= (-4d-52)) then
        tmp = a * 120.0d0
    else if (a <= (-1.5d-112)) then
        tmp = 60.0d0 * (x / z)
    else if (a <= 1.42d-67) then
        tmp = 60.0d0 / (t / y)
    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 <= -4e-52) {
		tmp = a * 120.0;
	} else if (a <= -1.5e-112) {
		tmp = 60.0 * (x / z);
	} else if (a <= 1.42e-67) {
		tmp = 60.0 / (t / y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4e-52:
		tmp = a * 120.0
	elif a <= -1.5e-112:
		tmp = 60.0 * (x / z)
	elif a <= 1.42e-67:
		tmp = 60.0 / (t / y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4e-52)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.5e-112)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (a <= 1.42e-67)
		tmp = Float64(60.0 / Float64(t / y));
	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 <= -4e-52)
		tmp = a * 120.0;
	elseif (a <= -1.5e-112)
		tmp = 60.0 * (x / z);
	elseif (a <= 1.42e-67)
		tmp = 60.0 / (t / y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4e-52], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.5e-112], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e-67], N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4e-52 or 1.42000000000000004e-67 < 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 71.0%

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

   if -4e-52 < a < -1.5e-112

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.6%

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

   5. Taylor expanded in x around inf 61.8%

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

   6. Taylor expanded in z around inf 38.0%

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

   if -1.5e-112 < a < 1.42000000000000004e-67

   1. Initial program 98.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 62.1%

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

      2. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in z around 0 42.8%

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

   8. Taylor expanded in a around 0 36.3%

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

      1. associate-*r/ 36.4%

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

      2. associate-/l* 36.3%

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

   10. Simplified 36.3%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-112}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-67}:\\ \;\;\;\;\frac{60}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-67}:\\ \;\;\;\;\frac{60}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e-52)
   (* a 120.0)
   (if (<= a -3.8e-114)
     (/ (* 60.0 x) z)
     (if (<= a 2.55e-67) (/ 60.0 (/ t y)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-52) {
		tmp = a * 120.0;
	} else if (a <= -3.8e-114) {
		tmp = (60.0 * x) / z;
	} else if (a <= 2.55e-67) {
		tmp = 60.0 / (t / y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.8d-52)) then
        tmp = a * 120.0d0
    else if (a <= (-3.8d-114)) then
        tmp = (60.0d0 * x) / z
    else if (a <= 2.55d-67) then
        tmp = 60.0d0 / (t / y)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-52) {
		tmp = a * 120.0;
	} else if (a <= -3.8e-114) {
		tmp = (60.0 * x) / z;
	} else if (a <= 2.55e-67) {
		tmp = 60.0 / (t / y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e-52:
		tmp = a * 120.0
	elif a <= -3.8e-114:
		tmp = (60.0 * x) / z
	elif a <= 2.55e-67:
		tmp = 60.0 / (t / y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e-52)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.8e-114)
		tmp = Float64(Float64(60.0 * x) / z);
	elseif (a <= 2.55e-67)
		tmp = Float64(60.0 / Float64(t / y));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e-52)
		tmp = a * 120.0;
	elseif (a <= -3.8e-114)
		tmp = (60.0 * x) / z;
	elseif (a <= 2.55e-67)
		tmp = 60.0 / (t / y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e-52], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.8e-114], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.55e-67], N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8000000000000003e-52 or 2.54999999999999991e-67 < 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 71.0%

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

   if -5.8000000000000003e-52 < a < -3.7999999999999998e-114

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.6%

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

   5. Taylor expanded in x around inf 61.8%

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

   6. Taylor expanded in z around inf 38.0%

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

      1. associate-*r/ 38.2%

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

   8. Simplified 38.2%

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

   if -3.7999999999999998e-114 < a < 2.54999999999999991e-67

   1. Initial program 98.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 62.1%

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

      2. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in z around 0 42.8%

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

   8. Taylor expanded in a around 0 36.3%

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

      1. associate-*r/ 36.4%

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

      2. associate-/l* 36.3%

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

   10. Simplified 36.3%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-67}:\\ \;\;\;\;\frac{60}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-112}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.4e-53)
   (* a 120.0)
   (if (<= a -2e-112)
     (/ (* 60.0 x) z)
     (if (<= a 4.7e-67) (/ (* 60.0 y) t) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.4e-53) {
		tmp = a * 120.0;
	} else if (a <= -2e-112) {
		tmp = (60.0 * x) / z;
	} else if (a <= 4.7e-67) {
		tmp = (60.0 * y) / 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 <= (-8.4d-53)) then
        tmp = a * 120.0d0
    else if (a <= (-2d-112)) then
        tmp = (60.0d0 * x) / z
    else if (a <= 4.7d-67) then
        tmp = (60.0d0 * y) / 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 <= -8.4e-53) {
		tmp = a * 120.0;
	} else if (a <= -2e-112) {
		tmp = (60.0 * x) / z;
	} else if (a <= 4.7e-67) {
		tmp = (60.0 * y) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.4e-53:
		tmp = a * 120.0
	elif a <= -2e-112:
		tmp = (60.0 * x) / z
	elif a <= 4.7e-67:
		tmp = (60.0 * y) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.4e-53)
		tmp = Float64(a * 120.0);
	elseif (a <= -2e-112)
		tmp = Float64(Float64(60.0 * x) / z);
	elseif (a <= 4.7e-67)
		tmp = Float64(Float64(60.0 * y) / 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 <= -8.4e-53)
		tmp = a * 120.0;
	elseif (a <= -2e-112)
		tmp = (60.0 * x) / z;
	elseif (a <= 4.7e-67)
		tmp = (60.0 * y) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.4e-53], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2e-112], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 4.7e-67], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.3999999999999991e-53 or 4.70000000000000004e-67 < 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 71.0%

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

   if -8.3999999999999991e-53 < a < -1.9999999999999999e-112

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.6%

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

   5. Taylor expanded in x around inf 61.8%

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

   6. Taylor expanded in z around inf 38.0%

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

      1. associate-*r/ 38.2%

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

   8. Simplified 38.2%

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

   if -1.9999999999999999e-112 < a < 4.70000000000000004e-67

   1. Initial program 98.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 62.1%

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

      2. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in z around 0 42.8%

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

   8. Taylor expanded in a around 0 36.3%

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

      1. associate-*r/ 36.4%

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

   10. Simplified 36.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-112}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 57.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-52} \lor \neg \left(a \leq 4.5 \cdot 10^{-58}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e-52) (not (<= a 4.5e-58)))
   (* a 120.0)
   (* 60.0 (/ x (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e-52) || !(a <= 4.5e-58)) {
		tmp = a * 120.0;
	} else {
		tmp = 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 ((a <= (-1.4d-52)) .or. (.not. (a <= 4.5d-58))) then
        tmp = a * 120.0d0
    else
        tmp = 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 ((a <= -1.4e-52) || !(a <= 4.5e-58)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.4e-52) or not (a <= 4.5e-58):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.4e-52) || !(a <= 4.5e-58))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.4e-52) || ~((a <= 4.5e-58)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.4e-52], N[Not[LessEqual[a, 4.5e-58]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.39999999999999997e-52 or 4.5000000000000003e-58 < 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 71.9%

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

   if -1.39999999999999997e-52 < a < 4.5000000000000003e-58

   1. Initial program 98.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 88.2%

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

   5. Taylor expanded in x around inf 45.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-52} \lor \neg \left(a \leq 4.5 \cdot 10^{-58}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]

Alternative 14: 57.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-57}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-52)
   (* a 120.0)
   (if (<= a 1.85e-57) (/ 60.0 (/ (- z t) x)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-52) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-57) {
		tmp = 60.0 / ((z - t) / 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 <= (-1.6d-52)) then
        tmp = a * 120.0d0
    else if (a <= 1.85d-57) then
        tmp = 60.0d0 / ((z - t) / 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 <= -1.6e-52) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-57) {
		tmp = 60.0 / ((z - t) / x);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-52:
		tmp = a * 120.0
	elif a <= 1.85e-57:
		tmp = 60.0 / ((z - t) / x)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-52)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.85e-57)
		tmp = Float64(60.0 / Float64(Float64(z - t) / 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 <= -1.6e-52)
		tmp = a * 120.0;
	elseif (a <= 1.85e-57)
		tmp = 60.0 / ((z - t) / x);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-52], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.85e-57], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.60000000000000005e-52 or 1.85e-57 < 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 71.9%

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

   if -1.60000000000000005e-52 < a < 1.85e-57

   1. Initial program 98.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 88.2%

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

   5. Taylor expanded in x around inf 45.0%

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

      1. clear-num 44.9%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x}}} \]

      2. un-div-inv 45.0%

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

   7. Applied egg-rr 45.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-57}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15: 52.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+140} \lor \neg \left(x \leq 1.05 \cdot 10^{+236}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.5e+140) (not (<= x 1.05e+236)))
   (* -60.0 (/ x t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.5e+140) || !(x <= 1.05e+236)) {
		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 ((x <= (-3.5d+140)) .or. (.not. (x <= 1.05d+236))) 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 ((x <= -3.5e+140) || !(x <= 1.05e+236)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.5e+140) or not (x <= 1.05e+236):
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.5e+140) || !(x <= 1.05e+236))
		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 ((x <= -3.5e+140) || ~((x <= 1.05e+236)))
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.5e+140], N[Not[LessEqual[x, 1.05e+236]], $MachinePrecision]], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.49999999999999989e140 or 1.05000000000000003e236 < x

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 78.3%

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

   5. Taylor expanded in x around inf 78.0%

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

   6. Taylor expanded in z around 0 53.1%

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

   if -3.49999999999999989e140 < x < 1.05000000000000003e236

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 56.0%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+140} \lor \neg \left(x \leq 1.05 \cdot 10^{+236}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16: 50.9% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around inf 49.8%

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

5. Final simplification 49.8%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023194 
(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)))