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

Percentage Accurate: 99.3% → 99.8%

Time: 15.8s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-define 99.8%

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

   3. associate-*r/ 99.1%

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

   4. *-commutative 99.1%

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

   5. associate-/l* 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 77.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+292}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ x z)))))
   (if (<= z -6.5e+36)
     t_1
     (if (<= z -1.8e-6)
       (* (- x y) (/ 60.0 (- z t)))
       (if (<= z 5.2e-68)
         (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
         (if (<= z 2.0)
           (/ (* (- x y) 60.0) (- z t))
           (if (<= z 1.45e+292) (+ (* a 120.0) (* -60.0 (/ y z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (z <= -6.5e+36) {
		tmp = t_1;
	} else if (z <= -1.8e-6) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (z <= 5.2e-68) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 2.0) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else if (z <= 1.45e+292) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 * (x / z))
    if (z <= (-6.5d+36)) then
        tmp = t_1
    else if (z <= (-1.8d-6)) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if (z <= 5.2d-68) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else if (z <= 2.0d0) then
        tmp = ((x - y) * 60.0d0) / (z - t)
    else if (z <= 1.45d+292) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (z <= -6.5e+36) {
		tmp = t_1;
	} else if (z <= -1.8e-6) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (z <= 5.2e-68) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 2.0) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else if (z <= 1.45e+292) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (x / z))
	tmp = 0
	if z <= -6.5e+36:
		tmp = t_1
	elif z <= -1.8e-6:
		tmp = (x - y) * (60.0 / (z - t))
	elif z <= 5.2e-68:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	elif z <= 2.0:
		tmp = ((x - y) * 60.0) / (z - t)
	elif z <= 1.45e+292:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)))
	tmp = 0.0
	if (z <= -6.5e+36)
		tmp = t_1;
	elseif (z <= -1.8e-6)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (z <= 5.2e-68)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	elseif (z <= 2.0)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	elseif (z <= 1.45e+292)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * (x / z));
	tmp = 0.0;
	if (z <= -6.5e+36)
		tmp = t_1;
	elseif (z <= -1.8e-6)
		tmp = (x - y) * (60.0 / (z - t));
	elseif (z <= 5.2e-68)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	elseif (z <= 2.0)
		tmp = ((x - y) * 60.0) / (z - t);
	elseif (z <= 1.45e+292)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+36], t$95$1, If[LessEqual[z, -1.8e-6], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-68], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.0], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+292], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.4999999999999998e36 or 1.44999999999999995e292 < z

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.3%

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

   6. Taylor expanded in x around inf 80.9%

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

   if -6.4999999999999998e36 < z < -1.79999999999999992e-6

   1. Initial program 99.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. associate-*r/ 99.7%

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

      2. remove-double-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. times-frac 99.6%

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

      5. metadata-eval 99.6%

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

      6. distribute-neg-frac2 99.6%

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

      7. distribute-lft-in 99.6%

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

      8. +-commutative 99.6%

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

      9. sub-neg 99.6%

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

      10. div-sub 99.6%

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

      11. *-commutative 99.6%

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

      12. associate-*l/ 99.5%

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

      13. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around 0 93.4%

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

      1. associate-*r/ 93.3%

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

      2. associate-*l/ 93.6%

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

      3. *-commutative 93.6%

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

   10. Simplified 93.6%

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

   if -1.79999999999999992e-6 < z < 5.1999999999999996e-68

   1. Initial program 98.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 92.6%

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

   if 5.1999999999999996e-68 < z < 2

   1. Initial program 99.9%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. remove-double-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. times-frac 99.7%

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

      5. metadata-eval 99.7%

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

      6. distribute-neg-frac2 99.7%

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

      7. distribute-lft-in 99.7%

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

      8. +-commutative 99.7%

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

      9. sub-neg 99.7%

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

      10. div-sub 99.6%

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

      11. *-commutative 99.6%

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

      12. associate-*l/ 99.9%

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

      13. associate-*r/ 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in a around 0 73.9%

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

      1. associate-*r/ 74.2%

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

   10. Simplified 74.2%

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

   if 2 < z < 1.44999999999999995e292

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.7%

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

   6. Taylor expanded in x around 0 80.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+292}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -400000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-52}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 1.1 \cdot 10^{+189}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -400000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 4e-52)
     (* (- x y) (/ 60.0 (- z t)))
     (if (<= (* a 120.0) 1.1e+189)
       (+ (* a 120.0) (/ (* y 60.0) t))
       (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -400000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e-52) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 1.1e+189) {
		tmp = (a * 120.0) + ((y * 60.0) / 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 * 120.0d0) <= (-400000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 4d-52) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if ((a * 120.0d0) <= 1.1d+189) then
        tmp = (a * 120.0d0) + ((y * 60.0d0) / 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 * 120.0) <= -400000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e-52) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if ((a * 120.0) <= 1.1e+189) {
		tmp = (a * 120.0) + ((y * 60.0) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -400000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 4e-52:
		tmp = (x - y) * (60.0 / (z - t))
	elif (a * 120.0) <= 1.1e+189:
		tmp = (a * 120.0) + ((y * 60.0) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -400000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 4e-52)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1.1e+189)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * 60.0) / 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 * 120.0) <= -400000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 4e-52)
		tmp = (x - y) * (60.0 / (z - t));
	elseif ((a * 120.0) <= 1.1e+189)
		tmp = (a * 120.0) + ((y * 60.0) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -400000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-52], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1.1e+189], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4e8 or 1.10000000000000003e189 < (*.f64 a 120)

   1. Initial program 98.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.4%

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

   if -4e8 < (*.f64 a 120) < 4e-52

   1. Initial program 98.9%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. associate-*r/ 99.7%

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

      2. remove-double-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. times-frac 99.6%

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

      5. metadata-eval 99.6%

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

      6. distribute-neg-frac2 99.6%

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

      7. distribute-lft-in 99.6%

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

      8. +-commutative 99.6%

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

      9. sub-neg 99.6%

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

      10. div-sub 99.6%

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

      11. *-commutative 99.6%

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

      12. associate-*l/ 98.9%

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

      13. associate-*r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in a around 0 78.0%

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

      1. associate-*r/ 77.3%

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

      2. associate-*l/ 78.0%

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

      3. *-commutative 78.0%

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

   10. Simplified 78.0%

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

   if 4e-52 < (*.f64 a 120) < 1.10000000000000003e189

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in x around 0 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-*l/ 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -400000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-52}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 1.1 \cdot 10^{+189}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ (- x y) z)))))
   (if (<= z -2.4e+46)
     t_1
     (if (<= z -1.6e-6)
       (* (- x y) (/ 60.0 (- z t)))
       (if (<= z 3.9e-29) (+ (* a 120.0) (* -60.0 (/ (- x y) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -2.4e+46) {
		tmp = t_1;
	} else if (z <= -1.6e-6) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (z <= 3.9e-29) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    if (z <= (-2.4d+46)) then
        tmp = t_1
    else if (z <= (-1.6d-6)) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if (z <= 3.9d-29) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -2.4e+46) {
		tmp = t_1;
	} else if (z <= -1.6e-6) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (z <= 3.9e-29) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z))
	tmp = 0
	if z <= -2.4e+46:
		tmp = t_1
	elif z <= -1.6e-6:
		tmp = (x - y) * (60.0 / (z - t))
	elif z <= 3.9e-29:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)))
	tmp = 0.0
	if (z <= -2.4e+46)
		tmp = t_1;
	elseif (z <= -1.6e-6)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (z <= 3.9e-29)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	tmp = 0.0;
	if (z <= -2.4e+46)
		tmp = t_1;
	elseif (z <= -1.6e-6)
		tmp = (x - y) * (60.0 / (z - t));
	elseif (z <= 3.9e-29)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+46], t$95$1, If[LessEqual[z, -1.6e-6], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-29], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000008e46 or 3.8999999999999998e-29 < z

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.7%

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

   if -2.40000000000000008e46 < z < -1.5999999999999999e-6

   1. Initial program 99.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 99.6%

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

      2. remove-double-neg 99.6%

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

      3. neg-mul-1 99.6%

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

      4. times-frac 99.5%

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

      5. metadata-eval 99.5%

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

      6. distribute-neg-frac2 99.5%

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

      7. distribute-lft-in 99.5%

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

      8. +-commutative 99.5%

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

      9. sub-neg 99.5%

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

      10. div-sub 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-*l/ 99.4%

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

      13. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around 0 88.3%

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

      1. associate-*r/ 88.2%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

   10. Simplified 88.6%

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

   if -1.5999999999999999e-6 < z < 3.8999999999999998e-29

   1. Initial program 98.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 91.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ (- x y) z)))))
   (if (<= z -3.6e+48)
     t_1
     (if (<= z -2.1e-6)
       (* (- x y) (/ 60.0 (- z t)))
       (if (<= z 9.2e-26) (+ (* a 120.0) (* (- x y) (/ -60.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -3.6e+48) {
		tmp = t_1;
	} else if (z <= -2.1e-6) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (z <= 9.2e-26) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    if (z <= (-3.6d+48)) then
        tmp = t_1
    else if (z <= (-2.1d-6)) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if (z <= 9.2d-26) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -3.6e+48) {
		tmp = t_1;
	} else if (z <= -2.1e-6) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (z <= 9.2e-26) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z))
	tmp = 0
	if z <= -3.6e+48:
		tmp = t_1
	elif z <= -2.1e-6:
		tmp = (x - y) * (60.0 / (z - t))
	elif z <= 9.2e-26:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)))
	tmp = 0.0
	if (z <= -3.6e+48)
		tmp = t_1;
	elseif (z <= -2.1e-6)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (z <= 9.2e-26)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	tmp = 0.0;
	if (z <= -3.6e+48)
		tmp = t_1;
	elseif (z <= -2.1e-6)
		tmp = (x - y) * (60.0 / (z - t));
	elseif (z <= 9.2e-26)
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+48], t$95$1, If[LessEqual[z, -2.1e-6], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-26], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999983e48 or 9.20000000000000035e-26 < z

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.7%

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

   if -3.59999999999999983e48 < z < -2.0999999999999998e-6

   1. Initial program 99.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 99.6%

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

      2. remove-double-neg 99.6%

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

      3. neg-mul-1 99.6%

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

      4. times-frac 99.5%

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

      5. metadata-eval 99.5%

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

      6. distribute-neg-frac2 99.5%

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

      7. distribute-lft-in 99.5%

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

      8. +-commutative 99.5%

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

      9. sub-neg 99.5%

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

      10. div-sub 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-*l/ 99.4%

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

      13. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around 0 88.3%

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

      1. associate-*r/ 88.2%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

   10. Simplified 88.6%

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

   if -2.0999999999999998e-6 < z < 9.20000000000000035e-26

   1. Initial program 98.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 91.0%

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

      1. associate-*r/ 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-/l* 91.0%

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

   7. Simplified 91.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+48}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -400000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-65}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -400000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-65)
     (* (- x y) (/ 60.0 (- z t)))
     (+ (* a 120.0) (* -60.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -400000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-65) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-400000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-65) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -400000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-65) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -400000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-65:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -400000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-65)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -400000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-65)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = (a * 120.0) + (-60.0 * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -400000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-65], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4e8

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.7%

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

   if -4e8 < (*.f64 a 120) < 9.99999999999999923e-66

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. associate-*r/ 99.7%

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

      2. remove-double-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. times-frac 99.6%

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

      5. metadata-eval 99.6%

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

      6. distribute-neg-frac2 99.6%

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

      7. distribute-lft-in 99.6%

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

      8. +-commutative 99.6%

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

      9. sub-neg 99.6%

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

      10. div-sub 99.6%

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

      11. *-commutative 99.6%

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

      12. associate-*l/ 99.7%

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

      13. associate-*r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around 0 77.6%

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

      1. associate-*r/ 77.7%

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

      2. associate-*l/ 77.7%

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

      3. *-commutative 77.7%

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

   10. Simplified 77.7%

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

   if 9.99999999999999923e-66 < (*.f64 a 120)

   1. Initial program 97.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 89.8%

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

      1. associate-*r/ 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in z around 0 77.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -400000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-65}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+69} \lor \neg \left(x \leq 1.3 \cdot 10^{+36}\right):\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.8e+69) (not (<= x 1.3e+36)))
   (+ (* a 120.0) (/ (* x 60.0) (- z t)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.8e+69) || !(x <= 1.3e+36)) {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.8d+69)) .or. (.not. (x <= 1.3d+36))) then
        tmp = (a * 120.0d0) + ((x * 60.0d0) / (z - t))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.8e+69) || !(x <= 1.3e+36)) {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.8e+69) or not (x <= 1.3e+36):
		tmp = (a * 120.0) + ((x * 60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.8e+69) || !(x <= 1.3e+36))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * 60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.8e+69) || ~((x <= 1.3e+36)))
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.8e+69], N[Not[LessEqual[x, 1.3e+36]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000003e69 or 1.3000000000000001e36 < x

   1. Initial program 98.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 89.5%

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

      1. associate-*r/ 87.8%

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

   7. Simplified 87.8%

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

   if -4.8000000000000003e69 < x < 1.3000000000000001e36

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.6%

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

      1. associate-*r/ 93.6%

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

   7. Simplified 93.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+69} \lor \neg \left(x \leq 1.3 \cdot 10^{+36}\right):\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -860000 \lor \neg \left(a \leq 6.2 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -860000.0) (not (<= a 6.2e-51)))
   (* a 120.0)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -860000.0) || !(a <= 6.2e-51)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-860000.0d0)) .or. (.not. (a <= 6.2d-51))) then
        tmp = a * 120.0d0
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -860000.0) || !(a <= 6.2e-51)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -860000.0) or not (a <= 6.2e-51):
		tmp = a * 120.0
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -860000.0) || !(a <= 6.2e-51))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -860000.0) || ~((a <= 6.2e-51)))
		tmp = a * 120.0;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -860000.0], N[Not[LessEqual[a, 6.2e-51]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.6e5 or 6.1999999999999995e-51 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.1%

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

   if -8.6e5 < a < 6.1999999999999995e-51

   1. Initial program 98.9%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. associate-*r/ 99.7%

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

      2. remove-double-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. times-frac 99.6%

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

      5. metadata-eval 99.6%

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

      6. distribute-neg-frac2 99.6%

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

      7. distribute-lft-in 99.6%

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

      8. +-commutative 99.6%

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

      9. sub-neg 99.6%

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

      10. div-sub 99.6%

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

      11. *-commutative 99.6%

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

      12. associate-*l/ 98.9%

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

      13. associate-*r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in a around 0 78.0%

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

      1. associate-*r/ 77.3%

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

      2. associate-*l/ 78.0%

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

      3. *-commutative 78.0%

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

   10. Simplified 78.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -860000 \lor \neg \left(a \leq 6.2 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-127} \lor \neg \left(a \leq 9.6 \cdot 10^{-164}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e-127) (not (<= a 9.6e-164)))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e-127) || !(a <= 9.6e-164)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.35d-127)) .or. (.not. (a <= 9.6d-164))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e-127) || !(a <= 9.6e-164)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.35e-127) or not (a <= 9.6e-164):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.35e-127) || !(a <= 9.6e-164))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.35e-127) || ~((a <= 9.6e-164)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.35e-127], N[Not[LessEqual[a, 9.6e-164]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35e-127 or 9.59999999999999932e-164 < a

   1. Initial program 98.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 67.2%

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

   if -1.35e-127 < a < 9.59999999999999932e-164

   1. Initial program 99.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 99.7%

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

      2. remove-double-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. times-frac 99.5%

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

      5. metadata-eval 99.5%

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

      6. distribute-neg-frac2 99.5%

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

      7. distribute-lft-in 99.5%

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

      8. +-commutative 99.5%

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

      9. sub-neg 99.5%

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

      10. div-sub 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-*l/ 99.7%

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

      13. associate-*r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 44.1%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-127} \lor \neg \left(a \leq 9.6 \cdot 10^{-164}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-113} \lor \neg \left(a \leq 1.45 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.75e-113) (not (<= a 1.45e-52)))
   (* a 120.0)
   (* 60.0 (/ x (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e-113) || !(a <= 1.45e-52)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.75d-113)) .or. (.not. (a <= 1.45d-52))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (x / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e-113) || !(a <= 1.45e-52)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.75e-113) or not (a <= 1.45e-52):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.75e-113) || !(a <= 1.45e-52))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.75e-113) || ~((a <= 1.45e-52)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.75e-113], N[Not[LessEqual[a, 1.45e-52]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.75000000000000014e-113 or 1.4500000000000001e-52 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -1.75000000000000014e-113 < a < 1.4500000000000001e-52

   1. Initial program 98.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 99.7%

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

      2. remove-double-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. times-frac 99.5%

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

      5. metadata-eval 99.5%

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

      6. distribute-neg-frac2 99.5%

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

      7. distribute-lft-in 99.5%

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

      8. +-commutative 99.5%

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

      9. sub-neg 99.5%

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

      10. div-sub 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-*l/ 98.7%

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

      13. associate-*r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 51.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-113} \lor \neg \left(a \leq 1.45 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+162}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.2e+162)
   (* 60.0 (/ x z))
   (if (<= x 5.2e+207) (* a 120.0) (* -60.0 (/ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.2e+162) {
		tmp = 60.0 * (x / z);
	} else if (x <= 5.2e+207) {
		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 <= (-6.2d+162)) then
        tmp = 60.0d0 * (x / z)
    else if (x <= 5.2d+207) 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 <= -6.2e+162) {
		tmp = 60.0 * (x / z);
	} else if (x <= 5.2e+207) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.2e+162:
		tmp = 60.0 * (x / z)
	elif x <= 5.2e+207:
		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 <= -6.2e+162)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (x <= 5.2e+207)
		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 <= -6.2e+162)
		tmp = 60.0 * (x / z);
	elseif (x <= 5.2e+207)
		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, -6.2e+162], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+207], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999999e162

   1. Initial program 97.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 58.2%

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

   6. Taylor expanded in x around inf 45.7%

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

   if -6.1999999999999999e162 < x < 5.1999999999999996e207

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 63.2%

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

   if 5.1999999999999996e207 < x

   1. Initial program 95.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 92.5%

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

      1. associate-*r/ 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 71.5%

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

   9. Taylor expanded in x around inf 61.8%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+162}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * ((x - y) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) * (60.0 / (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 = ((x - y) * (60.0d0 / (z - t))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 99.8%

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

   1. associate-*r/ 99.8%

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

   2. remove-double-neg 99.8%

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

   3. neg-mul-1 99.8%

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

   4. times-frac 99.8%

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

   5. metadata-eval 99.8%

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

   6. distribute-neg-frac2 99.8%

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

   7. distribute-lft-in 99.8%

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

   8. +-commutative 99.8%

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

   9. sub-neg 99.8%

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

   10. div-sub 99.8%

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

   11. *-commutative 99.8%

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

   12. associate-*l/ 99.1%

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

   13. associate-*r/ 99.8%

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

7. Simplified 99.8%

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

8. Final simplification 99.8%

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

Alternative 14: 51.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{+207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.02e+207) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.02e+207) {
		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 <= 1.02d+207) 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 <= 1.02e+207) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.02e+207:
		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 <= 1.02e+207)
		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 <= 1.02e+207)
		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, 1.02e+207], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.0200000000000001e207

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 57.2%

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

   if 1.0200000000000001e207 < x

   1. Initial program 95.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 92.5%

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

      1. associate-*r/ 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 71.5%

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

   9. Taylor expanded in x around inf 61.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{+207}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.3% 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 99.1%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 54.0%

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

6. Final simplification 54.0%

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

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 2024044 
(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)))