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

Percentage Accurate: 99.4% → 99.8%

Time: 14.1s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 2: 55.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-234}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))) (t_2 (* 60.0 (/ x (- z t)))))
   (if (<= x -7.2e+150)
     t_2
     (if (<= x 4.3e-234)
       (* a 120.0)
       (if (<= x 2.75e-157)
         t_1
         (if (<= x 2.1e-112)
           (* a 120.0)
           (if (<= x 1.25e-91) t_1 (if (<= x 1.85e+93) (* a 120.0) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = 60.0 * (x / (z - t));
	double tmp;
	if (x <= -7.2e+150) {
		tmp = t_2;
	} else if (x <= 4.3e-234) {
		tmp = a * 120.0;
	} else if (x <= 2.75e-157) {
		tmp = t_1;
	} else if (x <= 2.1e-112) {
		tmp = a * 120.0;
	} else if (x <= 1.25e-91) {
		tmp = t_1;
	} else if (x <= 1.85e+93) {
		tmp = a * 120.0;
	} else {
		tmp = t_2;
	}
	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) * (y / (z - t))
    t_2 = 60.0d0 * (x / (z - t))
    if (x <= (-7.2d+150)) then
        tmp = t_2
    else if (x <= 4.3d-234) then
        tmp = a * 120.0d0
    else if (x <= 2.75d-157) then
        tmp = t_1
    else if (x <= 2.1d-112) then
        tmp = a * 120.0d0
    else if (x <= 1.25d-91) then
        tmp = t_1
    else if (x <= 1.85d+93) then
        tmp = a * 120.0d0
    else
        tmp = t_2
    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 * (y / (z - t));
	double t_2 = 60.0 * (x / (z - t));
	double tmp;
	if (x <= -7.2e+150) {
		tmp = t_2;
	} else if (x <= 4.3e-234) {
		tmp = a * 120.0;
	} else if (x <= 2.75e-157) {
		tmp = t_1;
	} else if (x <= 2.1e-112) {
		tmp = a * 120.0;
	} else if (x <= 1.25e-91) {
		tmp = t_1;
	} else if (x <= 1.85e+93) {
		tmp = a * 120.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	t_2 = 60.0 * (x / (z - t))
	tmp = 0
	if x <= -7.2e+150:
		tmp = t_2
	elif x <= 4.3e-234:
		tmp = a * 120.0
	elif x <= 2.75e-157:
		tmp = t_1
	elif x <= 2.1e-112:
		tmp = a * 120.0
	elif x <= 1.25e-91:
		tmp = t_1
	elif x <= 1.85e+93:
		tmp = a * 120.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	t_2 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (x <= -7.2e+150)
		tmp = t_2;
	elseif (x <= 4.3e-234)
		tmp = Float64(a * 120.0);
	elseif (x <= 2.75e-157)
		tmp = t_1;
	elseif (x <= 2.1e-112)
		tmp = Float64(a * 120.0);
	elseif (x <= 1.25e-91)
		tmp = t_1;
	elseif (x <= 1.85e+93)
		tmp = Float64(a * 120.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	t_2 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if (x <= -7.2e+150)
		tmp = t_2;
	elseif (x <= 4.3e-234)
		tmp = a * 120.0;
	elseif (x <= 2.75e-157)
		tmp = t_1;
	elseif (x <= 2.1e-112)
		tmp = a * 120.0;
	elseif (x <= 1.25e-91)
		tmp = t_1;
	elseif (x <= 1.85e+93)
		tmp = a * 120.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e+150], t$95$2, If[LessEqual[x, 4.3e-234], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 2.75e-157], t$95$1, If[LessEqual[x, 2.1e-112], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 1.25e-91], t$95$1, If[LessEqual[x, 1.85e+93], N[(a * 120.0), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999972e150 or 1.84999999999999994e93 < 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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 82.1%

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

   5. Taylor expanded in x around inf 73.5%

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

   if -7.19999999999999972e150 < x < 4.3000000000000001e-234 or 2.7499999999999999e-157 < x < 2.1000000000000001e-112 or 1.24999999999999999e-91 < x < 1.84999999999999994e93

   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 61.7%

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

   if 4.3000000000000001e-234 < x < 2.7499999999999999e-157 or 2.1000000000000001e-112 < x < 1.24999999999999999e-91

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. associate-*r/ 99.9%

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

      7. associate-*r/ 99.9%

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

      8. associate-*l/ 99.9%

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

      9. *-commutative 99.9%

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

      10. +-commutative 99.9%

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

      11. distribute-rgt-out 99.9%

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

      12. sub-neg 99.9%

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

      13. associate-*l/ 99.9%

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

      14. /-rgt-identity 99.9%

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

      15. *-commutative 99.9%

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

      16. associate-/l* 99.9%

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

      17. metadata-eval 99.9%

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

      18. associate-/r* 99.6%

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

      19. *-commutative 99.6%

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

   6. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.6%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

      2. times-frac 99.8%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in a around 0 70.1%

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

       1. associate-*r/ 70.0%

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

       2. associate-/l* 69.9%

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

   11. Simplified 69.9%

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

   12. Taylor expanded in x around 0 70.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+150}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-234}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-157}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-91}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]

Alternative 3: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+80} \lor \neg \left(z - t \leq 5 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -1e+80) (not (<= (- z t) 5e+18)))
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (/ (- x y) (* (- z t) 0.016666666666666666))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -1e+80) || !((z - t) <= 5e+18)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - t) <= (-1d+80)) .or. (.not. ((z - t) <= 5d+18))) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else
        tmp = (x - y) / ((z - t) * 0.016666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -1e+80) || !((z - t) <= 5e+18)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -1e+80) or not ((z - t) <= 5e+18):
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = (x - y) / ((z - t) * 0.016666666666666666)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -1e+80) || !(Float64(z - t) <= 5e+18))
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) <= -1e+80) || ~(((z - t) <= 5e+18)))
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	else
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -1e+80], N[Not[LessEqual[N[(z - t), $MachinePrecision], 5e+18]], $MachinePrecision]], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -1e80 or 5e18 < (-.f64 z t)

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 81.2%

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

      1. associate-*r/ 81.2%

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

      2. associate-*l/ 81.2%

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

      3. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   if -1e80 < (-.f64 z t) < 5e18

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.7%

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

      1. *-commutative 97.7%

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

      2. associate-*l/ 97.6%

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

      3. metadata-eval 97.6%

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

      4. distribute-rgt-neg-in 97.6%

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

      5. distribute-lft-neg-out 97.6%

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

      6. associate-*r/ 97.6%

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

      7. associate-*r/ 97.7%

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

      8. associate-*l/ 97.6%

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

      9. *-commutative 97.6%

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

      10. +-commutative 97.6%

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

      11. distribute-rgt-out 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*l/ 99.8%

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

      14. /-rgt-identity 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.8%

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

      17. metadata-eval 99.8%

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

      18. associate-/r* 99.8%

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

      19. *-commutative 99.8%

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

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.8%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in a around 0 81.8%

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

       1. associate-*r/ 81.7%

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

       2. associate-/l* 81.8%

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

   11. Simplified 81.8%

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

   12. Taylor expanded in x around 0 79.6%

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

       1. *-commutative 97.7%

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

       2. associate-*l/ 97.6%

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

       3. metadata-eval 97.6%

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

       4. distribute-rgt-neg-in 97.6%

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

       5. distribute-lft-neg-out 97.6%

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

       6. associate-*r/ 97.6%

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

       7. associate-*r/ 97.7%

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

       8. associate-*l/ 97.6%

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

       9. *-commutative 97.6%

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

       10. +-commutative 97.6%

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

       11. distribute-rgt-out 99.8%

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

       12. sub-neg 99.8%

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

       13. associate-*l/ 99.8%

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

       14. /-rgt-identity 99.8%

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

       15. *-commutative 99.8%

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

       16. associate-/l* 99.8%

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

       17. metadata-eval 99.8%

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

       18. associate-/r* 99.8%

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

       19. *-commutative 99.8%

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

   14. Simplified 81.8%

       \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+80} \lor \neg \left(z - t \leq 5 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \]

Alternative 4: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6900000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-66}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-119}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+70}:\\ \;\;\;\;\frac{60}{\frac{-t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6900000000.0)
   (* a 120.0)
   (if (<= t -1.45e-66)
     (/ (* 60.0 x) (- z t))
     (if (<= t -4.5e-127)
       (* a 120.0)
       (if (<= t 5.8e-119)
         (* 60.0 (/ (- x y) z))
         (if (<= t 7e+70) (/ 60.0 (/ (- t) (- x y))) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6900000000.0) {
		tmp = a * 120.0;
	} else if (t <= -1.45e-66) {
		tmp = (60.0 * x) / (z - t);
	} else if (t <= -4.5e-127) {
		tmp = a * 120.0;
	} else if (t <= 5.8e-119) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 7e+70) {
		tmp = 60.0 / (-t / (x - y));
	} 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 (t <= (-6900000000.0d0)) then
        tmp = a * 120.0d0
    else if (t <= (-1.45d-66)) then
        tmp = (60.0d0 * x) / (z - t)
    else if (t <= (-4.5d-127)) then
        tmp = a * 120.0d0
    else if (t <= 5.8d-119) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (t <= 7d+70) then
        tmp = 60.0d0 / (-t / (x - y))
    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 (t <= -6900000000.0) {
		tmp = a * 120.0;
	} else if (t <= -1.45e-66) {
		tmp = (60.0 * x) / (z - t);
	} else if (t <= -4.5e-127) {
		tmp = a * 120.0;
	} else if (t <= 5.8e-119) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 7e+70) {
		tmp = 60.0 / (-t / (x - y));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6900000000.0:
		tmp = a * 120.0
	elif t <= -1.45e-66:
		tmp = (60.0 * x) / (z - t)
	elif t <= -4.5e-127:
		tmp = a * 120.0
	elif t <= 5.8e-119:
		tmp = 60.0 * ((x - y) / z)
	elif t <= 7e+70:
		tmp = 60.0 / (-t / (x - y))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6900000000.0)
		tmp = Float64(a * 120.0);
	elseif (t <= -1.45e-66)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (t <= -4.5e-127)
		tmp = Float64(a * 120.0);
	elseif (t <= 5.8e-119)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (t <= 7e+70)
		tmp = Float64(60.0 / Float64(Float64(-t) / Float64(x - y)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6900000000.0)
		tmp = a * 120.0;
	elseif (t <= -1.45e-66)
		tmp = (60.0 * x) / (z - t);
	elseif (t <= -4.5e-127)
		tmp = a * 120.0;
	elseif (t <= 5.8e-119)
		tmp = 60.0 * ((x - y) / z);
	elseif (t <= 7e+70)
		tmp = 60.0 / (-t / (x - y));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6900000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, -1.45e-66], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e-127], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, 5.8e-119], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+70], N[(60.0 / N[((-t) / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.9e9 or -1.45000000000000006e-66 < t < -4.4999999999999999e-127 or 7.00000000000000005e70 < t

   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 67.8%

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

   if -6.9e9 < t < -1.45000000000000006e-66

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 83.9%

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

   5. Taylor expanded in x around inf 59.7%

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

      1. associate-*r/ 59.8%

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

   7. Applied egg-rr 59.8%

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

   if -4.4999999999999999e-127 < t < 5.8e-119

   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 78.3%

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

   5. Taylor expanded in z around inf 70.1%

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

   if 5.8e-119 < t < 7.00000000000000005e70

   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 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. associate-*r/ 99.8%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*l/ 99.7%

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

      14. /-rgt-identity 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.8%

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

      17. metadata-eval 99.8%

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

      18. associate-/r* 99.9%

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

      19. *-commutative 99.9%

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

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.9%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in a around 0 64.6%

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

       1. associate-*r/ 64.5%

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

       2. associate-/l* 64.6%

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

   11. Simplified 64.6%

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

   12. Taylor expanded in z around 0 50.7%

       \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{t}{x - y}}} \]
   13. Step-by-step derivation

       1. neg-mul-1 50.7%

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

       2. distribute-neg-frac 50.7%

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

   14. Simplified 50.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6900000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-66}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-119}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+70}:\\ \;\;\;\;\frac{60}{\frac{-t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 52.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))))
   (if (<= t -1.8e-26)
     (* a 120.0)
     (if (<= t -4.1e-75)
       t_1
       (if (<= t -6.3e-127)
         (* a 120.0)
         (if (<= t 9e-119)
           t_1
           (if (<= t 9.5e+70) (* -60.0 (/ (- x y) t)) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (t <= -1.8e-26) {
		tmp = a * 120.0;
	} else if (t <= -4.1e-75) {
		tmp = t_1;
	} else if (t <= -6.3e-127) {
		tmp = a * 120.0;
	} else if (t <= 9e-119) {
		tmp = t_1;
	} else if (t <= 9.5e+70) {
		tmp = -60.0 * ((x - y) / 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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    if (t <= (-1.8d-26)) then
        tmp = a * 120.0d0
    else if (t <= (-4.1d-75)) then
        tmp = t_1
    else if (t <= (-6.3d-127)) then
        tmp = a * 120.0d0
    else if (t <= 9d-119) then
        tmp = t_1
    else if (t <= 9.5d+70) then
        tmp = (-60.0d0) * ((x - y) / 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 t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (t <= -1.8e-26) {
		tmp = a * 120.0;
	} else if (t <= -4.1e-75) {
		tmp = t_1;
	} else if (t <= -6.3e-127) {
		tmp = a * 120.0;
	} else if (t <= 9e-119) {
		tmp = t_1;
	} else if (t <= 9.5e+70) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	tmp = 0
	if t <= -1.8e-26:
		tmp = a * 120.0
	elif t <= -4.1e-75:
		tmp = t_1
	elif t <= -6.3e-127:
		tmp = a * 120.0
	elif t <= 9e-119:
		tmp = t_1
	elif t <= 9.5e+70:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (t <= -1.8e-26)
		tmp = Float64(a * 120.0);
	elseif (t <= -4.1e-75)
		tmp = t_1;
	elseif (t <= -6.3e-127)
		tmp = Float64(a * 120.0);
	elseif (t <= 9e-119)
		tmp = t_1;
	elseif (t <= 9.5e+70)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (t <= -1.8e-26)
		tmp = a * 120.0;
	elseif (t <= -4.1e-75)
		tmp = t_1;
	elseif (t <= -6.3e-127)
		tmp = a * 120.0;
	elseif (t <= 9e-119)
		tmp = t_1;
	elseif (t <= 9.5e+70)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e-26], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, -4.1e-75], t$95$1, If[LessEqual[t, -6.3e-127], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, 9e-119], t$95$1, If[LessEqual[t, 9.5e+70], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8000000000000001e-26 or -4.10000000000000002e-75 < t < -6.2999999999999999e-127 or 9.5000000000000002e70 < t

   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 67.5%

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

   if -1.8000000000000001e-26 < t < -4.10000000000000002e-75 or -6.2999999999999999e-127 < t < 9.0000000000000005e-119

   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 79.8%

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

   5. Taylor expanded in z around inf 69.1%

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

   if 9.0000000000000005e-119 < t < 9.5000000000000002e70

   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 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. associate-*r/ 99.8%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*l/ 99.7%

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

      14. /-rgt-identity 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.8%

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

      17. metadata-eval 99.8%

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

      18. associate-/r* 99.9%

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

      19. *-commutative 99.9%

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

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.9%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in a around 0 64.6%

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

       1. associate-*r/ 64.5%

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

       2. associate-/l* 64.6%

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

   11. Simplified 64.6%

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

   12. Taylor expanded in z around 0 50.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-75}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-119}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7200000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-68}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-119}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+71}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7200000.0)
   (* a 120.0)
   (if (<= t -1.25e-68)
     (/ (* 60.0 x) (- z t))
     (if (<= t -1.7e-128)
       (* a 120.0)
       (if (<= t 9.6e-119)
         (* 60.0 (/ (- x y) z))
         (if (<= t 1.06e+71) (* -60.0 (/ (- x y) t)) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7200000.0) {
		tmp = a * 120.0;
	} else if (t <= -1.25e-68) {
		tmp = (60.0 * x) / (z - t);
	} else if (t <= -1.7e-128) {
		tmp = a * 120.0;
	} else if (t <= 9.6e-119) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 1.06e+71) {
		tmp = -60.0 * ((x - y) / 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 (t <= (-7200000.0d0)) then
        tmp = a * 120.0d0
    else if (t <= (-1.25d-68)) then
        tmp = (60.0d0 * x) / (z - t)
    else if (t <= (-1.7d-128)) then
        tmp = a * 120.0d0
    else if (t <= 9.6d-119) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (t <= 1.06d+71) then
        tmp = (-60.0d0) * ((x - y) / 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 (t <= -7200000.0) {
		tmp = a * 120.0;
	} else if (t <= -1.25e-68) {
		tmp = (60.0 * x) / (z - t);
	} else if (t <= -1.7e-128) {
		tmp = a * 120.0;
	} else if (t <= 9.6e-119) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 1.06e+71) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7200000.0:
		tmp = a * 120.0
	elif t <= -1.25e-68:
		tmp = (60.0 * x) / (z - t)
	elif t <= -1.7e-128:
		tmp = a * 120.0
	elif t <= 9.6e-119:
		tmp = 60.0 * ((x - y) / z)
	elif t <= 1.06e+71:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7200000.0)
		tmp = Float64(a * 120.0);
	elseif (t <= -1.25e-68)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (t <= -1.7e-128)
		tmp = Float64(a * 120.0);
	elseif (t <= 9.6e-119)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (t <= 1.06e+71)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 (t <= -7200000.0)
		tmp = a * 120.0;
	elseif (t <= -1.25e-68)
		tmp = (60.0 * x) / (z - t);
	elseif (t <= -1.7e-128)
		tmp = a * 120.0;
	elseif (t <= 9.6e-119)
		tmp = 60.0 * ((x - y) / z);
	elseif (t <= 1.06e+71)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7200000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, -1.25e-68], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-128], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, 9.6e-119], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+71], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2e6 or -1.24999999999999993e-68 < t < -1.69999999999999987e-128 or 1.06e71 < t

   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 67.8%

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

   if -7.2e6 < t < -1.24999999999999993e-68

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 83.9%

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

   5. Taylor expanded in x around inf 59.7%

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

      1. associate-*r/ 59.8%

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

   7. Applied egg-rr 59.8%

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

   if -1.69999999999999987e-128 < t < 9.60000000000000034e-119

   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 78.3%

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

   5. Taylor expanded in z around inf 70.1%

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

   if 9.60000000000000034e-119 < t < 1.06e71

   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 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. associate-*r/ 99.8%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*l/ 99.7%

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

      14. /-rgt-identity 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.8%

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

      17. metadata-eval 99.8%

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

      18. associate-/r* 99.9%

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

      19. *-commutative 99.9%

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

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.9%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in a around 0 64.6%

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

       1. associate-*r/ 64.5%

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

       2. associate-/l* 64.6%

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

   11. Simplified 64.6%

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

   12. Taylor expanded in z around 0 50.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7200000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-68}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-119}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+71}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+86}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+86)
   (+ (* a 120.0) (* 60.0 (/ x z)))
   (if (<= (* a 120.0) 1e-30)
     (* 60.0 (/ (- x y) (- 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) <= -5e+86) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 1e-30) {
		tmp = 60.0 * ((x - y) / (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) <= (-5d+86)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if ((a * 120.0d0) <= 1d-30) then
        tmp = 60.0d0 * ((x - y) / (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) <= -5e+86) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 1e-30) {
		tmp = 60.0 * ((x - y) / (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) <= -5e+86:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif (a * 120.0) <= 1e-30:
		tmp = 60.0 * ((x - y) / (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) <= -5e+86)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (Float64(a * 120.0) <= 1e-30)
		tmp = Float64(60.0 * Float64(Float64(x - y) / 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) <= -5e+86)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif ((a * 120.0) <= 1e-30)
		tmp = 60.0 * ((x - y) / (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], -5e+86], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-30], N[(60.0 * N[(N[(x - y), $MachinePrecision] / 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) < -4.9999999999999998e86

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.2%

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

      1. fma-def 96.2%

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

      2. associate-*r/ 96.2%

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

      3. associate-*l/ 96.2%

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

      4. *-commutative 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in z around inf 87.8%

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

   if -4.9999999999999998e86 < (*.f64 a 120) < 1e-30

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 78.2%

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

   if 1e-30 < (*.f64 a 120)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 83.2%

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

      1. fma-def 83.2%

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

      2. associate-*r/ 83.2%

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

      3. associate-*l/ 83.2%

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

      4. *-commutative 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in z around 0 75.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+86}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 8: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+86}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+86)
   (+ (* a 120.0) (* 60.0 (/ x z)))
   (if (<= (* a 120.0) 1e-30)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (/ x (* t -0.016666666666666666))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+86) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 1e-30) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d+86)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if ((a * 120.0d0) <= 1d-30) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (x / (t * (-0.016666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+86) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 1e-30) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+86:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif (a * 120.0) <= 1e-30:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+86)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (Float64(a * 120.0) <= 1e-30)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(t * -0.016666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e+86)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif ((a * 120.0) <= 1e-30)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+86], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-30], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4.9999999999999998e86

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.2%

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

      1. fma-def 96.2%

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

      2. associate-*r/ 96.2%

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

      3. associate-*l/ 96.2%

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

      4. *-commutative 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in z around inf 87.8%

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

   if -4.9999999999999998e86 < (*.f64 a 120) < 1e-30

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 78.2%

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

   if 1e-30 < (*.f64 a 120)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 83.2%

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

      1. associate-*r/ 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-/l* 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

   9. Simplified 75.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+86}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \end{array} \]

Alternative 9: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+69} \lor \neg \left(x \leq 1.4 \cdot 10^{+62}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2e+69) (not (<= x 1.4e+62)))
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2e+69) || !(x <= 1.4e+62)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2d+69)) .or. (.not. (x <= 1.4d+62))) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2e+69) || !(x <= 1.4e+62)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2e+69) or not (x <= 1.4e+62):
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2e+69) || !(x <= 1.4e+62))
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2e+69) || ~((x <= 1.4e+62)))
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	else
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2e+69], N[Not[LessEqual[x, 1.4e+62]], $MachinePrecision]], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e69 or 1.40000000000000007e62 < 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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. associate-*l/ 87.8%

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

      3. *-commutative 87.8%

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

   6. Simplified 87.8%

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

   if -2.0000000000000001e69 < x < 1.40000000000000007e62

   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 x around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. associate-/l* 96.8%

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

   6. Simplified 96.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+69} \lor \neg \left(x \leq 1.4 \cdot 10^{+62}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \]

Alternative 10: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+68} \lor \neg \left(x \leq 2.2 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.4e+68) (not (<= x 2.2e+62)))
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.4e+68) || !(x <= 2.2e+62)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.4d+68)) .or. (.not. (x <= 2.2d+62))) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.4e+68) || !(x <= 2.2e+62)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.4e+68) or not (x <= 2.2e+62):
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	else:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.4e+68) || !(x <= 2.2e+62))
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.4e+68) || ~((x <= 2.2e+62)))
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	else
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.4e+68], N[Not[LessEqual[x, 2.2e+62]], $MachinePrecision]], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.39999999999999974e68 or 2.20000000000000015e62 < 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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. *-commutative 87.8%

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

      3. associate-/l* 87.9%

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

   6. Simplified 87.9%

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

   if -4.39999999999999974e68 < x < 2.20000000000000015e62

   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 x around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. associate-/l* 96.8%

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

   6. Simplified 96.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+68} \lor \neg \left(x \leq 2.2 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \]

Alternative 11: 55.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 10^{-29}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -1e+80)
   (* a 120.0)
   (if (<= (- z t) 1e-29) (* -60.0 (/ (- x y) t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -1e+80) {
		tmp = a * 120.0;
	} else if ((z - t) <= 1e-29) {
		tmp = -60.0 * ((x - y) / 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 ((z - t) <= (-1d+80)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 1d-29) then
        tmp = (-60.0d0) * ((x - y) / 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 ((z - t) <= -1e+80) {
		tmp = a * 120.0;
	} else if ((z - t) <= 1e-29) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -1e+80:
		tmp = a * 120.0
	elif (z - t) <= 1e-29:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -1e+80)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 1e-29)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 ((z - t) <= -1e+80)
		tmp = a * 120.0;
	elseif ((z - t) <= 1e-29)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -1e+80], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 1e-29], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -1e80 or 9.99999999999999943e-30 < (-.f64 z t)

   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 60.5%

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

   if -1e80 < (-.f64 z t) < 9.99999999999999943e-30

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.5%

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

      1. *-commutative 97.5%

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

      2. associate-*l/ 97.4%

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

      3. metadata-eval 97.4%

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

      4. distribute-rgt-neg-in 97.4%

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

      5. distribute-lft-neg-out 97.4%

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

      6. associate-*r/ 97.4%

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

      7. associate-*r/ 97.4%

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

      8. associate-*l/ 97.4%

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

      9. *-commutative 97.4%

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

      10. +-commutative 97.4%

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

      11. distribute-rgt-out 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*l/ 99.8%

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

      14. /-rgt-identity 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.8%

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

      17. metadata-eval 99.8%

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

      18. associate-/r* 99.9%

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

      19. *-commutative 99.9%

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

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.9%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in a around 0 83.5%

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

       1. associate-*r/ 83.5%

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

       2. associate-/l* 83.5%

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

   11. Simplified 83.5%

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

   12. Taylor expanded in z around 0 58.9%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 10^{-29}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+83}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+45}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+83)
   (* a 120.0)
   (if (<= a 4.1e+45) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+83) {
		tmp = a * 120.0;
	} else if (a <= 4.1e+45) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.1d+83)) then
        tmp = a * 120.0d0
    else if (a <= 4.1d+45) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+83) {
		tmp = a * 120.0;
	} else if (a <= 4.1e+45) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+83:
		tmp = a * 120.0
	elif a <= 4.1e+45:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+83)
		tmp = Float64(a * 120.0);
	elseif (a <= 4.1e+45)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+83)
		tmp = a * 120.0;
	elseif (a <= 4.1e+45)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+83], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 4.1e+45], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.10000000000000002e83 or 4.10000000000000012e45 < a

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 80.1%

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

   if -2.10000000000000002e83 < a < 4.10000000000000012e45

   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 75.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+83}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+45}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+83}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e+83)
   (* a 120.0)
   (if (<= a 5.6e-30)
     (* 60.0 (/ (- x y) (- 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 <= -2.45e+83) {
		tmp = a * 120.0;
	} else if (a <= 5.6e-30) {
		tmp = 60.0 * ((x - y) / (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 <= (-2.45d+83)) then
        tmp = a * 120.0d0
    else if (a <= 5.6d-30) then
        tmp = 60.0d0 * ((x - y) / (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 <= -2.45e+83) {
		tmp = a * 120.0;
	} else if (a <= 5.6e-30) {
		tmp = 60.0 * ((x - y) / (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 <= -2.45e+83:
		tmp = a * 120.0
	elif a <= 5.6e-30:
		tmp = 60.0 * ((x - y) / (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 (a <= -2.45e+83)
		tmp = Float64(a * 120.0);
	elseif (a <= 5.6e-30)
		tmp = Float64(60.0 * Float64(Float64(x - y) / 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 <= -2.45e+83)
		tmp = a * 120.0;
	elseif (a <= 5.6e-30)
		tmp = 60.0 * ((x - y) / (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[a, -2.45e+83], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5.6e-30], N[(60.0 * N[(N[(x - y), $MachinePrecision] / 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 a < -2.44999999999999989e83

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 83.6%

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

   if -2.44999999999999989e83 < a < 5.59999999999999977e-30

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 78.2%

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

   if 5.59999999999999977e-30 < a

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 83.2%

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

      1. fma-def 83.2%

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

      2. associate-*r/ 83.2%

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

      3. associate-*l/ 83.2%

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

      4. *-commutative 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in z around 0 75.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+83}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Final simplification 99.8%

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

Alternative 15: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 16: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (- x y) (* (- z t) 0.016666666666666666)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (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) / ((z - t) * 0.016666666666666666d0)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around 0 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-*l/ 99.0%

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

   3. metadata-eval 99.0%

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

   4. distribute-rgt-neg-in 99.0%

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

   5. distribute-lft-neg-out 99.0%

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

   6. associate-*r/ 99.0%

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

   7. associate-*r/ 99.0%

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

   8. associate-*l/ 99.0%

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

   9. *-commutative 99.0%

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

   10. +-commutative 99.0%

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

   11. distribute-rgt-out 99.8%

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

   12. sub-neg 99.8%

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

   13. associate-*l/ 99.8%

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

   14. /-rgt-identity 99.8%

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

   15. *-commutative 99.8%

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

   16. associate-/l* 99.8%

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

   17. metadata-eval 99.8%

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

   18. associate-/r* 99.8%

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

   19. *-commutative 99.8%

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

6. Simplified 99.8%

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

7. Final simplification 99.8%

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

Alternative 17: 56.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-94}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e+79)
   (* a 120.0)
   (if (<= a 1.75e-94) (* -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 <= -2.9e+79) {
		tmp = a * 120.0;
	} else if (a <= 1.75e-94) {
		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 <= (-2.9d+79)) then
        tmp = a * 120.0d0
    else if (a <= 1.75d-94) 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 <= -2.9e+79) {
		tmp = a * 120.0;
	} else if (a <= 1.75e-94) {
		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 <= -2.9e+79:
		tmp = a * 120.0
	elif a <= 1.75e-94:
		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 <= -2.9e+79)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.75e-94)
		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 <= -2.9e+79)
		tmp = a * 120.0;
	elseif (a <= 1.75e-94)
		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, -2.9e+79], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.75e-94], 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 < -2.89999999999999992e79 or 1.74999999999999999e-94 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 74.0%

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

   if -2.89999999999999992e79 < a < 1.74999999999999999e-94

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-*l/ 99.0%

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

      3. metadata-eval 99.0%

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

      4. distribute-rgt-neg-in 99.0%

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

      5. distribute-lft-neg-out 99.0%

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

      6. associate-*r/ 99.0%

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

      7. associate-*r/ 98.9%

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

      8. associate-*l/ 98.9%

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

      9. *-commutative 98.9%

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

      10. +-commutative 98.9%

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

      11. distribute-rgt-out 99.7%

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

      12. sub-neg 99.7%

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

      13. associate-*l/ 99.6%

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

      14. /-rgt-identity 99.6%

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

      15. *-commutative 99.6%

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

      16. associate-/l* 99.6%

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

      17. metadata-eval 99.6%

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

      18. associate-/r* 99.7%

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

      19. *-commutative 99.7%

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

   6. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   7. Step-by-step derivation

      1. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

      2. times-frac 99.5%

         \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   8. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{1}{z - t} \cdot \frac{x - y}{0.016666666666666666}} + a \cdot 120 \]

   9. Taylor expanded in a around 0 79.1%

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

       1. associate-*r/ 79.0%

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

       2. associate-/l* 79.0%

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

   11. Simplified 79.0%

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

   12. Taylor expanded in x around 0 42.6%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-94}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{+235} \lor \neg \left(x \leq 6.5 \cdot 10^{+142}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.14e+235) (not (<= x 6.5e+142)))
   (* 60.0 (/ x z))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.14e+235) || !(x <= 6.5e+142)) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.14d+235)) .or. (.not. (x <= 6.5d+142))) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.14e+235) || !(x <= 6.5e+142)) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.14e+235) or not (x <= 6.5e+142):
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.14e+235) || !(x <= 6.5e+142))
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.14e+235) || ~((x <= 6.5e+142)))
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.14e+235], N[Not[LessEqual[x, 6.5e+142]], $MachinePrecision]], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14000000000000001e235 or 6.4999999999999997e142 < 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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 85.2%

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

   5. Taylor expanded in x around inf 80.3%

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

   6. Taylor expanded in z around inf 49.6%

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

   if -1.14000000000000001e235 < x < 6.4999999999999997e142

   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 54.8%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{+235} \lor \neg \left(x \leq 6.5 \cdot 10^{+142}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19: 52.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+237}:\\ \;\;\;\;60 \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4e+237)
   (* 60.0 (/ (- x) t))
   (if (<= x 5.8e+141) (* a 120.0) (* 60.0 (/ x z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+237) {
		tmp = 60.0 * (-x / t);
	} else if (x <= 5.8e+141) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4d+237)) then
        tmp = 60.0d0 * (-x / t)
    else if (x <= 5.8d+141) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+237) {
		tmp = 60.0 * (-x / t);
	} else if (x <= 5.8e+141) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4e+237:
		tmp = 60.0 * (-x / t)
	elif x <= 5.8e+141:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4e+237)
		tmp = Float64(60.0 * Float64(Float64(-x) / t));
	elseif (x <= 5.8e+141)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4e+237)
		tmp = 60.0 * (-x / t);
	elseif (x <= 5.8e+141)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4e+237], N[(60.0 * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+141], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.99999999999999976e237

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 87.4%

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

   5. Taylor expanded in x around inf 87.4%

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

   6. Taylor expanded in z around 0 69.5%

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

      1. associate-*r/ 69.5%

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

      2. neg-mul-1 69.5%

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

   8. Simplified 69.5%

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

   if -3.99999999999999976e237 < x < 5.80000000000000013e141

   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 54.6%

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

   if 5.80000000000000013e141 < x

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 83.9%

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

   5. Taylor expanded in x around inf 76.8%

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

   6. Taylor expanded in z around inf 45.5%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+237}:\\ \;\;\;\;60 \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 20: 50.7% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 46.6%

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

5. Final simplification 46.6%

   \[\leadsto a \cdot 120 \]

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 2023208 
(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)))