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

Percentage Accurate: 99.3% → 99.8%

Time: 15.7s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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 99.0%

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

   1. +-commutative 99.0%

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

   2. fma-def 99.5%

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

   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. Add Preprocessing

5. Final simplification 99.8%

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

Alternative 2: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \cdot 120 \leq 500000 \lor \neg \left(a \cdot 120 \leq 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ x t)))))
   (if (<= (* a 120.0) -5e+60)
     t_2
     (if (<= (* a 120.0) -4e-20)
       t_1
       (if (<= (* a 120.0) -5e-97)
         t_2
         (if (<= (* a 120.0) 5e-60)
           (* (/ 60.0 (- z t)) (- x y))
           (if (or (<= (* a 120.0) 500000.0) (not (<= (* a 120.0) 1e+66)))
             (* a 120.0)
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = t_2;
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-60) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (((a * 120.0) <= 500000.0) || !((a * 120.0) <= 1e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (x / t))
    if ((a * 120.0d0) <= (-5d+60)) then
        tmp = t_2
    else if ((a * 120.0d0) <= (-4d-20)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-5d-97)) then
        tmp = t_2
    else if ((a * 120.0d0) <= 5d-60) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if (((a * 120.0d0) <= 500000.0d0) .or. (.not. ((a * 120.0d0) <= 1d+66))) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = t_2;
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-60) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (((a * 120.0) <= 500000.0) || !((a * 120.0) <= 1e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	t_2 = (a * 120.0) + (-60.0 * (x / t))
	tmp = 0
	if (a * 120.0) <= -5e+60:
		tmp = t_2
	elif (a * 120.0) <= -4e-20:
		tmp = t_1
	elif (a * 120.0) <= -5e-97:
		tmp = t_2
	elif (a * 120.0) <= 5e-60:
		tmp = (60.0 / (z - t)) * (x - y)
	elif ((a * 120.0) <= 500000.0) or not ((a * 120.0) <= 1e+66):
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+60)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -5e-97)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= 5e-60)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif ((Float64(a * 120.0) <= 500000.0) || !(Float64(a * 120.0) <= 1e+66))
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	t_2 = (a * 120.0) + (-60.0 * (x / t));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+60)
		tmp = t_2;
	elseif ((a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif ((a * 120.0) <= -5e-97)
		tmp = t_2;
	elseif ((a * 120.0) <= 5e-60)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif (((a * 120.0) <= 500000.0) || ~(((a * 120.0) <= 1e+66)))
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+60], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-20], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-97], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-60], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 500000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+66]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -4.99999999999999975e60 or -3.99999999999999978e-20 < (*.f64 a 120) < -4.9999999999999995e-97

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 91.5%

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

   6. Taylor expanded in z around 0 81.6%

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

   if -4.99999999999999975e60 < (*.f64 a 120) < -3.99999999999999978e-20 or 5e5 < (*.f64 a 120) < 9.99999999999999945e65

   1. Initial program 96.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 73.2%

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

   if -4.9999999999999995e-97 < (*.f64 a 120) < 5.0000000000000001e-60

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 81.1%

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

      1. expm1-log1p-u 57.3%

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

      2. expm1-udef 20.5%

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

      3. associate-*r/ 20.5%

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

   7. Applied egg-rr 20.5%

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

      1. expm1-def 57.4%

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

      2. expm1-log1p 81.3%

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

      3. associate-*l/ 81.2%

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

   9. Simplified 81.2%

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

   if 5.0000000000000001e-60 < (*.f64 a 120) < 5e5 or 9.99999999999999945e65 < (*.f64 a 120)

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around inf 87.3%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \cdot 120 \leq 500000 \lor \neg \left(a \cdot 120 \leq 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x - y}}\\ t_2 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60} \lor \neg \left(a \cdot 120 \leq 500000\right) \land a \cdot 120 \leq 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ (- z t) (- x y))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ x t)))))
   (if (<= (* a 120.0) -5e+60)
     t_2
     (if (<= (* a 120.0) -4e-20)
       t_1
       (if (<= (* a 120.0) -5e-97)
         t_2
         (if (or (<= (* a 120.0) 5e-60)
                 (and (not (<= (* a 120.0) 500000.0)) (<= (* a 120.0) 1e+66)))
           t_1
           (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / (x - y));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = t_2;
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = t_2;
	} else if (((a * 120.0) <= 5e-60) || (!((a * 120.0) <= 500000.0) && ((a * 120.0) <= 1e+66))) {
		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) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 / ((z - t) / (x - y))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (x / t))
    if ((a * 120.0d0) <= (-5d+60)) then
        tmp = t_2
    else if ((a * 120.0d0) <= (-4d-20)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-5d-97)) then
        tmp = t_2
    else if (((a * 120.0d0) <= 5d-60) .or. (.not. ((a * 120.0d0) <= 500000.0d0)) .and. ((a * 120.0d0) <= 1d+66)) 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 / ((z - t) / (x - y));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = t_2;
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = t_2;
	} else if (((a * 120.0) <= 5e-60) || (!((a * 120.0) <= 500000.0) && ((a * 120.0) <= 1e+66))) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / ((z - t) / (x - y))
	t_2 = (a * 120.0) + (-60.0 * (x / t))
	tmp = 0
	if (a * 120.0) <= -5e+60:
		tmp = t_2
	elif (a * 120.0) <= -4e-20:
		tmp = t_1
	elif (a * 120.0) <= -5e-97:
		tmp = t_2
	elif ((a * 120.0) <= 5e-60) or (not ((a * 120.0) <= 500000.0) and ((a * 120.0) <= 1e+66)):
		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(z - t) / Float64(x - y)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+60)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -5e-97)
		tmp = t_2;
	elseif ((Float64(a * 120.0) <= 5e-60) || (!(Float64(a * 120.0) <= 500000.0) && (Float64(a * 120.0) <= 1e+66)))
		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 / ((z - t) / (x - y));
	t_2 = (a * 120.0) + (-60.0 * (x / t));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+60)
		tmp = t_2;
	elseif ((a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif ((a * 120.0) <= -5e-97)
		tmp = t_2;
	elseif (((a * 120.0) <= 5e-60) || (~(((a * 120.0) <= 500000.0)) && ((a * 120.0) <= 1e+66)))
		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[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+60], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-20], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-97], t$95$2, If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-60], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 500000.0]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 1e+66]]], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4.99999999999999975e60 or -3.99999999999999978e-20 < (*.f64 a 120) < -4.9999999999999995e-97

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 91.5%

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

   6. Taylor expanded in z around 0 81.6%

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

   if -4.99999999999999975e60 < (*.f64 a 120) < -3.99999999999999978e-20 or -4.9999999999999995e-97 < (*.f64 a 120) < 5.0000000000000001e-60 or 5e5 < (*.f64 a 120) < 9.99999999999999945e65

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 79.3%

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

      1. clear-num 79.2%

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

      2. un-div-inv 79.4%

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

   7. Applied egg-rr 79.4%

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

   if 5.0000000000000001e-60 < (*.f64 a 120) < 5e5 or 9.99999999999999945e65 < (*.f64 a 120)

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around inf 87.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60} \lor \neg \left(a \cdot 120 \leq 500000\right) \land a \cdot 120 \leq 10^{+66}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x - y}}\\ t_2 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 500000 \lor \neg \left(a \cdot 120 \leq 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ (- z t) (- x y))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ x t)))))
   (if (<= (* a 120.0) -5e+60)
     t_2
     (if (<= (* a 120.0) -4e-20)
       t_1
       (if (<= (* a 120.0) -5e-97)
         t_2
         (if (<= (* a 120.0) 5e-60)
           (/ (* 60.0 (- x y)) (- z t))
           (if (or (<= (* a 120.0) 500000.0) (not (<= (* a 120.0) 1e+66)))
             (* a 120.0)
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / (x - y));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = t_2;
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-60) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (((a * 120.0) <= 500000.0) || !((a * 120.0) <= 1e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 / ((z - t) / (x - y))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (x / t))
    if ((a * 120.0d0) <= (-5d+60)) then
        tmp = t_2
    else if ((a * 120.0d0) <= (-4d-20)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-5d-97)) then
        tmp = t_2
    else if ((a * 120.0d0) <= 5d-60) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if (((a * 120.0d0) <= 500000.0d0) .or. (.not. ((a * 120.0d0) <= 1d+66))) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / (x - y));
	double t_2 = (a * 120.0) + (-60.0 * (x / t));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = t_2;
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = t_2;
	} else if ((a * 120.0) <= 5e-60) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (((a * 120.0) <= 500000.0) || !((a * 120.0) <= 1e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / ((z - t) / (x - y))
	t_2 = (a * 120.0) + (-60.0 * (x / t))
	tmp = 0
	if (a * 120.0) <= -5e+60:
		tmp = t_2
	elif (a * 120.0) <= -4e-20:
		tmp = t_1
	elif (a * 120.0) <= -5e-97:
		tmp = t_2
	elif (a * 120.0) <= 5e-60:
		tmp = (60.0 * (x - y)) / (z - t)
	elif ((a * 120.0) <= 500000.0) or not ((a * 120.0) <= 1e+66):
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+60)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -5e-97)
		tmp = t_2;
	elseif (Float64(a * 120.0) <= 5e-60)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif ((Float64(a * 120.0) <= 500000.0) || !(Float64(a * 120.0) <= 1e+66))
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / ((z - t) / (x - y));
	t_2 = (a * 120.0) + (-60.0 * (x / t));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+60)
		tmp = t_2;
	elseif ((a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif ((a * 120.0) <= -5e-97)
		tmp = t_2;
	elseif ((a * 120.0) <= 5e-60)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif (((a * 120.0) <= 500000.0) || ~(((a * 120.0) <= 1e+66)))
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+60], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-20], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-97], t$95$2, If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-60], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 500000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+66]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -4.99999999999999975e60 or -3.99999999999999978e-20 < (*.f64 a 120) < -4.9999999999999995e-97

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 91.5%

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

   6. Taylor expanded in z around 0 81.6%

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

   if -4.99999999999999975e60 < (*.f64 a 120) < -3.99999999999999978e-20 or 5e5 < (*.f64 a 120) < 9.99999999999999945e65

   1. Initial program 96.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 73.2%

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

      1. clear-num 73.3%

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

      2. un-div-inv 73.3%

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

   7. Applied egg-rr 73.3%

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

   if -4.9999999999999995e-97 < (*.f64 a 120) < 5.0000000000000001e-60

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 81.1%

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

      1. associate-*r/ 81.3%

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

   7. Applied egg-rr 81.3%

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

   if 5.0000000000000001e-60 < (*.f64 a 120) < 5e5 or 9.99999999999999945e65 < (*.f64 a 120)

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around inf 87.3%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 500000 \lor \neg \left(a \cdot 120 \leq 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x - y}}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-t}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 500000 \lor \neg \left(a \cdot 120 \leq 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ (- z t) (- x y)))))
   (if (<= (* a 120.0) -5e+60)
     (+ (* a 120.0) (/ 60.0 (/ (- t) x)))
     (if (<= (* a 120.0) -4e-20)
       t_1
       (if (<= (* a 120.0) -5e-97)
         (+ (* a 120.0) (* -60.0 (/ x t)))
         (if (<= (* a 120.0) 5e-60)
           (/ (* 60.0 (- x y)) (- z t))
           (if (or (<= (* a 120.0) 500000.0) (not (<= (* a 120.0) 1e+66)))
             (* a 120.0)
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / (x - y));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = (a * 120.0) + (60.0 / (-t / x));
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 5e-60) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (((a * 120.0) <= 500000.0) || !((a * 120.0) <= 1e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / ((z - t) / (x - y))
    if ((a * 120.0d0) <= (-5d+60)) then
        tmp = (a * 120.0d0) + (60.0d0 / (-t / x))
    else if ((a * 120.0d0) <= (-4d-20)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-5d-97)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a * 120.0d0) <= 5d-60) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if (((a * 120.0d0) <= 500000.0d0) .or. (.not. ((a * 120.0d0) <= 1d+66))) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((z - t) / (x - y));
	double tmp;
	if ((a * 120.0) <= -5e+60) {
		tmp = (a * 120.0) + (60.0 / (-t / x));
	} else if ((a * 120.0) <= -4e-20) {
		tmp = t_1;
	} else if ((a * 120.0) <= -5e-97) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 5e-60) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (((a * 120.0) <= 500000.0) || !((a * 120.0) <= 1e+66)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / ((z - t) / (x - y))
	tmp = 0
	if (a * 120.0) <= -5e+60:
		tmp = (a * 120.0) + (60.0 / (-t / x))
	elif (a * 120.0) <= -4e-20:
		tmp = t_1
	elif (a * 120.0) <= -5e-97:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a * 120.0) <= 5e-60:
		tmp = (60.0 * (x - y)) / (z - t)
	elif ((a * 120.0) <= 500000.0) or not ((a * 120.0) <= 1e+66):
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+60)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(-t) / x)));
	elseif (Float64(a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -5e-97)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 5e-60)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif ((Float64(a * 120.0) <= 500000.0) || !(Float64(a * 120.0) <= 1e+66))
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / ((z - t) / (x - y));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+60)
		tmp = (a * 120.0) + (60.0 / (-t / x));
	elseif ((a * 120.0) <= -4e-20)
		tmp = t_1;
	elseif ((a * 120.0) <= -5e-97)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a * 120.0) <= 5e-60)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif (((a * 120.0) <= 500000.0) || ~(((a * 120.0) <= 1e+66)))
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+60], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[((-t) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-20], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-97], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-60], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 500000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+66]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -4.99999999999999975e60

   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. Add Preprocessing

   5. Taylor expanded in x around inf 93.0%

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

   6. Taylor expanded in z around 0 82.6%

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

      1. neg-mul-1 82.6%

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

      2. distribute-neg-frac 82.6%

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

   8. Simplified 82.6%

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

   if -4.99999999999999975e60 < (*.f64 a 120) < -3.99999999999999978e-20 or 5e5 < (*.f64 a 120) < 9.99999999999999945e65

   1. Initial program 96.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 73.2%

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

      1. clear-num 73.3%

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

      2. un-div-inv 73.3%

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

   7. Applied egg-rr 73.3%

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

   if -3.99999999999999978e-20 < (*.f64 a 120) < -4.9999999999999995e-97

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 84.7%

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

   6. Taylor expanded in z around 0 77.3%

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

   if -4.9999999999999995e-97 < (*.f64 a 120) < 5.0000000000000001e-60

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 81.1%

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

      1. associate-*r/ 81.3%

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

   7. Applied egg-rr 81.3%

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

   if 5.0000000000000001e-60 < (*.f64 a 120) < 5e5 or 9.99999999999999945e65 < (*.f64 a 120)

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around inf 87.3%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-t}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-20}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 500000 \lor \neg \left(a \cdot 120 \leq 10^{+66}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -2000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-193}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* (/ 60.0 (- z t)) x))))
   (if (<= (* a 120.0) -2e+24)
     t_1
     (if (<= (* a 120.0) -2000.0)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (or (<= (* a 120.0) -5e-97) (not (<= (* a 120.0) 2e-193)))
         t_1
         (/ (* 60.0 (- x y)) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 / (z - t)) * x);
	double tmp;
	if ((a * 120.0) <= -2e+24) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2000.0) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (((a * 120.0) <= -5e-97) || !((a * 120.0) <= 2e-193)) {
		tmp = t_1;
	} else {
		tmp = (60.0 * (x - y)) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    if ((a * 120.0d0) <= (-2d+24)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2000.0d0)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (((a * 120.0d0) <= (-5d-97)) .or. (.not. ((a * 120.0d0) <= 2d-193))) then
        tmp = t_1
    else
        tmp = (60.0d0 * (x - y)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 / (z - t)) * x);
	double tmp;
	if ((a * 120.0) <= -2e+24) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2000.0) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (((a * 120.0) <= -5e-97) || !((a * 120.0) <= 2e-193)) {
		tmp = t_1;
	} else {
		tmp = (60.0 * (x - y)) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((60.0 / (z - t)) * x)
	tmp = 0
	if (a * 120.0) <= -2e+24:
		tmp = t_1
	elif (a * 120.0) <= -2000.0:
		tmp = 60.0 / ((z - t) / (x - y))
	elif ((a * 120.0) <= -5e-97) or not ((a * 120.0) <= 2e-193):
		tmp = t_1
	else:
		tmp = (60.0 * (x - y)) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+24)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2000.0)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif ((Float64(a * 120.0) <= -5e-97) || !(Float64(a * 120.0) <= 2e-193))
		tmp = t_1;
	else
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((60.0 / (z - t)) * x);
	tmp = 0.0;
	if ((a * 120.0) <= -2e+24)
		tmp = t_1;
	elseif ((a * 120.0) <= -2000.0)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (((a * 120.0) <= -5e-97) || ~(((a * 120.0) <= 2e-193)))
		tmp = t_1;
	else
		tmp = (60.0 * (x - y)) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+24], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2000.0], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-97], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-193]], $MachinePrecision]], t$95$1, N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2e24 or -2e3 < (*.f64 a 120) < -4.9999999999999995e-97 or 2.0000000000000001e-193 < (*.f64 a 120)

   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* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 89.2%

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

      1. associate-*r/ 89.2%

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

      2. associate-*l/ 89.2%

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

      3. *-commutative 89.2%

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

   7. Simplified 89.2%

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

   if -2e24 < (*.f64 a 120) < -2e3

   1. Initial program 86.5%

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

   5. Taylor expanded in a around 0 99.3%

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

      1. clear-num 99.3%

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

      2. un-div-inv 99.6%

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

   7. Applied egg-rr 99.6%

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

   if -4.9999999999999995e-97 < (*.f64 a 120) < 2.0000000000000001e-193

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 86.2%

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

      1. associate-*r/ 86.3%

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

   7. Applied egg-rr 86.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \cdot 120 \leq -2000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-193}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -2000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-193}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))))
   (if (<= (* a 120.0) -2e+24)
     t_1
     (if (<= (* a 120.0) -2000.0)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (<= (* a 120.0) -5e-97)
         (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
         (if (<= (* a 120.0) 2e-193) (/ (* 60.0 (- x y)) (- z t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 / ((z - t) / x));
	double tmp;
	if ((a * 120.0) <= -2e+24) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2000.0) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= -5e-97) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if ((a * 120.0) <= 2e-193) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    if ((a * 120.0d0) <= (-2d+24)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2000.0d0)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if ((a * 120.0d0) <= (-5d-97)) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else if ((a * 120.0d0) <= 2d-193) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 / ((z - t) / x));
	double tmp;
	if ((a * 120.0) <= -2e+24) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2000.0) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((a * 120.0) <= -5e-97) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if ((a * 120.0) <= 2e-193) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 / ((z - t) / x))
	tmp = 0
	if (a * 120.0) <= -2e+24:
		tmp = t_1
	elif (a * 120.0) <= -2000.0:
		tmp = 60.0 / ((z - t) / (x - y))
	elif (a * 120.0) <= -5e-97:
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	elif (a * 120.0) <= 2e-193:
		tmp = (60.0 * (x - y)) / (z - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+24)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2000.0)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (Float64(a * 120.0) <= -5e-97)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	elseif (Float64(a * 120.0) <= 2e-193)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 / ((z - t) / x));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+24)
		tmp = t_1;
	elseif ((a * 120.0) <= -2000.0)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif ((a * 120.0) <= -5e-97)
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	elseif ((a * 120.0) <= 2e-193)
		tmp = (60.0 * (x - y)) / (z - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+24], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2000.0], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-97], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-193], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2e24 or 2.0000000000000001e-193 < (*.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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 89.3%

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

   if -2e24 < (*.f64 a 120) < -2e3

   1. Initial program 86.5%

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

   5. Taylor expanded in a around 0 99.3%

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

      1. clear-num 99.3%

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

      2. un-div-inv 99.6%

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

   7. Applied egg-rr 99.6%

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

   if -2e3 < (*.f64 a 120) < -4.9999999999999995e-97

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 88.3%

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

      1. associate-*r/ 88.2%

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

      2. associate-*l/ 88.3%

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

      3. *-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -4.9999999999999995e-97 < (*.f64 a 120) < 2.0000000000000001e-193

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 86.2%

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

      1. associate-*r/ 86.3%

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

   7. Applied egg-rr 86.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq -2000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-193}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+20} \lor \neg \left(a \leq 2.1 \cdot 10^{-60}\right) \land \left(a \leq 68000 \lor \neg \left(a \leq 5.5 \cdot 10^{+63}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.65e+20)
         (and (not (<= a 2.1e-60)) (or (<= a 68000.0) (not (<= a 5.5e+63)))))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.65e+20) || (!(a <= 2.1e-60) && ((a <= 68000.0) || !(a <= 5.5e+63)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.65d+20)) .or. (.not. (a <= 2.1d-60)) .and. (a <= 68000.0d0) .or. (.not. (a <= 5.5d+63))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.65e+20) || (!(a <= 2.1e-60) && ((a <= 68000.0) || !(a <= 5.5e+63)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.65e+20) or (not (a <= 2.1e-60) and ((a <= 68000.0) or not (a <= 5.5e+63))):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.65e+20) || (!(a <= 2.1e-60) && ((a <= 68000.0) || !(a <= 5.5e+63))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.65e+20) || (~((a <= 2.1e-60)) && ((a <= 68000.0) || ~((a <= 5.5e+63)))))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.65e+20], And[N[Not[LessEqual[a, 2.1e-60]], $MachinePrecision], Or[LessEqual[a, 68000.0], N[Not[LessEqual[a, 5.5e+63]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.65e20 or 2.09999999999999991e-60 < a < 68000 or 5.50000000000000004e63 < 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* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 82.1%

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

   if -2.65e20 < a < 2.09999999999999991e-60 or 68000 < a < 5.50000000000000004e63

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 77.5%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+20} \lor \neg \left(a \leq 2.1 \cdot 10^{-60}\right) \land \left(a \leq 68000 \lor \neg \left(a \leq 5.5 \cdot 10^{+63}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 150000 \lor \neg \left(a \leq 4.6 \cdot 10^{+63}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+20)
   (* a 120.0)
   (if (<= a 4.4e-60)
     (* (/ 60.0 (- z t)) (- x y))
     (if (or (<= a 150000.0) (not (<= a 4.6e+63)))
       (* a 120.0)
       (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+20) {
		tmp = a * 120.0;
	} else if (a <= 4.4e-60) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((a <= 150000.0) || !(a <= 4.6e+63)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.1d+20)) then
        tmp = a * 120.0d0
    else if (a <= 4.4d-60) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if ((a <= 150000.0d0) .or. (.not. (a <= 4.6d+63))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+20) {
		tmp = a * 120.0;
	} else if (a <= 4.4e-60) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((a <= 150000.0) || !(a <= 4.6e+63)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+20:
		tmp = a * 120.0
	elif a <= 4.4e-60:
		tmp = (60.0 / (z - t)) * (x - y)
	elif (a <= 150000.0) or not (a <= 4.6e+63):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+20)
		tmp = Float64(a * 120.0);
	elseif (a <= 4.4e-60)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif ((a <= 150000.0) || !(a <= 4.6e+63))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+20)
		tmp = a * 120.0;
	elseif (a <= 4.4e-60)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif ((a <= 150000.0) || ~((a <= 4.6e+63)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+20], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 4.4e-60], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 150000.0], N[Not[LessEqual[a, 4.6e+63]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1e20 or 4.3999999999999998e-60 < a < 1.5e5 or 4.59999999999999986e63 < 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* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 82.1%

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

   if -2.1e20 < a < 4.3999999999999998e-60

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 77.6%

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

      1. expm1-log1p-u 53.9%

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

      2. expm1-udef 22.9%

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

      3. associate-*r/ 22.2%

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

   7. Applied egg-rr 22.2%

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

      1. expm1-def 53.3%

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

      2. expm1-log1p 77.0%

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

      3. associate-*l/ 77.7%

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

   9. Simplified 77.7%

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

   if 1.5e5 < a < 4.59999999999999986e63

   1. Initial program 99.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 75.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 150000 \lor \neg \left(a \leq 4.6 \cdot 10^{+63}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+20} \lor \neg \left(a \leq -7.5 \cdot 10^{-6}\right) \land \left(a \leq -2.8 \cdot 10^{-111} \lor \neg \left(a \leq 8 \cdot 10^{-125}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e+20)
         (and (not (<= a -7.5e-6)) (or (<= a -2.8e-111) (not (<= a 8e-125)))))
   (* a 120.0)
   (* -60.0 (/ (- x y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e+20) || (!(a <= -7.5e-6) && ((a <= -2.8e-111) || !(a <= 8e-125)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.9d+20)) .or. (.not. (a <= (-7.5d-6))) .and. (a <= (-2.8d-111)) .or. (.not. (a <= 8d-125))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e+20) || (!(a <= -7.5e-6) && ((a <= -2.8e-111) || !(a <= 8e-125)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e+20) or (not (a <= -7.5e-6) and ((a <= -2.8e-111) or not (a <= 8e-125))):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e+20) || (!(a <= -7.5e-6) && ((a <= -2.8e-111) || !(a <= 8e-125))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e+20) || (~((a <= -7.5e-6)) && ((a <= -2.8e-111) || ~((a <= 8e-125)))))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e+20], And[N[Not[LessEqual[a, -7.5e-6]], $MachinePrecision], Or[LessEqual[a, -2.8e-111], N[Not[LessEqual[a, 8e-125]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e20 or -7.50000000000000019e-6 < a < -2.79999999999999995e-111 or 8.0000000000000001e-125 < 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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 71.3%

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

   if -1.9e20 < a < -7.50000000000000019e-6 or -2.79999999999999995e-111 < a < 8.0000000000000001e-125

   1. Initial program 98.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 85.0%

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

   6. Taylor expanded in z around 0 45.4%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+20} \lor \neg \left(a \leq -7.5 \cdot 10^{-6}\right) \land \left(a \leq -2.8 \cdot 10^{-111} \lor \neg \left(a \leq 8 \cdot 10^{-125}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+89} \lor \neg \left(y \leq 2.95 \cdot 10^{+41}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.45e+89) (not (<= y 2.95e+41)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.45e+89) || !(y <= 2.95e+41)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.45d+89)) .or. (.not. (y <= 2.95d+41))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.45e+89) || !(y <= 2.95e+41)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.45e+89) or not (y <= 2.95e+41):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.45e+89) || !(y <= 2.95e+41))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.45e+89) || ~((y <= 2.95e+41)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.45e+89], N[Not[LessEqual[y, 2.95e+41]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45000000000000013e89 or 2.95e41 < y

   1. Initial program 98.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 90.0%

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

      1. associate-*r/ 89.0%

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

   7. Simplified 89.0%

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

   if -1.45000000000000013e89 < y < 2.95e41

   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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 93.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+89} \lor \neg \left(y \leq 2.95 \cdot 10^{+41}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+93}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.1e+93)
   (+ (* a 120.0) (/ 60.0 (/ (- t z) y)))
   (if (<= y 6.5e+40)
     (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
     (+ (* a 120.0) (/ (* y -60.0) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+93) {
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	} else if (y <= 6.5e+40) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.1d+93)) then
        tmp = (a * 120.0d0) + (60.0d0 / ((t - z) / y))
    else if (y <= 6.5d+40) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+93) {
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	} else if (y <= 6.5e+40) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.1e+93:
		tmp = (a * 120.0) + (60.0 / ((t - z) / y))
	elif y <= 6.5e+40:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.1e+93)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(t - z) / y)));
	elseif (y <= 6.5e+40)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.1e+93)
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	elseif (y <= 6.5e+40)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.1e+93], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+40], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.10000000000000011e93

   1. Initial program 96.8%

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

   5. Taylor expanded in x around 0 93.6%

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

      1. associate-*r/ 93.6%

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

      2. neg-mul-1 93.6%

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

   7. Simplified 93.6%

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

   if -1.10000000000000011e93 < y < 6.5000000000000001e40

   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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 93.7%

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

   if 6.5000000000000001e40 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. associate-*r/ 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+93}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+40}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

5. Final simplification 99.4%

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

Alternative 14: 57.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+73} \lor \neg \left(x \leq 1.95 \cdot 10^{+101}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2e+73) (not (<= x 1.95e+101)))
   (* 60.0 (/ x (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2e+73) || !(x <= 1.95e+101)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2d+73)) .or. (.not. (x <= 1.95d+101))) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2e+73) || !(x <= 1.95e+101)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2e+73) or not (x <= 1.95e+101):
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2e+73) || !(x <= 1.95e+101))
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2e+73) || ~((x <= 1.95e+101)))
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2e+73], N[Not[LessEqual[x, 1.95e+101]], $MachinePrecision]], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999997e73 or 1.95e101 < x

   1. Initial program 97.6%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in a around 0 70.3%

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

   6. Taylor expanded in x around inf 59.7%

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

   if -1.99999999999999997e73 < x < 1.95e101

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 63.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+73} \lor \neg \left(x \leq 1.95 \cdot 10^{+101}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3 \cdot 10^{+218}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 3e+218) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 3e+218) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 3d+218) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 3e+218) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 3e+218:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 3e+218)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 3e+218)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 3e+218], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.0000000000000001e218

   1. Initial program 99.0%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 53.7%

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

   if 3.0000000000000001e218 < x

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 66.4%

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

   6. Taylor expanded in z around 0 62.5%

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

   7. Taylor expanded in x around inf 62.9%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3 \cdot 10^{+218}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{+221}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 2.7e+221) (* a 120.0) (/ -60.0 (/ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 2.7e+221) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (t / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 2.7d+221) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / (t / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 2.7e+221) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 2.7e+221:
		tmp = a * 120.0
	else:
		tmp = -60.0 / (t / x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 2.7e+221)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 2.7e+221)
		tmp = a * 120.0;
	else
		tmp = -60.0 / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 2.7e+221], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7e221

   1. Initial program 99.0%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 53.7%

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

   if 2.7e221 < x

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 66.4%

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

   6. Taylor expanded in z around 0 62.5%

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

   7. Taylor expanded in x around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. associate-/l* 62.9%

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

   9. Simplified 62.9%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{+221}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.7% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

5. Taylor expanded in z around inf 52.4%

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

6. Final simplification 52.4%

   \[\leadsto a \cdot 120 \]
7. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(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)))