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

Percentage Accurate: 99.5% → 99.8%

Time: 14.4s

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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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 99.7%

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

   1. +-commutative 99.7%

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

   2. fma-def 99.8%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-*r/ 99.8%

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

   2. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-46}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+85}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+93}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ x (* t -0.016666666666666666)))))
   (if (<= (* a 120.0) -4e+141)
     (* a 120.0)
     (if (<= (* a 120.0) -1e-6)
       t_1
       (if (<= (* a 120.0) 1e-46)
         (* 60.0 (/ (- x y) (- z t)))
         (if (<= (* a 120.0) 1e+85)
           (+ (* a 120.0) (* -60.0 (/ y z)))
           (if (<= (* a 120.0) 2e+93) (* 60.0 (/ x (- z t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x / (t * -0.016666666666666666));
	double tmp;
	if ((a * 120.0) <= -4e+141) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-6) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-46) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+85) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e+93) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x / (t * (-0.016666666666666666d0)))
    if ((a * 120.0d0) <= (-4d+141)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-6)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 1d-46) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 1d+85) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 2d+93) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x / (t * -0.016666666666666666));
	double tmp;
	if ((a * 120.0) <= -4e+141) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-6) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-46) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+85) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e+93) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x / (t * -0.016666666666666666))
	tmp = 0
	if (a * 120.0) <= -4e+141:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-6:
		tmp = t_1
	elif (a * 120.0) <= 1e-46:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 1e+85:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 2e+93:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x / Float64(t * -0.016666666666666666)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+141)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-6)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 1e-46)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e+85)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 2e+93)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x / (t * -0.016666666666666666));
	tmp = 0.0;
	if ((a * 120.0) <= -4e+141)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-6)
		tmp = t_1;
	elseif ((a * 120.0) <= 1e-46)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 1e+85)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 2e+93)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+141], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-6], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-46], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+85], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+93], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -4.00000000000000007e141

   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 93.7%

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

   if -4.00000000000000007e141 < (*.f64 a 120) < -9.99999999999999955e-7 or 2.00000000000000009e93 < (*.f64 a 120)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 92.6%

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

      1. associate-*r/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in z around 0 82.7%

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

      1. *-commutative 82.7%

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

   9. Simplified 82.7%

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

   if -9.99999999999999955e-7 < (*.f64 a 120) < 1.00000000000000002e-46

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 82.5%

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

   if 1.00000000000000002e-46 < (*.f64 a 120) < 1e85

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in t around 0 68.6%

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

   if 1e85 < (*.f64 a 120) < 2.00000000000000009e93

   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 a around 0 99.5%

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

   5. Taylor expanded in x around inf 99.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-6}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-46}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+85}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+93}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-46}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+85}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ x (* t -0.016666666666666666)))))
   (if (<= (* a 120.0) -4e+141)
     (* a 120.0)
     (if (<= (* a 120.0) -1e-6)
       t_1
       (if (<= (* a 120.0) 1e-46)
         (* 60.0 (/ (- x y) (- z t)))
         (if (<= (* a 120.0) 1e+85)
           (+ (* a 120.0) (* -60.0 (/ y z)))
           (if (<= (* a 120.0) 2e+111)
             t_1
             (+ (* a 120.0) (/ x (* z 0.016666666666666666))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x / (t * -0.016666666666666666));
	double tmp;
	if ((a * 120.0) <= -4e+141) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-6) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-46) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+85) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e+111) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x / (z * 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) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x / (t * (-0.016666666666666666d0)))
    if ((a * 120.0d0) <= (-4d+141)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-6)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 1d-46) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 1d+85) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 2d+111) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x / (t * -0.016666666666666666));
	double tmp;
	if ((a * 120.0) <= -4e+141) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-6) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-46) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+85) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e+111) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x / (t * -0.016666666666666666))
	tmp = 0
	if (a * 120.0) <= -4e+141:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-6:
		tmp = t_1
	elif (a * 120.0) <= 1e-46:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 1e+85:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 2e+111:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x / Float64(t * -0.016666666666666666)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+141)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-6)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 1e-46)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e+85)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 2e+111)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x / (t * -0.016666666666666666));
	tmp = 0.0;
	if ((a * 120.0) <= -4e+141)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-6)
		tmp = t_1;
	elseif ((a * 120.0) <= 1e-46)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 1e+85)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 2e+111)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+141], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-6], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-46], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+85], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+111], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -4.00000000000000007e141

   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 93.7%

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

   if -4.00000000000000007e141 < (*.f64 a 120) < -9.99999999999999955e-7 or 1e85 < (*.f64 a 120) < 1.99999999999999991e111

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 91.3%

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

      1. associate-*r/ 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-/l* 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   9. Simplified 78.3%

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

   if -9.99999999999999955e-7 < (*.f64 a 120) < 1.00000000000000002e-46

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 82.5%

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

   if 1.00000000000000002e-46 < (*.f64 a 120) < 1e85

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in t around 0 68.6%

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

   if 1.99999999999999991e111 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 94.0%

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

      1. associate-*r/ 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-/l* 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in z around inf 87.7%

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

      1. *-commutative 87.7%

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

   9. Simplified 87.7%

      \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} + a \cdot 120 \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-6}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-46}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+85}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \]

Alternative 5: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-11}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))) (t_2 (* -60.0 (/ y (- z t)))))
   (if (<= a -1.25e-17)
     (* a 120.0)
     (if (<= a -2.3e-83)
       t_2
       (if (<= a -1.05e-157)
         t_1
         (if (<= a -1.75e-199)
           t_2
           (if (<= a -6e-300)
             t_1
             (if (<= a 1.28e-11) (* 60.0 (/ (- x y) z)) (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.25e-17) {
		tmp = a * 120.0;
	} else if (a <= -2.3e-83) {
		tmp = t_2;
	} else if (a <= -1.05e-157) {
		tmp = t_1;
	} else if (a <= -1.75e-199) {
		tmp = t_2;
	} else if (a <= -6e-300) {
		tmp = t_1;
	} else if (a <= 1.28e-11) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    t_2 = (-60.0d0) * (y / (z - t))
    if (a <= (-1.25d-17)) then
        tmp = a * 120.0d0
    else if (a <= (-2.3d-83)) then
        tmp = t_2
    else if (a <= (-1.05d-157)) then
        tmp = t_1
    else if (a <= (-1.75d-199)) then
        tmp = t_2
    else if (a <= (-6d-300)) then
        tmp = t_1
    else if (a <= 1.28d-11) then
        tmp = 60.0d0 * ((x - y) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.25e-17) {
		tmp = a * 120.0;
	} else if (a <= -2.3e-83) {
		tmp = t_2;
	} else if (a <= -1.05e-157) {
		tmp = t_1;
	} else if (a <= -1.75e-199) {
		tmp = t_2;
	} else if (a <= -6e-300) {
		tmp = t_1;
	} else if (a <= 1.28e-11) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	t_2 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -1.25e-17:
		tmp = a * 120.0
	elif a <= -2.3e-83:
		tmp = t_2
	elif a <= -1.05e-157:
		tmp = t_1
	elif a <= -1.75e-199:
		tmp = t_2
	elif a <= -6e-300:
		tmp = t_1
	elif a <= 1.28e-11:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	t_2 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.25e-17)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.3e-83)
		tmp = t_2;
	elseif (a <= -1.05e-157)
		tmp = t_1;
	elseif (a <= -1.75e-199)
		tmp = t_2;
	elseif (a <= -6e-300)
		tmp = t_1;
	elseif (a <= 1.28e-11)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	t_2 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -1.25e-17)
		tmp = a * 120.0;
	elseif (a <= -2.3e-83)
		tmp = t_2;
	elseif (a <= -1.05e-157)
		tmp = t_1;
	elseif (a <= -1.75e-199)
		tmp = t_2;
	elseif (a <= -6e-300)
		tmp = t_1;
	elseif (a <= 1.28e-11)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e-17], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.3e-83], t$95$2, If[LessEqual[a, -1.05e-157], t$95$1, If[LessEqual[a, -1.75e-199], t$95$2, If[LessEqual[a, -6e-300], t$95$1, If[LessEqual[a, 1.28e-11], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.25e-17 or 1.28e-11 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 75.8%

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

   if -1.25e-17 < a < -2.2999999999999999e-83 or -1.05e-157 < a < -1.7499999999999999e-199

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 78.0%

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

   5. Taylor expanded in x around 0 62.2%

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

   if -2.2999999999999999e-83 < a < -1.05e-157 or -1.7499999999999999e-199 < a < -6.00000000000000048e-300

   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 85.6%

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

   5. Taylor expanded in x around inf 64.1%

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

   if -6.00000000000000048e-300 < a < 1.28e-11

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 79.7%

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

   5. Taylor expanded in z around inf 53.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-157}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-199}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-300}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-11}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-14} \lor \neg \left(a \cdot 120 \leq 0.1\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-14) (not (<= (* a 120.0) 0.1)))
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-14) || !((a * 120.0) <= 0.1)) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-14)) .or. (.not. ((a * 120.0d0) <= 0.1d0))) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-14) || !((a * 120.0) <= 0.1)) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-14) or not ((a * 120.0) <= 0.1):
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-14) || !(Float64(a * 120.0) <= 0.1))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-14) || ~(((a * 120.0) <= 0.1)))
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-14], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 0.1]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -2e-14 or 0.10000000000000001 < (*.f64 a 120)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 91.0%

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

      1. associate-*r/ 90.9%

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

      2. associate-*l/ 91.0%

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

      3. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   if -2e-14 < (*.f64 a 120) < 0.10000000000000001

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 81.0%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-14} \lor \neg \left(a \cdot 120 \leq 0.1\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 7: 56.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-291}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+154}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= x -1.55e+147)
     t_1
     (if (<= x -9.5e-241)
       (* a 120.0)
       (if (<= x 1.18e-291)
         (* -60.0 (/ y (- z t)))
         (if (<= x 9e+154) (* 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 <= -1.55e+147) {
		tmp = t_1;
	} else if (x <= -9.5e-241) {
		tmp = a * 120.0;
	} else if (x <= 1.18e-291) {
		tmp = -60.0 * (y / (z - t));
	} else if (x <= 9e+154) {
		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 <= (-1.55d+147)) then
        tmp = t_1
    else if (x <= (-9.5d-241)) then
        tmp = a * 120.0d0
    else if (x <= 1.18d-291) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (x <= 9d+154) 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 <= -1.55e+147) {
		tmp = t_1;
	} else if (x <= -9.5e-241) {
		tmp = a * 120.0;
	} else if (x <= 1.18e-291) {
		tmp = -60.0 * (y / (z - t));
	} else if (x <= 9e+154) {
		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 <= -1.55e+147:
		tmp = t_1
	elif x <= -9.5e-241:
		tmp = a * 120.0
	elif x <= 1.18e-291:
		tmp = -60.0 * (y / (z - t))
	elif x <= 9e+154:
		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 <= -1.55e+147)
		tmp = t_1;
	elseif (x <= -9.5e-241)
		tmp = Float64(a * 120.0);
	elseif (x <= 1.18e-291)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (x <= 9e+154)
		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 <= -1.55e+147)
		tmp = t_1;
	elseif (x <= -9.5e-241)
		tmp = a * 120.0;
	elseif (x <= 1.18e-291)
		tmp = -60.0 * (y / (z - t));
	elseif (x <= 9e+154)
		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, -1.55e+147], t$95$1, If[LessEqual[x, -9.5e-241], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 1.18e-291], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+154], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e147 or 9.00000000000000018e154 < x

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 75.4%

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

   5. Taylor expanded in x around inf 65.4%

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

   if -1.55e147 < x < -9.49999999999999971e-241 or 1.18e-291 < x < 9.00000000000000018e154

   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 59.1%

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

   if -9.49999999999999971e-241 < x < 1.18e-291

   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 a around 0 69.9%

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

   5. Taylor expanded in x around 0 69.9%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+147}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-241}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-291}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+154}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]

Alternative 8: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-48}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e+45)
   (* a 120.0)
   (if (<= a 1.2e-48)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= a 9.5e+84)
       (+ (* a 120.0) (* -60.0 (/ y z)))
       (if (<= a 1.5e+91) (* 60.0 (/ x (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+45) {
		tmp = a * 120.0;
	} else if (a <= 1.2e-48) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (a <= 9.5e+84) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (a <= 1.5e+91) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.2d+45)) then
        tmp = a * 120.0d0
    else if (a <= 1.2d-48) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (a <= 9.5d+84) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (a <= 1.5d+91) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+45) {
		tmp = a * 120.0;
	} else if (a <= 1.2e-48) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (a <= 9.5e+84) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (a <= 1.5e+91) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e+45:
		tmp = a * 120.0
	elif a <= 1.2e-48:
		tmp = 60.0 * ((x - y) / (z - t))
	elif a <= 9.5e+84:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif a <= 1.5e+91:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+45)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.2e-48)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (a <= 9.5e+84)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (a <= 1.5e+91)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.2e+45)
		tmp = a * 120.0;
	elseif (a <= 1.2e-48)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (a <= 9.5e+84)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (a <= 1.5e+91)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+45], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.2e-48], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+84], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+91], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.2e45 or 1.50000000000000003e91 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 84.3%

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

   if -7.2e45 < a < 1.2e-48

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 80.6%

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

   if 1.2e-48 < a < 9.49999999999999979e84

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in t around 0 68.6%

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

   if 9.49999999999999979e84 < a < 1.50000000000000003e91

   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 a around 0 99.5%

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

   5. Taylor expanded in x around inf 99.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-48}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+36} \lor \neg \left(x \leq 2.7 \cdot 10^{+25}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.2e+36) (not (<= x 2.7e+25)))
   (+ (* 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 <= -1.2e+36) || !(x <= 2.7e+25)) {
		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 <= (-1.2d+36)) .or. (.not. (x <= 2.7d+25))) 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 <= -1.2e+36) || !(x <= 2.7e+25)) {
		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 <= -1.2e+36) or not (x <= 2.7e+25):
		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 <= -1.2e+36) || !(x <= 2.7e+25))
		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 <= -1.2e+36) || ~((x <= 2.7e+25)))
		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, -1.2e+36], N[Not[LessEqual[x, 2.7e+25]], $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 < -1.19999999999999996e36 or 2.7e25 < 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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 88.2%

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

      1. associate-*r/ 88.1%

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

      2. associate-*l/ 88.2%

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

      3. *-commutative 88.2%

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

   6. Simplified 88.2%

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

   if -1.19999999999999996e36 < x < 2.7e25

   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 0 95.6%

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

      1. associate-*r/ 95.6%

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

      2. associate-/l* 95.5%

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

   6. Simplified 95.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+36} \lor \neg \left(x \leq 2.7 \cdot 10^{+25}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 10: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+26}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.4e+35)
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
   (if (<= x 1.3e+26)
     (+ (* a 120.0) (/ -60.0 (/ (- z t) y)))
     (+ (* a 120.0) (/ x (/ (- z t) 60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.4e+35) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 1.3e+26) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	}
	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 <= (-6.4d+35)) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else if (x <= 1.3d+26) then
        tmp = (a * 120.0d0) + ((-60.0d0) / ((z - t) / y))
    else
        tmp = (a * 120.0d0) + (x / ((z - t) / 60.0d0))
    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 <= -6.4e+35) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 1.3e+26) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.4e+35:
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	elif x <= 1.3e+26:
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y))
	else:
		tmp = (a * 120.0) + (x / ((z - t) / 60.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.4e+35)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	elseif (x <= 1.3e+26)
		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) / 60.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.4e+35)
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	elseif (x <= 1.3e+26)
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	else
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.4e+35], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+26], 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] / 60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.39999999999999965e35

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 85.5%

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

      1. associate-*r/ 85.4%

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

      2. associate-*l/ 85.6%

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

      3. *-commutative 85.6%

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

   6. Simplified 85.6%

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

   if -6.39999999999999965e35 < x < 1.30000000000000001e26

   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 0 95.6%

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

      1. associate-*r/ 95.6%

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

      2. associate-/l* 95.5%

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

   6. Simplified 95.5%

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

   if 1.30000000000000001e26 < 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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-/l* 91.3%

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

   6. Simplified 91.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+26}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \end{array} \]

Alternative 11: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+37}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+16}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.8e+37)
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))
   (if (<= x 2.8e+16)
     (+ (* a 120.0) (/ (* y -60.0) (- z t)))
     (+ (* a 120.0) (/ x (/ (- z t) 60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.8e+37) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 2.8e+16) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	}
	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 <= (-4.8d+37)) then
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    else if (x <= 2.8d+16) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x / ((z - t) / 60.0d0))
    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 <= -4.8e+37) {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	} else if (x <= 2.8e+16) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.8e+37:
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	elif x <= 2.8e+16:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x / ((z - t) / 60.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.8e+37)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	elseif (x <= 2.8e+16)
		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) / 60.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.8e+37)
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	elseif (x <= 2.8e+16)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.8e+37], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+16], 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] / 60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e37

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 85.5%

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

      1. associate-*r/ 85.4%

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

      2. associate-*l/ 85.6%

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

      3. *-commutative 85.6%

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

   6. Simplified 85.6%

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

   if -4.8e37 < x < 2.8e16

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 95.6%

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

   if 2.8e16 < 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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-/l* 91.3%

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

   6. Simplified 91.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+37}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+16}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \end{array} \]

Alternative 12: 59.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-11}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-17)
   (* a 120.0)
   (if (<= a -1.65e-202)
     (* (- x y) (/ -60.0 t))
     (if (<= a 2e-11) (* 60.0 (/ (- x y) z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-17) {
		tmp = a * 120.0;
	} else if (a <= -1.65e-202) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 2e-11) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d-17)) then
        tmp = a * 120.0d0
    else if (a <= (-1.65d-202)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 2d-11) then
        tmp = 60.0d0 * ((x - y) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-17) {
		tmp = a * 120.0;
	} else if (a <= -1.65e-202) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 2e-11) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-17:
		tmp = a * 120.0
	elif a <= -1.65e-202:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 2e-11:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-17)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.65e-202)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 2e-11)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-17)
		tmp = a * 120.0;
	elseif (a <= -1.65e-202)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 2e-11)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-17], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.65e-202], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-11], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6000000000000001e-17 or 1.99999999999999988e-11 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 75.8%

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

   if -1.6000000000000001e-17 < a < -1.64999999999999995e-202

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 77.1%

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

   5. Taylor expanded in z around 0 52.4%

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

      1. associate-*r/ 52.3%

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

      2. associate-/l* 52.3%

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

   7. Simplified 52.3%

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

      1. associate-/r/ 52.5%

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

   9. Applied egg-rr 52.5%

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

   if -1.64999999999999995e-202 < a < 1.99999999999999988e-11

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 83.0%

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

   5. Taylor expanded in z around inf 54.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-11}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-203}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 10^{-11}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.08e-17)
   (* a 120.0)
   (if (<= a -2.25e-203)
     (* (- x y) (/ -60.0 t))
     (if (<= a 1e-11) (* (- x y) (/ 60.0 z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-17) {
		tmp = a * 120.0;
	} else if (a <= -2.25e-203) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1e-11) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.08d-17)) then
        tmp = a * 120.0d0
    else if (a <= (-2.25d-203)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 1d-11) then
        tmp = (x - y) * (60.0d0 / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-17) {
		tmp = a * 120.0;
	} else if (a <= -2.25e-203) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1e-11) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.08e-17:
		tmp = a * 120.0
	elif a <= -2.25e-203:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 1e-11:
		tmp = (x - y) * (60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.08e-17)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.25e-203)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 1e-11)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.08e-17)
		tmp = a * 120.0;
	elseif (a <= -2.25e-203)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 1e-11)
		tmp = (x - y) * (60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.08e-17], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.25e-203], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-11], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.07999999999999995e-17 or 9.99999999999999939e-12 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 75.8%

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

   if -1.07999999999999995e-17 < a < -2.2500000000000001e-203

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 77.1%

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

   5. Taylor expanded in z around 0 52.4%

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

      1. associate-*r/ 52.3%

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

      2. associate-/l* 52.3%

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

   7. Simplified 52.3%

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

      1. associate-/r/ 52.5%

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

   9. Applied egg-rr 52.5%

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

   if -2.2500000000000001e-203 < a < 9.99999999999999939e-12

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 83.0%

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

      1. expm1-log1p-u 54.3%

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

      2. expm1-udef 28.6%

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

   6. Applied egg-rr 28.6%

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

      1. expm1-def 54.3%

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

      2. expm1-log1p 83.0%

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

      3. associate-*r/ 82.9%

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

      4. associate-/l* 82.9%

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

      5. associate-/r/ 83.0%

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

   8. Simplified 83.0%

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

   9. Taylor expanded in z around inf 54.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-203}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 10^{-11}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+46)
   (* a 120.0)
   (if (<= a 1.5e+91) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+46) {
		tmp = a * 120.0;
	} else if (a <= 1.5e+91) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.3d+46)) then
        tmp = a * 120.0d0
    else if (a <= 1.5d+91) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+46) {
		tmp = a * 120.0;
	} else if (a <= 1.5e+91) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e+46:
		tmp = a * 120.0
	elif a <= 1.5e+91:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+46)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.5e+91)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e+46)
		tmp = a * 120.0;
	elseif (a <= 1.5e+91)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+46], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.5e+91], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.30000000000000007e46 or 1.50000000000000003e91 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 84.3%

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

   if -1.30000000000000007e46 < a < 1.50000000000000003e91

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 75.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (60.0d0 / ((z - t) / (x - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.7%

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

Alternative 16: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((x - y) / ((z - t) / 60.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around 0 99.4%

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

   1. associate-*r/ 99.4%

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

   2. metadata-eval 99.4%

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

   3. distribute-lft-neg-in 99.4%

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

   4. distribute-rgt-neg-out 99.4%

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

   5. associate-*l/ 99.4%

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

   6. +-commutative 99.4%

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

   7. associate-*r/ 99.3%

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

   8. associate-*l/ 99.4%

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

   9. distribute-lft-out 99.8%

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

   10. sub-neg 99.8%

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

   11. associate-*l/ 99.7%

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

   12. *-commutative 99.7%

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

   13. associate-/l* 99.8%

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

6. Simplified 99.8%

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

7. Final simplification 99.8%

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

Alternative 17: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 0.00055:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.35e-17)
   (* a 120.0)
   (if (<= a 0.00055) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.35e-17) {
		tmp = a * 120.0;
	} else if (a <= 0.00055) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.35d-17)) then
        tmp = a * 120.0d0
    else if (a <= 0.00055d0) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.35e-17) {
		tmp = a * 120.0;
	} else if (a <= 0.00055) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.35e-17:
		tmp = a * 120.0
	elif a <= 0.00055:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.35e-17)
		tmp = Float64(a * 120.0);
	elseif (a <= 0.00055)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.35e-17)
		tmp = a * 120.0;
	elseif (a <= 0.00055)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.35e-17], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 0.00055], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.35e-17 or 5.50000000000000033e-4 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 76.4%

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

   if -2.35e-17 < a < 5.50000000000000033e-4

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 81.0%

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

   5. Taylor expanded in x around 0 43.8%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 0.00055:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 51.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.2 \cdot 10^{+155}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.2e+155) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.2e+155) {
		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 <= 1.2d+155) 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 <= 1.2e+155) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.2e+155:
		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 <= 1.2e+155)
		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 <= 1.2e+155)
		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, 1.2e+155], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.2000000000000001e155

   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 inf 51.6%

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

   if 1.2000000000000001e155 < x

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 79.0%

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

   5. Taylor expanded in z around 0 61.2%

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

      1. associate-*r/ 61.1%

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

      2. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in x around inf 56.5%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.2 \cdot 10^{+155}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 19: 51.0% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 47.3%

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

5. Final simplification 47.3%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(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)))