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

Percentage Accurate: 99.3% → 99.8%

Time: 15.3s

Alternatives: 20

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.4%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 80.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-132}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-61} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+36}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))))
   (if (<= (* a 120.0) -2e-97)
     t_1
     (if (<= (* a 120.0) 5e-132)
       (/ (* 60.0 (- x y)) (- z t))
       (if (or (<= (* a 120.0) 5e-61) (not (<= (* a 120.0) 2e+36)))
         t_1
         (/ 60.0 (/ (- z t) (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / ((z - t) / y)) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-132) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (((a * 120.0) <= 5e-61) || !((a * 120.0) <= 2e+36)) {
		tmp = t_1;
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    if ((a * 120.0d0) <= (-2d-97)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d-132) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if (((a * 120.0d0) <= 5d-61) .or. (.not. ((a * 120.0d0) <= 2d+36))) then
        tmp = t_1
    else
        tmp = 60.0d0 / ((z - t) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / ((z - t) / y)) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e-132) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (((a * 120.0) <= 5e-61) || !((a * 120.0) <= 2e+36)) {
		tmp = t_1;
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / ((z - t) / y)) + (a * 120.0)
	tmp = 0
	if (a * 120.0) <= -2e-97:
		tmp = t_1
	elif (a * 120.0) <= 5e-132:
		tmp = (60.0 * (x - y)) / (z - t)
	elif ((a * 120.0) <= 5e-61) or not ((a * 120.0) <= 2e+36):
		tmp = t_1
	else:
		tmp = 60.0 / ((z - t) / (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-97)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e-132)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif ((Float64(a * 120.0) <= 5e-61) || !(Float64(a * 120.0) <= 2e+36))
		tmp = t_1;
	else
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / ((z - t) / y)) + (a * 120.0);
	tmp = 0.0;
	if ((a * 120.0) <= -2e-97)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e-132)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif (((a * 120.0) <= 5e-61) || ~(((a * 120.0) <= 2e+36)))
		tmp = t_1;
	else
		tmp = 60.0 / ((z - t) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = 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], -2e-97], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-132], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-61], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+36]], $MachinePrecision]], t$95$1, N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2.00000000000000007e-97 or 4.9999999999999999e-132 < (*.f64 a 120) < 4.9999999999999999e-61 or 2.00000000000000008e36 < (*.f64 a 120)

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. associate-/l* 86.5%

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

   6. Simplified 86.5%

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

   if -2.00000000000000007e-97 < (*.f64 a 120) < 4.9999999999999999e-132

   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* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 89.6%

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

      1. associate-*r/ 89.6%

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

   6. Applied egg-rr 89.6%

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

   if 4.9999999999999999e-61 < (*.f64 a 120) < 2.00000000000000008e36

   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 a around 0 79.2%

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

      1. div-inv 79.1%

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

   6. Applied egg-rr 79.1%

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

      1. expm1-log1p-u 20.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right)\right)\right)} \]

      2. expm1-udef 20.5%

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

      3. associate-*r* 20.5%

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

      4. un-div-inv 20.5%

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

   8. Applied egg-rr 20.5%

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

      1. expm1-def 20.8%

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

      2. expm1-log1p 79.0%

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

      3. associate-/l* 79.3%

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

   10. Simplified 79.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-132}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-61} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]

Alternative 3: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -2e-97)
     (* a 120.0)
     (if (<= (* a 120.0) 1e+59)
       t_1
       (if (<= (* a 120.0) 5e+160)
         (* a 120.0)
         (if (<= (* a 120.0) 1e+197) t_1 (+ (* a 120.0) (* 60.0 (/ x z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+59) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e+160) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+197) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-2d-97)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+59) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d+160) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+197) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+59) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e+160) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+197) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -2e-97:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+59:
		tmp = t_1
	elif (a * 120.0) <= 5e+160:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+197:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-97)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+59)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e+160)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+197)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e-97)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+59)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e+160)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+197)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-97], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+160], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+197], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2.00000000000000007e-97 or 9.99999999999999972e58 < (*.f64 a 120) < 5.0000000000000002e160

   1. Initial program 98.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 81.3%

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

   if -2.00000000000000007e-97 < (*.f64 a 120) < 9.99999999999999972e58 or 5.0000000000000002e160 < (*.f64 a 120) < 9.9999999999999995e196

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 82.6%

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

   if 9.9999999999999995e196 < (*.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 82.4%

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

   5. Taylor expanded in x around inf 85.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+59}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+197}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 70.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x - y}}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ (- z t) (- x y)))))
   (if (<= (* a 120.0) -2e-97)
     (* a 120.0)
     (if (<= (* a 120.0) 1e+59)
       t_1
       (if (<= (* a 120.0) 5e+160)
         (* a 120.0)
         (if (<= (* a 120.0) 1e+197) t_1 (+ (* a 120.0) (* 60.0 (/ x z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / (x - y));
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+59) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e+160) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+197) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / ((z - t) / (x - y))
    if ((a * 120.0d0) <= (-2d-97)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+59) then
        tmp = t_1
    else if ((a * 120.0d0) <= 5d+160) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+197) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / (x - y));
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+59) {
		tmp = t_1;
	} else if ((a * 120.0) <= 5e+160) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+197) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / ((z - t) / (x - y))
	tmp = 0
	if (a * 120.0) <= -2e-97:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+59:
		tmp = t_1
	elif (a * 120.0) <= 5e+160:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+197:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-97)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+59)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 5e+160)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+197)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / ((z - t) / (x - y));
	tmp = 0.0;
	if ((a * 120.0) <= -2e-97)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+59)
		tmp = t_1;
	elseif ((a * 120.0) <= 5e+160)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+197)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-97], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+160], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+197], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2.00000000000000007e-97 or 9.99999999999999972e58 < (*.f64 a 120) < 5.0000000000000002e160

   1. Initial program 98.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 81.3%

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

   if -2.00000000000000007e-97 < (*.f64 a 120) < 9.99999999999999972e58 or 5.0000000000000002e160 < (*.f64 a 120) < 9.9999999999999995e196

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 82.6%

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

      1. div-inv 82.4%

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

   6. Applied egg-rr 82.4%

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

      1. expm1-log1p-u 57.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right)\right)\right)} \]

      2. expm1-udef 29.0%

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

      3. associate-*r* 29.0%

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

      4. un-div-inv 29.0%

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

   8. Applied egg-rr 29.0%

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

      1. expm1-def 57.5%

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

      2. expm1-log1p 82.6%

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

      3. associate-/l* 82.6%

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

   10. Simplified 82.6%

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

   if 9.9999999999999995e196 < (*.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 82.4%

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

   5. Taylor expanded in x around inf 85.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+59}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+197}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+59}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+197}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-97)
   (* a 120.0)
   (if (<= (* a 120.0) 1e+59)
     (/ (* 60.0 (- x y)) (- z t))
     (if (<= (* a 120.0) 5e+160)
       (* a 120.0)
       (if (<= (* a 120.0) 1e+197)
         (/ 60.0 (/ (- z t) (- x y)))
         (+ (* a 120.0) (* 60.0 (/ x z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+59) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 5e+160) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+197) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-97)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+59) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if ((a * 120.0d0) <= 5d+160) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d+197) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-97) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+59) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 5e+160) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e+197) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-97:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+59:
		tmp = (60.0 * (x - y)) / (z - t)
	elif (a * 120.0) <= 5e+160:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e+197:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-97)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+59)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif (Float64(a * 120.0) <= 5e+160)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e+197)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-97)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+59)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif ((a * 120.0) <= 5e+160)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e+197)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-97], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+59], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+160], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+197], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2.00000000000000007e-97 or 9.99999999999999972e58 < (*.f64 a 120) < 5.0000000000000002e160

   1. Initial program 98.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 81.3%

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

   if -2.00000000000000007e-97 < (*.f64 a 120) < 9.99999999999999972e58

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 82.4%

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

      1. associate-*r/ 82.5%

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

   6. Applied egg-rr 82.5%

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

   if 5.0000000000000002e160 < (*.f64 a 120) < 9.9999999999999995e196

   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* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 86.6%

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

      1. div-inv 86.6%

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

   6. Applied egg-rr 86.6%

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

      1. expm1-log1p-u 54.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right)\right)\right)} \]

      2. expm1-udef 54.9%

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

      3. associate-*r* 54.9%

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

      4. un-div-inv 54.9%

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

   8. Applied egg-rr 54.9%

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

      1. expm1-def 54.9%

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

      2. expm1-log1p 86.9%

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

      3. associate-/l* 86.9%

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

   10. Simplified 86.9%

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

   if 9.9999999999999995e196 < (*.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 82.4%

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

   5. Taylor expanded in x around inf 85.8%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+59}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+197}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 6: 57.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{t}{x - y}}\\ \mathbf{if}\;a \leq -1.06 \cdot 10^{-108}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-298}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-273}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ -60.0 (/ t (- x y)))))
   (if (<= a -1.06e-108)
     (* a 120.0)
     (if (<= a 2.2e-298)
       (/ (* 60.0 x) (- z t))
       (if (<= a 5.2e-273)
         (* -60.0 (/ y (- z t)))
         (if (<= a 1.9e-154)
           t_1
           (if (<= a 5.5e-76)
             (* a 120.0)
             (if (<= a 7.1e-66)
               (* y (/ -60.0 (- z t)))
               (if (<= a 2.5e+26) t_1 (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -1.06e-108) {
		tmp = a * 120.0;
	} else if (a <= 2.2e-298) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 5.2e-273) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.9e-154) {
		tmp = t_1;
	} else if (a <= 5.5e-76) {
		tmp = a * 120.0;
	} else if (a <= 7.1e-66) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 2.5e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) / (t / (x - y))
    if (a <= (-1.06d-108)) then
        tmp = a * 120.0d0
    else if (a <= 2.2d-298) then
        tmp = (60.0d0 * x) / (z - t)
    else if (a <= 5.2d-273) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 1.9d-154) then
        tmp = t_1
    else if (a <= 5.5d-76) then
        tmp = a * 120.0d0
    else if (a <= 7.1d-66) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (a <= 2.5d+26) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -1.06e-108) {
		tmp = a * 120.0;
	} else if (a <= 2.2e-298) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 5.2e-273) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.9e-154) {
		tmp = t_1;
	} else if (a <= 5.5e-76) {
		tmp = a * 120.0;
	} else if (a <= 7.1e-66) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 2.5e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 / (t / (x - y))
	tmp = 0
	if a <= -1.06e-108:
		tmp = a * 120.0
	elif a <= 2.2e-298:
		tmp = (60.0 * x) / (z - t)
	elif a <= 5.2e-273:
		tmp = -60.0 * (y / (z - t))
	elif a <= 1.9e-154:
		tmp = t_1
	elif a <= 5.5e-76:
		tmp = a * 120.0
	elif a <= 7.1e-66:
		tmp = y * (-60.0 / (z - t))
	elif a <= 2.5e+26:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 / Float64(t / Float64(x - y)))
	tmp = 0.0
	if (a <= -1.06e-108)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.2e-298)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (a <= 5.2e-273)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 1.9e-154)
		tmp = t_1;
	elseif (a <= 5.5e-76)
		tmp = Float64(a * 120.0);
	elseif (a <= 7.1e-66)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (a <= 2.5e+26)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 / (t / (x - y));
	tmp = 0.0;
	if (a <= -1.06e-108)
		tmp = a * 120.0;
	elseif (a <= 2.2e-298)
		tmp = (60.0 * x) / (z - t);
	elseif (a <= 5.2e-273)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 1.9e-154)
		tmp = t_1;
	elseif (a <= 5.5e-76)
		tmp = a * 120.0;
	elseif (a <= 7.1e-66)
		tmp = y * (-60.0 / (z - t));
	elseif (a <= 2.5e+26)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.06e-108], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.2e-298], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-273], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-154], t$95$1, If[LessEqual[a, 5.5e-76], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 7.1e-66], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+26], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.06e-108 or 1.90000000000000005e-154 < a < 5.50000000000000014e-76 or 2.5e26 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 73.8%

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

   if -1.06e-108 < a < 2.2e-298

   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* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in a around 0 88.1%

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

   5. Taylor expanded in x around inf 56.7%

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

      1. associate-*r/ 56.7%

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

   7. Simplified 56.7%

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

   if 2.2e-298 < a < 5.19999999999999967e-273

   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 0 100.0%

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

   5. Taylor expanded in x around 0 86.8%

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

   if 5.19999999999999967e-273 < a < 1.90000000000000005e-154 or 7.09999999999999964e-66 < a < 2.5e26

   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 86.5%

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

      1. div-inv 86.2%

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

   6. Applied egg-rr 86.2%

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

   7. Taylor expanded in z around 0 55.9%

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

      1. associate-*r/ 55.9%

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

      2. associate-/l* 56.0%

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

   9. Simplified 56.0%

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

   if 5.50000000000000014e-76 < a < 7.09999999999999964e-66

   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* 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 a around 0 80.7%

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

   5. Taylor expanded in x around 0 61.4%

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

      1. associate-*r/ 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in y around 0 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-*l/ 61.7%

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

      3. associate-*r/ 62.0%

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

   10. Simplified 62.0%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-108}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-298}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-273}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-154}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{t}{x - y}}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{-104}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-280}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-67}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ -60.0 (/ t (- x y)))))
   (if (<= a -3.4e-104)
     (* a 120.0)
     (if (<= a -9e-282)
       t_1
       (if (<= a 1.35e-280)
         (/ 60.0 (/ z (- x y)))
         (if (<= a 6e-261)
           t_1
           (if (<= a 5.9e-67)
             (* -60.0 (/ y (- z t)))
             (if (<= a 1.8e+27) t_1 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -3.4e-104) {
		tmp = a * 120.0;
	} else if (a <= -9e-282) {
		tmp = t_1;
	} else if (a <= 1.35e-280) {
		tmp = 60.0 / (z / (x - y));
	} else if (a <= 6e-261) {
		tmp = t_1;
	} else if (a <= 5.9e-67) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.8e+27) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) / (t / (x - y))
    if (a <= (-3.4d-104)) then
        tmp = a * 120.0d0
    else if (a <= (-9d-282)) then
        tmp = t_1
    else if (a <= 1.35d-280) then
        tmp = 60.0d0 / (z / (x - y))
    else if (a <= 6d-261) then
        tmp = t_1
    else if (a <= 5.9d-67) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 1.8d+27) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -3.4e-104) {
		tmp = a * 120.0;
	} else if (a <= -9e-282) {
		tmp = t_1;
	} else if (a <= 1.35e-280) {
		tmp = 60.0 / (z / (x - y));
	} else if (a <= 6e-261) {
		tmp = t_1;
	} else if (a <= 5.9e-67) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.8e+27) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 / (t / (x - y))
	tmp = 0
	if a <= -3.4e-104:
		tmp = a * 120.0
	elif a <= -9e-282:
		tmp = t_1
	elif a <= 1.35e-280:
		tmp = 60.0 / (z / (x - y))
	elif a <= 6e-261:
		tmp = t_1
	elif a <= 5.9e-67:
		tmp = -60.0 * (y / (z - t))
	elif a <= 1.8e+27:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 / Float64(t / Float64(x - y)))
	tmp = 0.0
	if (a <= -3.4e-104)
		tmp = Float64(a * 120.0);
	elseif (a <= -9e-282)
		tmp = t_1;
	elseif (a <= 1.35e-280)
		tmp = Float64(60.0 / Float64(z / Float64(x - y)));
	elseif (a <= 6e-261)
		tmp = t_1;
	elseif (a <= 5.9e-67)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 1.8e+27)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 / (t / (x - y));
	tmp = 0.0;
	if (a <= -3.4e-104)
		tmp = a * 120.0;
	elseif (a <= -9e-282)
		tmp = t_1;
	elseif (a <= 1.35e-280)
		tmp = 60.0 / (z / (x - y));
	elseif (a <= 6e-261)
		tmp = t_1;
	elseif (a <= 5.9e-67)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 1.8e+27)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e-104], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9e-282], t$95$1, If[LessEqual[a, 1.35e-280], N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-261], t$95$1, If[LessEqual[a, 5.9e-67], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+27], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.40000000000000015e-104 or 1.79999999999999991e27 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -3.40000000000000015e-104 < a < -9.00000000000000017e-282 or 1.34999999999999992e-280 < a < 6.0000000000000001e-261 or 5.9e-67 < a < 1.79999999999999991e27

   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 86.0%

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

      1. div-inv 85.7%

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

   6. Applied egg-rr 85.7%

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

   7. Taylor expanded in z around 0 58.9%

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

      1. associate-*r/ 59.0%

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

      2. associate-/l* 59.0%

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

   9. Simplified 59.0%

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

   if -9.00000000000000017e-282 < a < 1.34999999999999992e-280

   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* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 94.7%

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

   5. Taylor expanded in z around inf 66.4%

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

      1. associate-*r/ 66.3%

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

      2. associate-/l* 66.2%

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

   7. Simplified 66.2%

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

   if 6.0000000000000001e-261 < a < 5.9e-67

   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 a around 0 75.9%

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

   5. Taylor expanded in x around 0 49.8%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-104}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-282}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-280}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-261}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-67}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{t}{x - y}}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-280}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-68}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ -60.0 (/ t (- x y)))))
   (if (<= a -1.02e-100)
     (* a 120.0)
     (if (<= a -2.3e-282)
       t_1
       (if (<= a 2.15e-280)
         (/ 60.0 (/ z (- x y)))
         (if (<= a 1.12e-260)
           t_1
           (if (<= a 2.75e-68)
             (/ (* y -60.0) (- z t))
             (if (<= a 3e+26) t_1 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -1.02e-100) {
		tmp = a * 120.0;
	} else if (a <= -2.3e-282) {
		tmp = t_1;
	} else if (a <= 2.15e-280) {
		tmp = 60.0 / (z / (x - y));
	} else if (a <= 1.12e-260) {
		tmp = t_1;
	} else if (a <= 2.75e-68) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 3e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) / (t / (x - y))
    if (a <= (-1.02d-100)) then
        tmp = a * 120.0d0
    else if (a <= (-2.3d-282)) then
        tmp = t_1
    else if (a <= 2.15d-280) then
        tmp = 60.0d0 / (z / (x - y))
    else if (a <= 1.12d-260) then
        tmp = t_1
    else if (a <= 2.75d-68) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (a <= 3d+26) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -1.02e-100) {
		tmp = a * 120.0;
	} else if (a <= -2.3e-282) {
		tmp = t_1;
	} else if (a <= 2.15e-280) {
		tmp = 60.0 / (z / (x - y));
	} else if (a <= 1.12e-260) {
		tmp = t_1;
	} else if (a <= 2.75e-68) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 3e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 / (t / (x - y))
	tmp = 0
	if a <= -1.02e-100:
		tmp = a * 120.0
	elif a <= -2.3e-282:
		tmp = t_1
	elif a <= 2.15e-280:
		tmp = 60.0 / (z / (x - y))
	elif a <= 1.12e-260:
		tmp = t_1
	elif a <= 2.75e-68:
		tmp = (y * -60.0) / (z - t)
	elif a <= 3e+26:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 / Float64(t / Float64(x - y)))
	tmp = 0.0
	if (a <= -1.02e-100)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.3e-282)
		tmp = t_1;
	elseif (a <= 2.15e-280)
		tmp = Float64(60.0 / Float64(z / Float64(x - y)));
	elseif (a <= 1.12e-260)
		tmp = t_1;
	elseif (a <= 2.75e-68)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (a <= 3e+26)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 / (t / (x - y));
	tmp = 0.0;
	if (a <= -1.02e-100)
		tmp = a * 120.0;
	elseif (a <= -2.3e-282)
		tmp = t_1;
	elseif (a <= 2.15e-280)
		tmp = 60.0 / (z / (x - y));
	elseif (a <= 1.12e-260)
		tmp = t_1;
	elseif (a <= 2.75e-68)
		tmp = (y * -60.0) / (z - t);
	elseif (a <= 3e+26)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.02e-100], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.3e-282], t$95$1, If[LessEqual[a, 2.15e-280], N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e-260], t$95$1, If[LessEqual[a, 2.75e-68], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+26], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.02e-100 or 2.99999999999999997e26 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -1.02e-100 < a < -2.2999999999999999e-282 or 2.1499999999999999e-280 < a < 1.12000000000000004e-260 or 2.7500000000000001e-68 < a < 2.99999999999999997e26

   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 86.0%

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

      1. div-inv 85.7%

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

   6. Applied egg-rr 85.7%

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

   7. Taylor expanded in z around 0 58.9%

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

      1. associate-*r/ 59.0%

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

      2. associate-/l* 59.0%

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

   9. Simplified 59.0%

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

   if -2.2999999999999999e-282 < a < 2.1499999999999999e-280

   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* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 94.7%

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

   5. Taylor expanded in z around inf 66.4%

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

      1. associate-*r/ 66.3%

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

      2. associate-/l* 66.2%

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

   7. Simplified 66.2%

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

   if 1.12000000000000004e-260 < a < 2.7500000000000001e-68

   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 a around 0 75.9%

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

   5. Taylor expanded in x around 0 49.8%

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

      1. associate-*r/ 49.9%

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

   7. Simplified 49.9%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-282}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-280}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-260}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-68}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+26}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+56} \lor \neg \left(a \leq 7.2 \cdot 10^{+159}\right) \land a \leq 5.8 \cdot 10^{+194}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-99)
   (* a 120.0)
   (if (or (<= a 6e+56) (and (not (<= a 7.2e+159)) (<= a 5.8e+194)))
     (* 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 <= -2.4e-99) {
		tmp = a * 120.0;
	} else if ((a <= 6e+56) || (!(a <= 7.2e+159) && (a <= 5.8e+194))) {
		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 <= (-2.4d-99)) then
        tmp = a * 120.0d0
    else if ((a <= 6d+56) .or. (.not. (a <= 7.2d+159)) .and. (a <= 5.8d+194)) 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 <= -2.4e-99) {
		tmp = a * 120.0;
	} else if ((a <= 6e+56) || (!(a <= 7.2e+159) && (a <= 5.8e+194))) {
		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 <= -2.4e-99:
		tmp = a * 120.0
	elif (a <= 6e+56) or (not (a <= 7.2e+159) and (a <= 5.8e+194)):
		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 <= -2.4e-99)
		tmp = Float64(a * 120.0);
	elseif ((a <= 6e+56) || (!(a <= 7.2e+159) && (a <= 5.8e+194)))
		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 <= -2.4e-99)
		tmp = a * 120.0;
	elseif ((a <= 6e+56) || (~((a <= 7.2e+159)) && (a <= 5.8e+194)))
		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, -2.4e-99], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[a, 6e+56], And[N[Not[LessEqual[a, 7.2e+159]], $MachinePrecision], LessEqual[a, 5.8e+194]]], 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 < -2.4e-99 or 6.00000000000000012e56 < a < 7.20000000000000073e159 or 5.8000000000000001e194 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 81.5%

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

   if -2.4e-99 < a < 6.00000000000000012e56 or 7.20000000000000073e159 < a < 5.8000000000000001e194

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 82.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+56} \lor \neg \left(a \leq 7.2 \cdot 10^{+159}\right) \land a \leq 5.8 \cdot 10^{+194}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-134}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))))
   (if (<= a -1.05e-176)
     (* a 120.0)
     (if (<= a -9.5e-243)
       t_1
       (if (<= a 2.7e-270)
         (* y (/ 60.0 t))
         (if (<= a 3.2e-243)
           t_1
           (if (<= a 4.4e-134) (* 60.0 (/ x z)) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.05e-176) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-243) {
		tmp = t_1;
	} else if (a <= 2.7e-270) {
		tmp = y * (60.0 / t);
	} else if (a <= 3.2e-243) {
		tmp = t_1;
	} else if (a <= 4.4e-134) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    if (a <= (-1.05d-176)) then
        tmp = a * 120.0d0
    else if (a <= (-9.5d-243)) then
        tmp = t_1
    else if (a <= 2.7d-270) then
        tmp = y * (60.0d0 / t)
    else if (a <= 3.2d-243) then
        tmp = t_1
    else if (a <= 4.4d-134) 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 t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.05e-176) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-243) {
		tmp = t_1;
	} else if (a <= 2.7e-270) {
		tmp = y * (60.0 / t);
	} else if (a <= 3.2e-243) {
		tmp = t_1;
	} else if (a <= 4.4e-134) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	tmp = 0
	if a <= -1.05e-176:
		tmp = a * 120.0
	elif a <= -9.5e-243:
		tmp = t_1
	elif a <= 2.7e-270:
		tmp = y * (60.0 / t)
	elif a <= 3.2e-243:
		tmp = t_1
	elif a <= 4.4e-134:
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	tmp = 0.0
	if (a <= -1.05e-176)
		tmp = Float64(a * 120.0);
	elseif (a <= -9.5e-243)
		tmp = t_1;
	elseif (a <= 2.7e-270)
		tmp = Float64(y * Float64(60.0 / t));
	elseif (a <= 3.2e-243)
		tmp = t_1;
	elseif (a <= 4.4e-134)
		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)
	t_1 = -60.0 * (x / t);
	tmp = 0.0;
	if (a <= -1.05e-176)
		tmp = a * 120.0;
	elseif (a <= -9.5e-243)
		tmp = t_1;
	elseif (a <= 2.7e-270)
		tmp = y * (60.0 / t);
	elseif (a <= 3.2e-243)
		tmp = t_1;
	elseif (a <= 4.4e-134)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-176], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9.5e-243], t$95$1, If[LessEqual[a, 2.7e-270], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-243], t$95$1, If[LessEqual[a, 4.4e-134], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.04999999999999996e-176 or 4.3999999999999999e-134 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 65.4%

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

   if -1.04999999999999996e-176 < a < -9.5000000000000005e-243 or 2.70000000000000007e-270 < a < 3.1999999999999998e-243

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 72.4%

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

      1. *-commutative 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in z around 0 57.2%

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

   6. Taylor expanded in a around 0 51.0%

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

   if -9.5000000000000005e-243 < a < 2.70000000000000007e-270

   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* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in a around 0 89.6%

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

   5. Taylor expanded in x around 0 51.1%

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

      1. associate-*r/ 51.0%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in z around 0 35.7%

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

      1. *-commutative 35.7%

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

      2. associate-*l/ 35.7%

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

      3. associate-*r/ 35.8%

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

   10. Simplified 35.8%

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

   if 3.1999999999999998e-243 < a < 4.3999999999999999e-134

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 59.8%

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

   5. Taylor expanded in x around inf 47.3%

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

   6. Taylor expanded in a around 0 42.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-243}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-243}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-134}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-175}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))))
   (if (<= a -1.55e-175)
     (* a 120.0)
     (if (<= a -3.6e-242)
       t_1
       (if (<= a 3.2e-271)
         (* y (/ 60.0 t))
         (if (<= a 2.8e-243)
           t_1
           (if (<= a 1.15e-131) (/ (* 60.0 x) z) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.55e-175) {
		tmp = a * 120.0;
	} else if (a <= -3.6e-242) {
		tmp = t_1;
	} else if (a <= 3.2e-271) {
		tmp = y * (60.0 / t);
	} else if (a <= 2.8e-243) {
		tmp = t_1;
	} else if (a <= 1.15e-131) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    if (a <= (-1.55d-175)) then
        tmp = a * 120.0d0
    else if (a <= (-3.6d-242)) then
        tmp = t_1
    else if (a <= 3.2d-271) then
        tmp = y * (60.0d0 / t)
    else if (a <= 2.8d-243) then
        tmp = t_1
    else if (a <= 1.15d-131) 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 t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.55e-175) {
		tmp = a * 120.0;
	} else if (a <= -3.6e-242) {
		tmp = t_1;
	} else if (a <= 3.2e-271) {
		tmp = y * (60.0 / t);
	} else if (a <= 2.8e-243) {
		tmp = t_1;
	} else if (a <= 1.15e-131) {
		tmp = (60.0 * x) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	tmp = 0
	if a <= -1.55e-175:
		tmp = a * 120.0
	elif a <= -3.6e-242:
		tmp = t_1
	elif a <= 3.2e-271:
		tmp = y * (60.0 / t)
	elif a <= 2.8e-243:
		tmp = t_1
	elif a <= 1.15e-131:
		tmp = (60.0 * x) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	tmp = 0.0
	if (a <= -1.55e-175)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.6e-242)
		tmp = t_1;
	elseif (a <= 3.2e-271)
		tmp = Float64(y * Float64(60.0 / t));
	elseif (a <= 2.8e-243)
		tmp = t_1;
	elseif (a <= 1.15e-131)
		tmp = Float64(Float64(60.0 * x) / z);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	tmp = 0.0;
	if (a <= -1.55e-175)
		tmp = a * 120.0;
	elseif (a <= -3.6e-242)
		tmp = t_1;
	elseif (a <= 3.2e-271)
		tmp = y * (60.0 / t);
	elseif (a <= 2.8e-243)
		tmp = t_1;
	elseif (a <= 1.15e-131)
		tmp = (60.0 * x) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e-175], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.6e-242], t$95$1, If[LessEqual[a, 3.2e-271], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-243], t$95$1, If[LessEqual[a, 1.15e-131], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.54999999999999999e-175 or 1.15000000000000011e-131 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 65.4%

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

   if -1.54999999999999999e-175 < a < -3.60000000000000014e-242 or 3.19999999999999978e-271 < a < 2.79999999999999994e-243

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 72.4%

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

      1. *-commutative 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in z around 0 57.2%

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

   6. Taylor expanded in a around 0 51.0%

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

   if -3.60000000000000014e-242 < a < 3.19999999999999978e-271

   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* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in a around 0 89.6%

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

   5. Taylor expanded in x around 0 51.1%

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

      1. associate-*r/ 51.0%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in z around 0 35.7%

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

      1. *-commutative 35.7%

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

      2. associate-*l/ 35.7%

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

      3. associate-*r/ 35.8%

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

   10. Simplified 35.8%

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

   if 2.79999999999999994e-243 < a < 1.15000000000000011e-131

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 59.8%

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

   5. Taylor expanded in x around inf 47.3%

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

   6. Taylor expanded in a around 0 42.9%

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

      1. associate-*r/ 43.1%

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

   8. Applied egg-rr 43.1%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-175}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-242}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-243}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 57.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-68}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))))
   (if (<= a -2.7e-100)
     (* a 120.0)
     (if (<= a 3.1e-261)
       t_1
       (if (<= a 2.3e-68)
         (* -60.0 (/ y (- z t)))
         (if (<= a 2.5e+26) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -2.7e-100) {
		tmp = a * 120.0;
	} else if (a <= 3.1e-261) {
		tmp = t_1;
	} else if (a <= 2.3e-68) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 2.5e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * ((x - y) / t)
    if (a <= (-2.7d-100)) then
        tmp = a * 120.0d0
    else if (a <= 3.1d-261) then
        tmp = t_1
    else if (a <= 2.3d-68) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 2.5d+26) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -2.7e-100) {
		tmp = a * 120.0;
	} else if (a <= 3.1e-261) {
		tmp = t_1;
	} else if (a <= 2.3e-68) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 2.5e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	tmp = 0
	if a <= -2.7e-100:
		tmp = a * 120.0
	elif a <= 3.1e-261:
		tmp = t_1
	elif a <= 2.3e-68:
		tmp = -60.0 * (y / (z - t))
	elif a <= 2.5e+26:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -2.7e-100)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.1e-261)
		tmp = t_1;
	elseif (a <= 2.3e-68)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 2.5e+26)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * ((x - y) / t);
	tmp = 0.0;
	if (a <= -2.7e-100)
		tmp = a * 120.0;
	elseif (a <= 3.1e-261)
		tmp = t_1;
	elseif (a <= 2.3e-68)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 2.5e+26)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e-100], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.1e-261], t$95$1, If[LessEqual[a, 2.3e-68], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+26], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.70000000000000016e-100 or 2.5e26 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -2.70000000000000016e-100 < a < 3.0999999999999998e-261 or 2.29999999999999997e-68 < a < 2.5e26

   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* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 87.9%

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

   5. Taylor expanded in z around 0 54.1%

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

   if 3.0999999999999998e-261 < a < 2.29999999999999997e-68

   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 a around 0 75.9%

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

   5. Taylor expanded in x around 0 49.8%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-261}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-68}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 57.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{t}{x - y}}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-103}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-66}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ -60.0 (/ t (- x y)))))
   (if (<= a -4.6e-103)
     (* a 120.0)
     (if (<= a 5.4e-261)
       t_1
       (if (<= a 1.05e-66)
         (* -60.0 (/ y (- z t)))
         (if (<= a 2.5e+26) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -4.6e-103) {
		tmp = a * 120.0;
	} else if (a <= 5.4e-261) {
		tmp = t_1;
	} else if (a <= 1.05e-66) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 2.5e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) / (t / (x - y))
    if (a <= (-4.6d-103)) then
        tmp = a * 120.0d0
    else if (a <= 5.4d-261) then
        tmp = t_1
    else if (a <= 1.05d-66) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 2.5d+26) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 / (t / (x - y));
	double tmp;
	if (a <= -4.6e-103) {
		tmp = a * 120.0;
	} else if (a <= 5.4e-261) {
		tmp = t_1;
	} else if (a <= 1.05e-66) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 2.5e+26) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 / (t / (x - y))
	tmp = 0
	if a <= -4.6e-103:
		tmp = a * 120.0
	elif a <= 5.4e-261:
		tmp = t_1
	elif a <= 1.05e-66:
		tmp = -60.0 * (y / (z - t))
	elif a <= 2.5e+26:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 / Float64(t / Float64(x - y)))
	tmp = 0.0
	if (a <= -4.6e-103)
		tmp = Float64(a * 120.0);
	elseif (a <= 5.4e-261)
		tmp = t_1;
	elseif (a <= 1.05e-66)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 2.5e+26)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 / (t / (x - y));
	tmp = 0.0;
	if (a <= -4.6e-103)
		tmp = a * 120.0;
	elseif (a <= 5.4e-261)
		tmp = t_1;
	elseif (a <= 1.05e-66)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 2.5e+26)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e-103], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5.4e-261], t$95$1, If[LessEqual[a, 1.05e-66], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+26], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.6000000000000001e-103 or 2.5e26 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -4.6000000000000001e-103 < a < 5.3999999999999998e-261 or 1.05e-66 < a < 2.5e26

   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* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 87.9%

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

      1. div-inv 87.7%

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

   6. Applied egg-rr 87.7%

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

   7. Taylor expanded in z around 0 54.1%

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

      1. associate-*r/ 54.1%

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

      2. associate-/l* 54.1%

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

   9. Simplified 54.1%

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

   if 5.3999999999999998e-261 < a < 1.05e-66

   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 a around 0 75.9%

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

   5. Taylor expanded in x around 0 49.8%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-103}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-261}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-66}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 88.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+88} \lor \neg \left(x \leq 9 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.15e+88) (not (<= x 9e-17)))
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.15e+88) || !(x <= 9e-17)) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.15d+88)) .or. (.not. (x <= 9d-17))) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.15e+88) || !(x <= 9e-17)) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.15e+88) or not (x <= 9e-17):
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	else:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.15e+88) || !(x <= 9e-17))
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.15e+88) || ~((x <= 9e-17)))
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	else
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.15e+88], N[Not[LessEqual[x, 9e-17]], $MachinePrecision]], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999987e88 or 8.99999999999999957e-17 < x

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 86.9%

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

      1. *-commutative 86.9%

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

   4. Simplified 86.9%

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

   if -2.14999999999999987e88 < x < 8.99999999999999957e-17

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 92.2%

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

      1. associate-*r/ 92.2%

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

      2. associate-/l* 92.2%

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

   6. Simplified 92.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+88} \lor \neg \left(x \leq 9 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \]

Alternative 15: 52.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-277}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))))
   (if (<= a -9.5e-177)
     (* a 120.0)
     (if (<= a -2.45e-290)
       t_1
       (if (<= a 3.1e-277)
         (* -60.0 (/ y z))
         (if (<= a 2e-154) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -9.5e-177) {
		tmp = a * 120.0;
	} else if (a <= -2.45e-290) {
		tmp = t_1;
	} else if (a <= 3.1e-277) {
		tmp = -60.0 * (y / z);
	} else if (a <= 2e-154) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    if (a <= (-9.5d-177)) then
        tmp = a * 120.0d0
    else if (a <= (-2.45d-290)) then
        tmp = t_1
    else if (a <= 3.1d-277) then
        tmp = (-60.0d0) * (y / z)
    else if (a <= 2d-154) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -9.5e-177) {
		tmp = a * 120.0;
	} else if (a <= -2.45e-290) {
		tmp = t_1;
	} else if (a <= 3.1e-277) {
		tmp = -60.0 * (y / z);
	} else if (a <= 2e-154) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	tmp = 0
	if a <= -9.5e-177:
		tmp = a * 120.0
	elif a <= -2.45e-290:
		tmp = t_1
	elif a <= 3.1e-277:
		tmp = -60.0 * (y / z)
	elif a <= 2e-154:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	tmp = 0.0
	if (a <= -9.5e-177)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.45e-290)
		tmp = t_1;
	elseif (a <= 3.1e-277)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (a <= 2e-154)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	tmp = 0.0;
	if (a <= -9.5e-177)
		tmp = a * 120.0;
	elseif (a <= -2.45e-290)
		tmp = t_1;
	elseif (a <= 3.1e-277)
		tmp = -60.0 * (y / z);
	elseif (a <= 2e-154)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e-177], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.45e-290], t$95$1, If[LessEqual[a, 3.1e-277], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-154], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000031e-177 or 1.9999999999999999e-154 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 64.9%

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

   if -9.50000000000000031e-177 < a < -2.45e-290 or 3.09999999999999979e-277 < a < 1.9999999999999999e-154

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 62.0%

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

      1. *-commutative 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in z around 0 40.4%

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

   6. Taylor expanded in a around 0 34.5%

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

   if -2.45e-290 < a < 3.09999999999999979e-277

   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* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in a around 0 93.6%

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

   5. Taylor expanded in x around 0 53.3%

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

      1. associate-*r/ 53.0%

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

   7. Simplified 53.0%

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

   8. Taylor expanded in z around inf 39.3%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-290}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-277}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-154}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16: 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* 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 17: 52.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-243}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-133}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.2e-176)
   (* a 120.0)
   (if (<= a 5.2e-243)
     (* -60.0 (/ x t))
     (if (<= a 3e-133) (* 60.0 (/ x z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e-176) {
		tmp = a * 120.0;
	} else if (a <= 5.2e-243) {
		tmp = -60.0 * (x / t);
	} else if (a <= 3e-133) {
		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 <= (-2.2d-176)) then
        tmp = a * 120.0d0
    else if (a <= 5.2d-243) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 3d-133) 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 <= -2.2e-176) {
		tmp = a * 120.0;
	} else if (a <= 5.2e-243) {
		tmp = -60.0 * (x / t);
	} else if (a <= 3e-133) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.2e-176:
		tmp = a * 120.0
	elif a <= 5.2e-243:
		tmp = -60.0 * (x / t)
	elif a <= 3e-133:
		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 <= -2.2e-176)
		tmp = Float64(a * 120.0);
	elseif (a <= 5.2e-243)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 3e-133)
		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 <= -2.2e-176)
		tmp = a * 120.0;
	elseif (a <= 5.2e-243)
		tmp = -60.0 * (x / t);
	elseif (a <= 3e-133)
		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, -2.2e-176], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5.2e-243], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-133], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1999999999999999e-176 or 3.00000000000000019e-133 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 65.4%

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

   if -2.1999999999999999e-176 < a < 5.1999999999999995e-243

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 63.5%

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

      1. *-commutative 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in z around 0 40.5%

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

   6. Taylor expanded in a around 0 35.5%

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

   if 5.1999999999999995e-243 < a < 3.00000000000000019e-133

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 59.8%

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

   5. Taylor expanded in x around inf 47.3%

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

   6. Taylor expanded in a around 0 42.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-243}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-133}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 56.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-102}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+26}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-102)
   (* a 120.0)
   (if (<= a 2.6e+26) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-102) {
		tmp = a * 120.0;
	} else if (a <= 2.6e+26) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.8d-102)) then
        tmp = a * 120.0d0
    else if (a <= 2.6d+26) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-102) {
		tmp = a * 120.0;
	} else if (a <= 2.6e+26) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-102:
		tmp = a * 120.0
	elif a <= 2.6e+26:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-102)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.6e+26)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e-102)
		tmp = a * 120.0;
	elseif (a <= 2.6e+26)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-102], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.6e+26], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8e-102 or 2.60000000000000002e26 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.0%

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

   if -4.8e-102 < a < 2.60000000000000002e26

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 83.3%

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

   5. Taylor expanded in x around 0 42.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-102}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+26}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19: 53.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-154}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e-176)
   (* a 120.0)
   (if (<= a 1.15e-154) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e-176) {
		tmp = a * 120.0;
	} else if (a <= 1.15e-154) {
		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 <= (-2.45d-176)) then
        tmp = a * 120.0d0
    else if (a <= 1.15d-154) 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 <= -2.45e-176) {
		tmp = a * 120.0;
	} else if (a <= 1.15e-154) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.45e-176:
		tmp = a * 120.0
	elif a <= 1.15e-154:
		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 <= -2.45e-176)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.15e-154)
		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 <= -2.45e-176)
		tmp = a * 120.0;
	elseif (a <= 1.15e-154)
		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, -2.45e-176], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.15e-154], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4499999999999998e-176 or 1.15e-154 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 64.9%

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

   if -2.4499999999999998e-176 < a < 1.15e-154

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 60.0%

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

      1. *-commutative 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in z around 0 34.9%

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

   6. Taylor expanded in a around 0 30.1%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-154}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 20: 50.8% 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* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 48.8%

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

5. Final simplification 48.8%

   \[\leadsto a \cdot 120 \]

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 2023224 
(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)))