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

Percentage Accurate: 99.4% → 99.8%

Time: 16.9s

Alternatives: 19

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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.5%

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

   3. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-76}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-123}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e-44)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= t_1 -4e-76)
       (+ (* a 120.0) (* x (/ 60.0 z)))
       (if (<= t_1 -1e-123)
         (+ (* a 120.0) (* 60.0 (/ y t)))
         (if (<= t_1 2e-5) (* 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 tmp;
	if (t_1 <= -5e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= -4e-76) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if (t_1 <= -1e-123) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (t_1 <= 2e-5) {
		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 * (x - y)) / (z - t)
    if (t_1 <= (-5d-44)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t_1 <= (-4d-76)) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / z))
    else if (t_1 <= (-1d-123)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if (t_1 <= 2d-5) 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 tmp;
	if (t_1 <= -5e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= -4e-76) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if (t_1 <= -1e-123) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (t_1 <= 2e-5) {
		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)
	tmp = 0
	if t_1 <= -5e-44:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t_1 <= -4e-76:
		tmp = (a * 120.0) + (x * (60.0 / z))
	elif t_1 <= -1e-123:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif t_1 <= 2e-5:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e-44)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t_1 <= -4e-76)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	elseif (t_1 <= -1e-123)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (t_1 <= 2e-5)
		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);
	tmp = 0.0;
	if (t_1 <= -5e-44)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t_1 <= -4e-76)
		tmp = (a * 120.0) + (x * (60.0 / z));
	elseif (t_1 <= -1e-123)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif (t_1 <= 2e-5)
		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[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-44], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-76], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-123], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-5], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -5.00000000000000039e-44

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 72.6%

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

   if -5.00000000000000039e-44 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -3.99999999999999971e-76

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.8%

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

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around inf 80.3%

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

   if -3.99999999999999971e-76 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -1.0000000000000001e-123

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 91.7%

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

   5. Taylor expanded in x around 0 86.2%

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

   if -1.0000000000000001e-123 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 2.00000000000000016e-5

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 84.3%

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

   if 2.00000000000000016e-5 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.5%

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

      2. associate-/r/ 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in a around 0 82.7%

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

      1. associate-*r/ 82.8%

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

   8. Simplified 82.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -4 \cdot 10^{-76}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{-123}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]

Alternative 3: 56.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-192}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-195} \lor \neg \left(a \leq 6.6 \cdot 10^{-249}\right) \land \left(a \leq 5.8 \cdot 10^{-173} \lor \neg \left(a \leq 8.5 \cdot 10^{-98}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.08e-69)
   (* a 120.0)
   (if (<= a -1.2e-192)
     (* -60.0 (/ x t))
     (if (or (<= a -1.38e-195)
             (and (not (<= a 6.6e-249))
                  (or (<= a 5.8e-173) (not (<= a 8.5e-98)))))
       (* a 120.0)
       (* -60.0 (/ y (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-69) {
		tmp = a * 120.0;
	} else if (a <= -1.2e-192) {
		tmp = -60.0 * (x / t);
	} else if ((a <= -1.38e-195) || (!(a <= 6.6e-249) && ((a <= 5.8e-173) || !(a <= 8.5e-98)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.08d-69)) then
        tmp = a * 120.0d0
    else if (a <= (-1.2d-192)) then
        tmp = (-60.0d0) * (x / t)
    else if ((a <= (-1.38d-195)) .or. (.not. (a <= 6.6d-249)) .and. (a <= 5.8d-173) .or. (.not. (a <= 8.5d-98))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-69) {
		tmp = a * 120.0;
	} else if (a <= -1.2e-192) {
		tmp = -60.0 * (x / t);
	} else if ((a <= -1.38e-195) || (!(a <= 6.6e-249) && ((a <= 5.8e-173) || !(a <= 8.5e-98)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.08e-69:
		tmp = a * 120.0
	elif a <= -1.2e-192:
		tmp = -60.0 * (x / t)
	elif (a <= -1.38e-195) or (not (a <= 6.6e-249) and ((a <= 5.8e-173) or not (a <= 8.5e-98))):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.08e-69)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.2e-192)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif ((a <= -1.38e-195) || (!(a <= 6.6e-249) && ((a <= 5.8e-173) || !(a <= 8.5e-98))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.08e-69)
		tmp = a * 120.0;
	elseif (a <= -1.2e-192)
		tmp = -60.0 * (x / t);
	elseif ((a <= -1.38e-195) || (~((a <= 6.6e-249)) && ((a <= 5.8e-173) || ~((a <= 8.5e-98)))))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.08e-69], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.2e-192], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.38e-195], And[N[Not[LessEqual[a, 6.6e-249]], $MachinePrecision], Or[LessEqual[a, 5.8e-173], N[Not[LessEqual[a, 8.5e-98]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.0800000000000001e-69 or -1.2e-192 < a < -1.37999999999999992e-195 or 6.6e-249 < a < 5.7999999999999997e-173 or 8.4999999999999997e-98 < 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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 69.0%

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

   if -1.0800000000000001e-69 < a < -1.2e-192

   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* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 69.0%

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

   5. Taylor expanded in t around 0 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-/r/ 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in x around inf 45.3%

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

   if -1.37999999999999992e-195 < a < 6.6e-249 or 5.7999999999999997e-173 < a < 8.4999999999999997e-98

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 52.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-192}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-195} \lor \neg \left(a \leq 6.6 \cdot 10^{-249}\right) \land \left(a \leq 5.8 \cdot 10^{-173} \lor \neg \left(a \leq 8.5 \cdot 10^{-98}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 4: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+55}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-36}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+91)
   (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
   (if (<= z -1.6e+55)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= z -8.6e+46)
       (* a 120.0)
       (if (<= z 4.9e-36)
         (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
         (+ (* a 120.0) (* x (/ 60.0 z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+91) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= -1.6e+55) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= -8.6e+46) {
		tmp = a * 120.0;
	} else if (z <= 4.9e-36) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.2d+91)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if (z <= (-1.6d+55)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (z <= (-8.6d+46)) then
        tmp = a * 120.0d0
    else if (z <= 4.9d-36) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+91) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= -1.6e+55) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= -8.6e+46) {
		tmp = a * 120.0;
	} else if (z <= 4.9e-36) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+91:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif z <= -1.6e+55:
		tmp = 60.0 * ((x - y) / (z - t))
	elif z <= -8.6e+46:
		tmp = a * 120.0
	elif z <= 4.9e-36:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	else:
		tmp = (a * 120.0) + (x * (60.0 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+91)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (z <= -1.6e+55)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (z <= -8.6e+46)
		tmp = Float64(a * 120.0);
	elseif (z <= 4.9e-36)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+91)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif (z <= -1.6e+55)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (z <= -8.6e+46)
		tmp = a * 120.0;
	elseif (z <= 4.9e-36)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	else
		tmp = (a * 120.0) + (x * (60.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+91], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e+55], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e+46], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 4.9e-36], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.20000000000000015e91

   1. Initial program 97.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 87.1%

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

      1. associate-*r/ 87.2%

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

      2. associate-*l/ 87.1%

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

      3. *-commutative 87.1%

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

   6. Simplified 87.1%

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

      1. clear-num 87.1%

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

      2. un-div-inv 87.1%

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

      3. div-inv 87.2%

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

      4. metadata-eval 87.2%

         \[\leadsto \frac{x}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 87.2%

      \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in z around inf 87.2%

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

       1. *-commutative 87.2%

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

   11. Simplified 87.2%

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

   if -4.20000000000000015e91 < z < -1.6000000000000001e55

   1. Initial program 99.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 81.5%

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

   if -1.6000000000000001e55 < z < -8.60000000000000009e46

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -8.60000000000000009e46 < z < 4.8999999999999997e-36

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 86.9%

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

   if 4.8999999999999997e-36 < z

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.8%

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

      1. associate-*r/ 84.7%

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

      2. associate-*l/ 84.8%

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

      3. *-commutative 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in z around inf 77.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+55}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-36}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \end{array} \]

Alternative 5: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+198}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+276}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x z))))
   (if (<= x -2.55e+209)
     t_1
     (if (<= x -9e+167)
       (* a 120.0)
       (if (<= x -1.05e+112)
         t_1
         (if (<= x 4.4e+153)
           (* a 120.0)
           (if (<= x 5.2e+198)
             (* -60.0 (/ x t))
             (if (<= x 1.25e+276) (* a 120.0) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / z);
	double tmp;
	if (x <= -2.55e+209) {
		tmp = t_1;
	} else if (x <= -9e+167) {
		tmp = a * 120.0;
	} else if (x <= -1.05e+112) {
		tmp = t_1;
	} else if (x <= 4.4e+153) {
		tmp = a * 120.0;
	} else if (x <= 5.2e+198) {
		tmp = -60.0 * (x / t);
	} else if (x <= 1.25e+276) {
		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 * (x / z)
    if (x <= (-2.55d+209)) then
        tmp = t_1
    else if (x <= (-9d+167)) then
        tmp = a * 120.0d0
    else if (x <= (-1.05d+112)) then
        tmp = t_1
    else if (x <= 4.4d+153) then
        tmp = a * 120.0d0
    else if (x <= 5.2d+198) then
        tmp = (-60.0d0) * (x / t)
    else if (x <= 1.25d+276) 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 / z);
	double tmp;
	if (x <= -2.55e+209) {
		tmp = t_1;
	} else if (x <= -9e+167) {
		tmp = a * 120.0;
	} else if (x <= -1.05e+112) {
		tmp = t_1;
	} else if (x <= 4.4e+153) {
		tmp = a * 120.0;
	} else if (x <= 5.2e+198) {
		tmp = -60.0 * (x / t);
	} else if (x <= 1.25e+276) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / z)
	tmp = 0
	if x <= -2.55e+209:
		tmp = t_1
	elif x <= -9e+167:
		tmp = a * 120.0
	elif x <= -1.05e+112:
		tmp = t_1
	elif x <= 4.4e+153:
		tmp = a * 120.0
	elif x <= 5.2e+198:
		tmp = -60.0 * (x / t)
	elif x <= 1.25e+276:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / z))
	tmp = 0.0
	if (x <= -2.55e+209)
		tmp = t_1;
	elseif (x <= -9e+167)
		tmp = Float64(a * 120.0);
	elseif (x <= -1.05e+112)
		tmp = t_1;
	elseif (x <= 4.4e+153)
		tmp = Float64(a * 120.0);
	elseif (x <= 5.2e+198)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (x <= 1.25e+276)
		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 / z);
	tmp = 0.0;
	if (x <= -2.55e+209)
		tmp = t_1;
	elseif (x <= -9e+167)
		tmp = a * 120.0;
	elseif (x <= -1.05e+112)
		tmp = t_1;
	elseif (x <= 4.4e+153)
		tmp = a * 120.0;
	elseif (x <= 5.2e+198)
		tmp = -60.0 * (x / t);
	elseif (x <= 1.25e+276)
		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[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.55e+209], t$95$1, If[LessEqual[x, -9e+167], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -1.05e+112], t$95$1, If[LessEqual[x, 4.4e+153], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 5.2e+198], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+276], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.55000000000000011e209 or -8.9999999999999998e167 < x < -1.0499999999999999e112 or 1.25e276 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 83.1%

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

   7. Taylor expanded in z around inf 60.3%

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

   if -2.55000000000000011e209 < x < -8.9999999999999998e167 or -1.0499999999999999e112 < x < 4.3999999999999999e153 or 5.19999999999999961e198 < x < 1.25e276

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 59.5%

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

   if 4.3999999999999999e153 < x < 5.19999999999999961e198

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.9%

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

   5. Taylor expanded in t around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-/r/ 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in x around inf 59.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+209}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+112}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+198}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+276}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 6: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -2 \cdot 10^{+80} \lor \neg \left(x - y \leq 5 \cdot 10^{+152}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- x y) -2e+80) (not (<= (- x y) 5e+152)))
   (* 60.0 (/ (- x y) (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -2e+80) || !((x - y) <= 5e+152)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x - y) <= (-2d+80)) .or. (.not. ((x - y) <= 5d+152))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -2e+80) || !((x - y) <= 5e+152)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x - y) <= -2e+80) or not ((x - y) <= 5e+152):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x - y) <= -2e+80) || !(Float64(x - y) <= 5e+152))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x - y) <= -2e+80) || ~(((x - y) <= 5e+152)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x - y), $MachinePrecision], -2e+80], N[Not[LessEqual[N[(x - y), $MachinePrecision], 5e+152]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x y) < -2e80 or 5e152 < (-.f64 x y)

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 74.1%

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

   if -2e80 < (-.f64 x y) < 5e152

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 73.6%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -2 \cdot 10^{+80} \lor \neg \left(x - y \leq 5 \cdot 10^{+152}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -31000:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+152} \lor \neg \left(x \leq 3.4 \cdot 10^{+197}\right) \land x \leq 1.95 \cdot 10^{+276}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.6e+52)
   (* a 120.0)
   (if (<= x -31000.0)
     (* -60.0 (/ y z))
     (if (or (<= x 8.5e+152) (and (not (<= x 3.4e+197)) (<= x 1.95e+276)))
       (* a 120.0)
       (* -60.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.6e+52) {
		tmp = a * 120.0;
	} else if (x <= -31000.0) {
		tmp = -60.0 * (y / z);
	} else if ((x <= 8.5e+152) || (!(x <= 3.4e+197) && (x <= 1.95e+276))) {
		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 <= (-1.6d+52)) then
        tmp = a * 120.0d0
    else if (x <= (-31000.0d0)) then
        tmp = (-60.0d0) * (y / z)
    else if ((x <= 8.5d+152) .or. (.not. (x <= 3.4d+197)) .and. (x <= 1.95d+276)) 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 <= -1.6e+52) {
		tmp = a * 120.0;
	} else if (x <= -31000.0) {
		tmp = -60.0 * (y / z);
	} else if ((x <= 8.5e+152) || (!(x <= 3.4e+197) && (x <= 1.95e+276))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.6e+52:
		tmp = a * 120.0
	elif x <= -31000.0:
		tmp = -60.0 * (y / z)
	elif (x <= 8.5e+152) or (not (x <= 3.4e+197) and (x <= 1.95e+276)):
		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 <= -1.6e+52)
		tmp = Float64(a * 120.0);
	elseif (x <= -31000.0)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif ((x <= 8.5e+152) || (!(x <= 3.4e+197) && (x <= 1.95e+276)))
		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 <= -1.6e+52)
		tmp = a * 120.0;
	elseif (x <= -31000.0)
		tmp = -60.0 * (y / z);
	elseif ((x <= 8.5e+152) || (~((x <= 3.4e+197)) && (x <= 1.95e+276)))
		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, -1.6e+52], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -31000.0], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8.5e+152], And[N[Not[LessEqual[x, 3.4e+197]], $MachinePrecision], LessEqual[x, 1.95e+276]]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e52 or -31000 < x < 8.4999999999999993e152 or 3.40000000000000017e197 < x < 1.9500000000000001e276

   1. Initial program 99.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 57.4%

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

   if -1.6e52 < x < -31000

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.1%

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

   7. Taylor expanded in z around inf 52.6%

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

   if 8.4999999999999993e152 < x < 3.40000000000000017e197 or 1.9500000000000001e276 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 70.6%

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

   5. Taylor expanded in t around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/r/ 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in x around inf 61.0%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+52}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -31000:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+152} \lor \neg \left(x \leq 3.4 \cdot 10^{+197}\right) \land x \leq 1.95 \cdot 10^{+276}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 8: 83.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+57} \lor \neg \left(z \leq 4.9 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+57) (not (<= z 4.9e-36)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+57) || !(z <= 4.9e-36)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-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 ((z <= (-4.5d+57)) .or. (.not. (z <= 4.9d-36))) then
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    else
        tmp = (a * 120.0d0) + ((-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 ((z <= -4.5e+57) || !(z <= 4.9e-36)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+57) or not (z <= 4.9e-36):
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	else:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+57) || !(z <= 4.9e-36))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	else
		tmp = Float64(Float64(a * 120.0) + 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 ((z <= -4.5e+57) || ~((z <= 4.9e-36)))
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	else
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+57], N[Not[LessEqual[z, 4.9e-36]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999996e57 or 4.8999999999999997e-36 < z

   1. Initial program 99.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 91.2%

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

   if -4.49999999999999996e57 < z < 4.8999999999999997e-36

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 86.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+57} \lor \neg \left(z \leq 4.9 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 9: 83.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+57} \lor \neg \left(z \leq 4 \cdot 10^{-37}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+57) (not (<= z 4e-37)))
   (+ (* a 120.0) (* (- x y) (/ 60.0 z)))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+57) || !(z <= 4e-37)) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + (-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 ((z <= (-4.4d+57)) .or. (.not. (z <= 4d-37))) then
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    else
        tmp = (a * 120.0d0) + ((-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 ((z <= -4.4e+57) || !(z <= 4e-37)) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+57) or not (z <= 4e-37):
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	else:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+57) || !(z <= 4e-37))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e+57) || ~((z <= 4e-37)))
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	else
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e+57], N[Not[LessEqual[z, 4e-37]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000001e57 or 4.00000000000000027e-37 < z

   1. Initial program 99.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 91.2%

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

   if -4.4000000000000001e57 < z < 4.00000000000000027e-37

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 86.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+57} \lor \neg \left(z \leq 4 \cdot 10^{-37}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 10: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+79} \lor \neg \left(x \leq 1.8 \cdot 10^{+135}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.5e+79) (not (<= x 1.8e+135)))
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
   (+ (* a 120.0) (/ -60.0 (/ (- z t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.5e+79) || !(x <= 1.8e+135)) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.5d+79)) .or. (.not. (x <= 1.8d+135))) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else
        tmp = (a * 120.0d0) + ((-60.0d0) / ((z - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.5e+79) || !(x <= 1.8e+135)) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.5e+79) or not (x <= 1.8e+135):
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	else:
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.5e+79) || !(x <= 1.8e+135))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(Float64(z - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.5e+79) || ~((x <= 1.8e+135)))
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	else
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.5e+79], N[Not[LessEqual[x, 1.8e+135]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999994e79 or 1.7999999999999999e135 < x

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in x around inf 94.0%

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

      1. associate-*r/ 94.1%

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

      2. associate-*l/ 94.0%

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

      3. *-commutative 94.0%

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

   6. Simplified 94.0%

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

   if -4.49999999999999994e79 < x < 1.7999999999999999e135

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. associate-*r/ 91.9%

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

      2. associate-/l* 91.8%

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

   6. Simplified 91.8%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+79} \lor \neg \left(x \leq 1.8 \cdot 10^{+135}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 11: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+135}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.4e+79)
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
   (if (<= x 4.3e+135)
     (+ (* a 120.0) (/ -60.0 (/ (- z t) y)))
     (+ (* a 120.0) (/ x (* (- z t) 0.016666666666666666))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e+79) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 4.3e+135) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.4d+79)) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else if (x <= 4.3d+135) then
        tmp = (a * 120.0d0) + ((-60.0d0) / ((z - t) / y))
    else
        tmp = (a * 120.0d0) + (x / ((z - t) * 0.016666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e+79) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 4.3e+135) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.4e+79:
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	elif x <= 4.3e+135:
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y))
	else:
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.4e+79)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	elseif (x <= 4.3e+135)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(Float64(z - t) / y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) * 0.016666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.4e+79)
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	elseif (x <= 4.3e+135)
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	else
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.4e+79], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+135], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000032e79

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in x around inf 94.2%

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

      1. associate-*r/ 94.2%

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

      2. associate-*l/ 94.2%

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

      3. *-commutative 94.2%

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

   6. Simplified 94.2%

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

   if -3.40000000000000032e79 < x < 4.29999999999999972e135

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. associate-*r/ 91.9%

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

      2. associate-/l* 91.8%

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

   6. Simplified 91.8%

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

   if 4.29999999999999972e135 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 93.9%

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

      1. associate-*r/ 94.0%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   6. Simplified 93.9%

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

      1. clear-num 93.8%

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

      2. un-div-inv 94.0%

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

      3. div-inv 94.1%

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

      4. metadata-eval 94.1%

         \[\leadsto \frac{x}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+135}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \]

Alternative 12: 89.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+135}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.4e+79)
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
   (if (<= x 2.55e+135)
     (+ (* a 120.0) (/ (* y -60.0) (- z t)))
     (+ (* a 120.0) (/ x (* (- z t) 0.016666666666666666))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e+79) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 2.55e+135) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.4d+79)) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else if (x <= 2.55d+135) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x / ((z - t) * 0.016666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e+79) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 2.55e+135) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.4e+79:
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	elif x <= 2.55e+135:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.4e+79)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	elseif (x <= 2.55e+135)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) * 0.016666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.4e+79)
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	elseif (x <= 2.55e+135)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.4e+79], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e+135], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000032e79

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in x around inf 94.2%

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

      1. associate-*r/ 94.2%

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

      2. associate-*l/ 94.2%

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

      3. *-commutative 94.2%

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

   6. Simplified 94.2%

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

   if -3.40000000000000032e79 < x < 2.54999999999999991e135

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 91.9%

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

   if 2.54999999999999991e135 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 93.9%

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

      1. associate-*r/ 94.0%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   6. Simplified 93.9%

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

      1. clear-num 93.8%

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

      2. un-div-inv 94.0%

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

      3. div-inv 94.1%

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

      4. metadata-eval 94.1%

         \[\leadsto \frac{x}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+135}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \]

Alternative 13: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.5e+79)
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))
   (if (<= x 1.45e+137)
     (+ (* a 120.0) (/ (* y -60.0) (- z t)))
     (+ (* a 120.0) (/ x (* (- z t) 0.016666666666666666))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.5e+79) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else if (x <= 1.45e+137) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.5d+79)) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - t))
    else if (x <= 1.45d+137) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x / ((z - t) * 0.016666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.5e+79) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else if (x <= 1.45e+137) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.5e+79:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	elif x <= 1.45e+137:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.5e+79)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	elseif (x <= 1.45e+137)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) * 0.016666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.5e+79)
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	elseif (x <= 1.45e+137)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.5e+79], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+137], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4999999999999998e79

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in x around inf 94.2%

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

      1. associate-*r/ 94.2%

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

      2. *-commutative 94.2%

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

   6. Simplified 94.2%

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

   if -3.4999999999999998e79 < x < 1.44999999999999992e137

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 91.9%

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

   if 1.44999999999999992e137 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 93.9%

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

      1. associate-*r/ 94.0%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   6. Simplified 93.9%

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

      1. clear-num 93.8%

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

      2. un-div-inv 94.0%

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

      3. div-inv 94.1%

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

      4. metadata-eval 94.1%

         \[\leadsto \frac{x}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \]

Alternative 14: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3000:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= x -1.45e+79)
     t_1
     (if (<= x -3000.0)
       (* -60.0 (/ y (- z t)))
       (if (<= x 4.8e+153) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (x <= -1.45e+79) {
		tmp = t_1;
	} else if (x <= -3000.0) {
		tmp = -60.0 * (y / (z - t));
	} else if (x <= 4.8e+153) {
		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 * (x / (z - t))
    if (x <= (-1.45d+79)) then
        tmp = t_1
    else if (x <= (-3000.0d0)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (x <= 4.8d+153) 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 / (z - t));
	double tmp;
	if (x <= -1.45e+79) {
		tmp = t_1;
	} else if (x <= -3000.0) {
		tmp = -60.0 * (y / (z - t));
	} else if (x <= 4.8e+153) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if x <= -1.45e+79:
		tmp = t_1
	elif x <= -3000.0:
		tmp = -60.0 * (y / (z - t))
	elif x <= 4.8e+153:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (x <= -1.45e+79)
		tmp = t_1;
	elseif (x <= -3000.0)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (x <= 4.8e+153)
		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 / (z - t));
	tmp = 0.0;
	if (x <= -1.45e+79)
		tmp = t_1;
	elseif (x <= -3000.0)
		tmp = -60.0 * (y / (z - t));
	elseif (x <= 4.8e+153)
		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[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+79], t$95$1, If[LessEqual[x, -3000.0], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+153], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999996e79 or 4.79999999999999985e153 < x

   1. Initial program 98.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 67.0%

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

   if -1.44999999999999996e79 < x < -3e3

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 61.2%

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

   if -3e3 < x < 4.79999999999999985e153

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+79}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq -3000:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]

Alternative 15: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -17000:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= x -1.12e+80)
     t_1
     (if (<= x -17000.0)
       (* y (/ -60.0 (- z t)))
       (if (<= x 3.2e+153) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (x <= -1.12e+80) {
		tmp = t_1;
	} else if (x <= -17000.0) {
		tmp = y * (-60.0 / (z - t));
	} else if (x <= 3.2e+153) {
		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 * (x / (z - t))
    if (x <= (-1.12d+80)) then
        tmp = t_1
    else if (x <= (-17000.0d0)) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (x <= 3.2d+153) 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 / (z - t));
	double tmp;
	if (x <= -1.12e+80) {
		tmp = t_1;
	} else if (x <= -17000.0) {
		tmp = y * (-60.0 / (z - t));
	} else if (x <= 3.2e+153) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if x <= -1.12e+80:
		tmp = t_1
	elif x <= -17000.0:
		tmp = y * (-60.0 / (z - t))
	elif x <= 3.2e+153:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (x <= -1.12e+80)
		tmp = t_1;
	elseif (x <= -17000.0)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (x <= 3.2e+153)
		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 / (z - t));
	tmp = 0.0;
	if (x <= -1.12e+80)
		tmp = t_1;
	elseif (x <= -17000.0)
		tmp = y * (-60.0 / (z - t));
	elseif (x <= 3.2e+153)
		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[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.12e+80], t$95$1, If[LessEqual[x, -17000.0], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+153], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.12e80 or 3.2000000000000001e153 < x

   1. Initial program 98.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 67.0%

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

   if -1.12e80 < x < -17000

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 61.2%

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

      1. associate-*r/ 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-commutative 61.5%

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

   8. Simplified 61.5%

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

   if -17000 < x < 3.2000000000000001e153

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+80}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq -17000:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]

Alternative 16: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{0.016666666666666666}}{z - t}\\ \mathbf{if}\;x \leq -2.85 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9500:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;x \leq 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (/ x 0.016666666666666666) (- z t))))
   (if (<= x -2.85e+79)
     t_1
     (if (<= x -9500.0)
       (* y (/ -60.0 (- z t)))
       (if (<= x 1e+153) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / 0.016666666666666666) / (z - t);
	double tmp;
	if (x <= -2.85e+79) {
		tmp = t_1;
	} else if (x <= -9500.0) {
		tmp = y * (-60.0 / (z - t));
	} else if (x <= 1e+153) {
		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 = (x / 0.016666666666666666d0) / (z - t)
    if (x <= (-2.85d+79)) then
        tmp = t_1
    else if (x <= (-9500.0d0)) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (x <= 1d+153) 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 = (x / 0.016666666666666666) / (z - t);
	double tmp;
	if (x <= -2.85e+79) {
		tmp = t_1;
	} else if (x <= -9500.0) {
		tmp = y * (-60.0 / (z - t));
	} else if (x <= 1e+153) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / 0.016666666666666666) / (z - t)
	tmp = 0
	if x <= -2.85e+79:
		tmp = t_1
	elif x <= -9500.0:
		tmp = y * (-60.0 / (z - t))
	elif x <= 1e+153:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / 0.016666666666666666) / Float64(z - t))
	tmp = 0.0
	if (x <= -2.85e+79)
		tmp = t_1;
	elseif (x <= -9500.0)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (x <= 1e+153)
		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 = (x / 0.016666666666666666) / (z - t);
	tmp = 0.0;
	if (x <= -2.85e+79)
		tmp = t_1;
	elseif (x <= -9500.0)
		tmp = y * (-60.0 / (z - t));
	elseif (x <= 1e+153)
		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[(N[(x / 0.016666666666666666), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.85e+79], t$95$1, If[LessEqual[x, -9500.0], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+153], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8499999999999998e79 or 1e153 < x

   1. Initial program 98.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 67.0%

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

      1. metadata-eval 67.0%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \frac{x}{z - t} \]

      2. times-frac 67.1%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{0.016666666666666666 \cdot \left(z - t\right)}} \]

      3. *-un-lft-identity 67.1%

         \[\leadsto \frac{\color{blue}{x}}{0.016666666666666666 \cdot \left(z - t\right)} \]

      4. associate-/r* 67.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{0.016666666666666666}}{z - t}} \]

   8. Applied egg-rr 67.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{0.016666666666666666}}{z - t}} \]

   if -2.8499999999999998e79 < x < -9500

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 61.2%

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

      1. associate-*r/ 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-commutative 61.5%

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

   8. Simplified 61.5%

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

   if -9500 < x < 1e153

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{x}{0.016666666666666666}}{z - t}\\ \mathbf{elif}\;x \leq -9500:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;x \leq 10^{+153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{0.016666666666666666}}{z - t}\\ \end{array} \]

Alternative 17: 99.8% accurate, 1.0× speedup

Math

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

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(Float64(60.0 / 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[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 18: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+153} \lor \neg \left(x \leq 1.55 \cdot 10^{+205}\right) \land x \leq 7.5 \cdot 10^{+276}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x 4.8e+153) (and (not (<= x 1.55e+205)) (<= x 7.5e+276)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= 4.8e+153) || (!(x <= 1.55e+205) && (x <= 7.5e+276))) {
		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 <= 4.8d+153) .or. (.not. (x <= 1.55d+205)) .and. (x <= 7.5d+276)) 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 <= 4.8e+153) || (!(x <= 1.55e+205) && (x <= 7.5e+276))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= 4.8e+153) or (not (x <= 1.55e+205) and (x <= 7.5e+276)):
		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 <= 4.8e+153) || (!(x <= 1.55e+205) && (x <= 7.5e+276)))
		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 <= 4.8e+153) || (~((x <= 1.55e+205)) && (x <= 7.5e+276)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, 4.8e+153], And[N[Not[LessEqual[x, 1.55e+205]], $MachinePrecision], LessEqual[x, 7.5e+276]]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.79999999999999985e153 or 1.55000000000000009e205 < x < 7.49999999999999953e276

   1. Initial program 99.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 55.2%

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

   if 4.79999999999999985e153 < x < 1.55000000000000009e205 or 7.49999999999999953e276 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 70.6%

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

   5. Taylor expanded in t around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/r/ 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in x around inf 61.0%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+153} \lor \neg \left(x \leq 1.55 \cdot 10^{+205}\right) \land x \leq 7.5 \cdot 10^{+276}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 19: 51.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 51.3%

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

5. Final simplification 51.3%

   \[\leadsto a \cdot 120 \]

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 2023331 
(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)))