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

Percentage Accurate: 99.3% → 99.8%

Time: 18.9s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-def 99.8%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 80.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ t_2 := a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+221}:\\ \;\;\;\;60 \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t)))
        (t_2 (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))))
   (if (<= t_1 -5e+221)
     (* 60.0 (* (- x y) (/ 1.0 (- z t))))
     (if (<= t_1 -5e+94)
       t_2
       (if (<= t_1 -5e-17)
         t_1
         (if (<= t_1 5e+71) t_2 (* 60.0 (/ (- x y) (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double t_2 = (a * 120.0) + (60.0 / ((z - t) / x));
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)));
	} else if (t_1 <= -5e+94) {
		tmp = t_2;
	} else if (t_1 <= -5e-17) {
		tmp = t_1;
	} else if (t_1 <= 5e+71) {
		tmp = t_2;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    t_2 = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    if (t_1 <= (-5d+221)) then
        tmp = 60.0d0 * ((x - y) * (1.0d0 / (z - t)))
    else if (t_1 <= (-5d+94)) then
        tmp = t_2
    else if (t_1 <= (-5d-17)) then
        tmp = t_1
    else if (t_1 <= 5d+71) then
        tmp = t_2
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double t_2 = (a * 120.0) + (60.0 / ((z - t) / x));
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)));
	} else if (t_1 <= -5e+94) {
		tmp = t_2;
	} else if (t_1 <= -5e-17) {
		tmp = t_1;
	} else if (t_1 <= 5e+71) {
		tmp = t_2;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	t_2 = (a * 120.0) + (60.0 / ((z - t) / x))
	tmp = 0
	if t_1 <= -5e+221:
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)))
	elif t_1 <= -5e+94:
		tmp = t_2
	elif t_1 <= -5e-17:
		tmp = t_1
	elif t_1 <= 5e+71:
		tmp = t_2
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	t_2 = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)))
	tmp = 0.0
	if (t_1 <= -5e+221)
		tmp = Float64(60.0 * Float64(Float64(x - y) * Float64(1.0 / Float64(z - t))));
	elseif (t_1 <= -5e+94)
		tmp = t_2;
	elseif (t_1 <= -5e-17)
		tmp = t_1;
	elseif (t_1 <= 5e+71)
		tmp = t_2;
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	t_2 = (a * 120.0) + (60.0 / ((z - t) / x));
	tmp = 0.0;
	if (t_1 <= -5e+221)
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)));
	elseif (t_1 <= -5e+94)
		tmp = t_2;
	elseif (t_1 <= -5e-17)
		tmp = t_1;
	elseif (t_1 <= 5e+71)
		tmp = t_2;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+221], N[(60.0 * N[(N[(x - y), $MachinePrecision] * N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+94], t$95$2, If[LessEqual[t$95$1, -5e-17], t$95$1, If[LessEqual[t$95$1, 5e+71], t$95$2, N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -5.0000000000000002e221

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 99.8%

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

      1. div-inv 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -5.0000000000000002e221 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -5.0000000000000001e94 or -4.9999999999999999e-17 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 4.99999999999999972e71

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.9%

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

   if -5.0000000000000001e94 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -4.9999999999999999e-17

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/l* 100.0%

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

      2. add-cube-cbrt 97.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}} \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right) \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}} + a \cdot 120 \]

      3. pow3 97.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right)}^{3}} + a \cdot 120 \]

      4. *-un-lft-identity 97.9%

         \[\leadsto {\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{\color{blue}{1 \cdot \left(z - t\right)}}}\right)}^{3} + a \cdot 120 \]

      5. times-frac 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}}}\right)}^{3} + a \cdot 120 \]

      6. metadata-eval 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{60} \cdot \frac{x - y}{z - t}}\right)}^{3} + a \cdot 120 \]

   6. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{60 \cdot \frac{x - y}{z - t}}\right)}^{3}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 86.7%

      \[\leadsto \color{blue}{60 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x - y}{z - t}\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 86.7%

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

      2. *-lft-identity 86.7%

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

      3. associate-*r/ 87.0%

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

   9. Simplified 87.0%

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

   if 4.99999999999999972e71 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 86.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+221}:\\ \;\;\;\;60 \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-17}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+71}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+221}:\\ \;\;\;\;60 \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+221)
     (* 60.0 (* (- x y) (/ 1.0 (- z t))))
     (if (<= t_1 -5e+94)
       (+ (* a 120.0) (/ x (/ (- z t) 60.0)))
       (if (<= t_1 -5e-17)
         t_1
         (if (<= t_1 5e+71)
           (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
           (* 60.0 (/ (- x y) (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)));
	} else if (t_1 <= -5e+94) {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	} else if (t_1 <= -5e-17) {
		tmp = t_1;
	} else if (t_1 <= 5e+71) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+221)) then
        tmp = 60.0d0 * ((x - y) * (1.0d0 / (z - t)))
    else if (t_1 <= (-5d+94)) then
        tmp = (a * 120.0d0) + (x / ((z - t) / 60.0d0))
    else if (t_1 <= (-5d-17)) then
        tmp = t_1
    else if (t_1 <= 5d+71) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+221) {
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)));
	} else if (t_1 <= -5e+94) {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	} else if (t_1 <= -5e-17) {
		tmp = t_1;
	} else if (t_1 <= 5e+71) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+221:
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)))
	elif t_1 <= -5e+94:
		tmp = (a * 120.0) + (x / ((z - t) / 60.0))
	elif t_1 <= -5e-17:
		tmp = t_1
	elif t_1 <= 5e+71:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+221)
		tmp = Float64(60.0 * Float64(Float64(x - y) * Float64(1.0 / Float64(z - t))));
	elseif (t_1 <= -5e+94)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) / 60.0)));
	elseif (t_1 <= -5e-17)
		tmp = t_1;
	elseif (t_1 <= 5e+71)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+221)
		tmp = 60.0 * ((x - y) * (1.0 / (z - t)));
	elseif (t_1 <= -5e+94)
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	elseif (t_1 <= -5e-17)
		tmp = t_1;
	elseif (t_1 <= 5e+71)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+221], N[(60.0 * N[(N[(x - y), $MachinePrecision] * N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+94], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-17], t$95$1, If[LessEqual[t$95$1, 5e+71], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -5.0000000000000002e221

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 99.8%

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

      1. div-inv 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -5.0000000000000002e221 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -5.0000000000000001e94

   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. Add Preprocessing

   5. Taylor expanded in x around inf 83.9%

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

      1. associate-*r/ 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-/l* 84.0%

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

   7. Simplified 84.0%

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

   if -5.0000000000000001e94 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -4.9999999999999999e-17

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/l* 100.0%

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

      2. add-cube-cbrt 97.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}} \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right) \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}} + a \cdot 120 \]

      3. pow3 97.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right)}^{3}} + a \cdot 120 \]

      4. *-un-lft-identity 97.9%

         \[\leadsto {\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{\color{blue}{1 \cdot \left(z - t\right)}}}\right)}^{3} + a \cdot 120 \]

      5. times-frac 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}}}\right)}^{3} + a \cdot 120 \]

      6. metadata-eval 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{60} \cdot \frac{x - y}{z - t}}\right)}^{3} + a \cdot 120 \]

   6. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{60 \cdot \frac{x - y}{z - t}}\right)}^{3}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 86.7%

      \[\leadsto \color{blue}{60 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x - y}{z - t}\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 86.7%

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

      2. *-lft-identity 86.7%

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

      3. associate-*r/ 87.0%

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

   9. Simplified 87.0%

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

   if -4.9999999999999999e-17 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 4.99999999999999972e71

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 89.4%

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

   if 4.99999999999999972e71 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 86.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+221}:\\ \;\;\;\;60 \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-17}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+71}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-228}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-205}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ 60.0 (/ z (- x y))))))
   (if (<= z -2.4e-46)
     t_1
     (if (<= z 1e-228)
       (/ (* 60.0 (- x y)) (- z t))
       (if (<= z 2.5e-205)
         (+ (* a 120.0) (/ (* x -60.0) t))
         (if (<= z 4.5e-26) (* 60.0 (/ (- x y) (- z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 / (z / (x - y)));
	double tmp;
	if (z <= -2.4e-46) {
		tmp = t_1;
	} else if (z <= 1e-228) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (z <= 2.5e-205) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 4.5e-26) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    if (z <= (-2.4d-46)) then
        tmp = t_1
    else if (z <= 1d-228) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if (z <= 2.5d-205) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if (z <= 4.5d-26) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 / (z / (x - y)));
	double tmp;
	if (z <= -2.4e-46) {
		tmp = t_1;
	} else if (z <= 1e-228) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (z <= 2.5e-205) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 4.5e-26) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 / (z / (x - y)))
	tmp = 0
	if z <= -2.4e-46:
		tmp = t_1
	elif z <= 1e-228:
		tmp = (60.0 * (x - y)) / (z - t)
	elif z <= 2.5e-205:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif z <= 4.5e-26:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))))
	tmp = 0.0
	if (z <= -2.4e-46)
		tmp = t_1;
	elseif (z <= 1e-228)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif (z <= 2.5e-205)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (z <= 4.5e-26)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 / (z / (x - y)));
	tmp = 0.0;
	if (z <= -2.4e-46)
		tmp = t_1;
	elseif (z <= 1e-228)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif (z <= 2.5e-205)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif (z <= 4.5e-26)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e-46], t$95$1, If[LessEqual[z, 1e-228], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-205], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-26], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000013e-46 or 4.4999999999999999e-26 < z

   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. Add Preprocessing

   5. Taylor expanded in z around inf 87.6%

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

   if -2.40000000000000013e-46 < z < 1.00000000000000003e-228

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/l* 99.9%

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

      2. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}} \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right) \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}} + a \cdot 120 \]

      3. pow3 99.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right)}^{3}} + a \cdot 120 \]

      4. *-un-lft-identity 99.0%

         \[\leadsto {\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{\color{blue}{1 \cdot \left(z - t\right)}}}\right)}^{3} + a \cdot 120 \]

      5. times-frac 99.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}}}\right)}^{3} + a \cdot 120 \]

      6. metadata-eval 99.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{60} \cdot \frac{x - y}{z - t}}\right)}^{3} + a \cdot 120 \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{60 \cdot \frac{x - y}{z - t}}\right)}^{3}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 76.4%

      \[\leadsto \color{blue}{60 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x - y}{z - t}\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 76.4%

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

      2. *-lft-identity 76.4%

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

      3. associate-*r/ 76.4%

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

   9. Simplified 76.4%

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

   if 1.00000000000000003e-228 < z < 2.5e-205

   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. Add Preprocessing

   5. Taylor expanded in x around inf 99.8%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 99.8%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 2.5e-205 < z < 4.4999999999999999e-26

   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. Add Preprocessing

   5. Taylor expanded in a around 0 77.4%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 10^{-228}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-205}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-206}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= z -2.9e-46)
     (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
     (if (<= z 5e-236)
       t_1
       (if (<= z 2.25e-206)
         (+ (* a 120.0) (* 60.0 (/ y t)))
         (if (<= z 2.6e-25) t_1 (+ (* a 120.0) (* -60.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 5e-236) {
		tmp = t_1;
	} else if (z <= 2.25e-206) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (z <= 2.6e-25) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (z <= (-2.9d-46)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if (z <= 5d-236) then
        tmp = t_1
    else if (z <= 2.25d-206) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if (z <= 2.6d-25) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 5e-236) {
		tmp = t_1;
	} else if (z <= 2.25e-206) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (z <= 2.6e-25) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if z <= -2.9e-46:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif z <= 5e-236:
		tmp = t_1
	elif z <= 2.25e-206:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif z <= 2.6e-25:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (z <= -2.9e-46)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (z <= 5e-236)
		tmp = t_1;
	elseif (z <= 2.25e-206)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (z <= 2.6e-25)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if (z <= -2.9e-46)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif (z <= 5e-236)
		tmp = t_1;
	elseif (z <= 2.25e-206)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif (z <= 2.6e-25)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-46], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-236], t$95$1, If[LessEqual[z, 2.25e-206], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-25], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000005e-46

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. associate-*r/ 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

   10. Simplified 80.3%

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

   if -2.90000000000000005e-46 < z < 4.9999999999999998e-236 or 2.2499999999999999e-206 < z < 2.6e-25

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 76.8%

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

   if 4.9999999999999998e-236 < z < 2.2499999999999999e-206

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-*r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around 0 100.0%

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

   if 2.6e-25 < z

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 88.3%

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

   6. Taylor expanded in x around 0 80.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-236}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-206}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-25}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-206}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{z}{-60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= z -2.9e-46)
     (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
     (if (<= z 9.5e-234)
       t_1
       (if (<= z 2.1e-206)
         (+ (* a 120.0) (* 60.0 (/ y t)))
         (if (<= z 4.4e-26) t_1 (+ (* a 120.0) (/ y (/ z -60.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 9.5e-234) {
		tmp = t_1;
	} else if (z <= 2.1e-206) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (z <= 4.4e-26) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (y / (z / -60.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (z <= (-2.9d-46)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if (z <= 9.5d-234) then
        tmp = t_1
    else if (z <= 2.1d-206) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if (z <= 4.4d-26) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (y / (z / (-60.0d0)))
    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 - t));
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 9.5e-234) {
		tmp = t_1;
	} else if (z <= 2.1e-206) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (z <= 4.4e-26) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (y / (z / -60.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if z <= -2.9e-46:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif z <= 9.5e-234:
		tmp = t_1
	elif z <= 2.1e-206:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif z <= 4.4e-26:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (y / (z / -60.0))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (z <= -2.9e-46)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (z <= 9.5e-234)
		tmp = t_1;
	elseif (z <= 2.1e-206)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (z <= 4.4e-26)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y / Float64(z / -60.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if (z <= -2.9e-46)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif (z <= 9.5e-234)
		tmp = t_1;
	elseif (z <= 2.1e-206)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif (z <= 4.4e-26)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (y / (z / -60.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-46], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-234], t$95$1, If[LessEqual[z, 2.1e-206], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-26], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(y / N[(z / -60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000005e-46

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. associate-*r/ 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

   10. Simplified 80.3%

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

   if -2.90000000000000005e-46 < z < 9.4999999999999999e-234 or 2.1000000000000001e-206 < z < 4.4000000000000002e-26

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 76.8%

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

   if 9.4999999999999999e-234 < z < 2.1000000000000001e-206

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-*r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around 0 100.0%

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

   if 4.4000000000000002e-26 < z

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 88.3%

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

   6. Taylor expanded in x around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-/l* 80.4%

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

   8. Applied egg-rr 80.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{-60}}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-234}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-206}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-26}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{z}{-60}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{z}{-60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= z -1.5e-46)
     (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
     (if (<= z 6e-231)
       t_1
       (if (<= z 1.32e-201)
         (+ (* a 120.0) (/ (* x -60.0) t))
         (if (<= z 1.9e-24) t_1 (+ (* a 120.0) (/ y (/ z -60.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (z <= -1.5e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 6e-231) {
		tmp = t_1;
	} else if (z <= 1.32e-201) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 1.9e-24) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (y / (z / -60.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (z <= (-1.5d-46)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if (z <= 6d-231) then
        tmp = t_1
    else if (z <= 1.32d-201) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if (z <= 1.9d-24) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (y / (z / (-60.0d0)))
    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 - t));
	double tmp;
	if (z <= -1.5e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 6e-231) {
		tmp = t_1;
	} else if (z <= 1.32e-201) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 1.9e-24) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (y / (z / -60.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if z <= -1.5e-46:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif z <= 6e-231:
		tmp = t_1
	elif z <= 1.32e-201:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif z <= 1.9e-24:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (y / (z / -60.0))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.5e-46)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (z <= 6e-231)
		tmp = t_1;
	elseif (z <= 1.32e-201)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (z <= 1.9e-24)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y / Float64(z / -60.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if (z <= -1.5e-46)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif (z <= 6e-231)
		tmp = t_1;
	elseif (z <= 1.32e-201)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif (z <= 1.9e-24)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (y / (z / -60.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-46], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-231], t$95$1, If[LessEqual[z, 1.32e-201], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-24], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(y / N[(z / -60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.49999999999999994e-46

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. associate-*r/ 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

   10. Simplified 80.3%

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

   if -1.49999999999999994e-46 < z < 6.0000000000000005e-231 or 1.31999999999999996e-201 < z < 1.90000000000000013e-24

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 76.8%

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

   if 6.0000000000000005e-231 < z < 1.31999999999999996e-201

   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. Add Preprocessing

   5. Taylor expanded in x around inf 99.8%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 99.8%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 1.90000000000000013e-24 < z

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 88.3%

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

   6. Taylor expanded in x around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-/l* 80.4%

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

   8. Applied egg-rr 80.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{-60}}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-231}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-24}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{z}{-60}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-25}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{z}{-60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e-46)
   (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
   (if (<= z 9.5e-228)
     (/ (* 60.0 (- x y)) (- z t))
     (if (<= z 2.4e-205)
       (+ (* a 120.0) (/ (* x -60.0) t))
       (if (<= z 1.75e-25)
         (* 60.0 (/ (- x y) (- z t)))
         (+ (* a 120.0) (/ y (/ z -60.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 9.5e-228) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (z <= 2.4e-205) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 1.75e-25) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (y / (z / -60.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.9d-46)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if (z <= 9.5d-228) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if (z <= 2.4d-205) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if (z <= 1.75d-25) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (y / (z / (-60.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if (z <= 9.5e-228) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if (z <= 2.4e-205) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 1.75e-25) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (y / (z / -60.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e-46:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif z <= 9.5e-228:
		tmp = (60.0 * (x - y)) / (z - t)
	elif z <= 2.4e-205:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif z <= 1.75e-25:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (y / (z / -60.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e-46)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif (z <= 9.5e-228)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif (z <= 2.4e-205)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (z <= 1.75e-25)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y / Float64(z / -60.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e-46)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif (z <= 9.5e-228)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif (z <= 2.4e-205)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif (z <= 1.75e-25)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (y / (z / -60.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e-46], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-228], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-205], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-25], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y / N[(z / -60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.90000000000000005e-46

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. associate-*r/ 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

   10. Simplified 80.3%

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

   if -2.90000000000000005e-46 < z < 9.50000000000000024e-228

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/l* 99.9%

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

      2. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}} \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right) \cdot \sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}} + a \cdot 120 \]

      3. pow3 99.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{z - t}}\right)}^{3}} + a \cdot 120 \]

      4. *-un-lft-identity 99.0%

         \[\leadsto {\left(\sqrt[3]{\frac{60 \cdot \left(x - y\right)}{\color{blue}{1 \cdot \left(z - t\right)}}}\right)}^{3} + a \cdot 120 \]

      5. times-frac 99.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}}}\right)}^{3} + a \cdot 120 \]

      6. metadata-eval 99.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{60} \cdot \frac{x - y}{z - t}}\right)}^{3} + a \cdot 120 \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{60 \cdot \frac{x - y}{z - t}}\right)}^{3}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 76.4%

      \[\leadsto \color{blue}{60 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x - y}{z - t}\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 76.4%

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

      2. *-lft-identity 76.4%

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

      3. associate-*r/ 76.4%

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

   9. Simplified 76.4%

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

   if 9.50000000000000024e-228 < z < 2.4000000000000002e-205

   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. Add Preprocessing

   5. Taylor expanded in x around inf 99.8%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 99.8%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 2.4000000000000002e-205 < z < 1.7500000000000001e-25

   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. Add Preprocessing

   5. Taylor expanded in a around 0 77.4%

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

   if 1.7500000000000001e-25 < z

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 88.3%

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

   6. Taylor expanded in x around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-/l* 80.4%

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

   8. Applied egg-rr 80.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-25}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{z}{-60}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= a -1.45e-39)
     (* a 120.0)
     (if (<= a -3.1e-205)
       t_1
       (if (<= a -4.6e-258)
         (* -60.0 (/ (- x y) t))
         (if (<= a 7.2e-111) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -1.45e-39) {
		tmp = a * 120.0;
	} else if (a <= -3.1e-205) {
		tmp = t_1;
	} else if (a <= -4.6e-258) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 7.2e-111) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    if (a <= (-1.45d-39)) then
        tmp = a * 120.0d0
    else if (a <= (-3.1d-205)) then
        tmp = t_1
    else if (a <= (-4.6d-258)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 7.2d-111) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -1.45e-39) {
		tmp = a * 120.0;
	} else if (a <= -3.1e-205) {
		tmp = t_1;
	} else if (a <= -4.6e-258) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 7.2e-111) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if a <= -1.45e-39:
		tmp = a * 120.0
	elif a <= -3.1e-205:
		tmp = t_1
	elif a <= -4.6e-258:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 7.2e-111:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.45e-39)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.1e-205)
		tmp = t_1;
	elseif (a <= -4.6e-258)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 7.2e-111)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if (a <= -1.45e-39)
		tmp = a * 120.0;
	elseif (a <= -3.1e-205)
		tmp = t_1;
	elseif (a <= -4.6e-258)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 7.2e-111)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e-39], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.1e-205], t$95$1, If[LessEqual[a, -4.6e-258], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-111], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.44999999999999994e-39 or 7.20000000000000019e-111 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 69.0%

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

   if -1.44999999999999994e-39 < a < -3.09999999999999983e-205 or -4.59999999999999986e-258 < a < 7.20000000000000019e-111

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 85.5%

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

   6. Taylor expanded in x around inf 50.6%

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

   if -3.09999999999999983e-205 < a < -4.59999999999999986e-258

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 79.0%

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

   6. Taylor expanded in z around 0 79.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-39}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-205}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-111}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-201}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-252}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-110}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.05e-30)
   (* a 120.0)
   (if (<= a -2.05e-201)
     (* 60.0 (/ (- x y) z))
     (if (<= a -1.16e-252)
       (* -60.0 (/ (- x y) t))
       (if (<= a 1.06e-110) (* 60.0 (/ x (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e-30) {
		tmp = a * 120.0;
	} else if (a <= -2.05e-201) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= -1.16e-252) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.06e-110) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.05d-30)) then
        tmp = a * 120.0d0
    else if (a <= (-2.05d-201)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= (-1.16d-252)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 1.06d-110) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e-30) {
		tmp = a * 120.0;
	} else if (a <= -2.05e-201) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= -1.16e-252) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.06e-110) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.05e-30:
		tmp = a * 120.0
	elif a <= -2.05e-201:
		tmp = 60.0 * ((x - y) / z)
	elif a <= -1.16e-252:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 1.06e-110:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.05e-30)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.05e-201)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= -1.16e-252)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 1.06e-110)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.05e-30)
		tmp = a * 120.0;
	elseif (a <= -2.05e-201)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= -1.16e-252)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 1.06e-110)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.05e-30], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.05e-201], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.16e-252], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e-110], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.0500000000000001e-30 or 1.0599999999999999e-110 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 69.4%

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

   if -1.0500000000000001e-30 < a < -2.05000000000000001e-201

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 80.7%

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

   6. Taylor expanded in z around inf 54.8%

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

   if -2.05000000000000001e-201 < a < -1.1599999999999999e-252

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 79.0%

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

   6. Taylor expanded in z around 0 79.2%

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

   if -1.1599999999999999e-252 < a < 1.0599999999999999e-110

   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. Add Preprocessing

   5. Taylor expanded in a around 0 89.4%

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

   6. Taylor expanded in x around inf 57.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-201}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-252}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-110}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-39}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-23)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (<= (* a 120.0) 4e-39) (* 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 * 120.0) <= -1e-23) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 4e-39) {
		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 * 120.0d0) <= (-1d-23)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 4d-39) 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 * 120.0) <= -1e-23) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 4e-39) {
		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 * 120.0) <= -1e-23:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 4e-39:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-23)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 4e-39)
		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 * 120.0) <= -1e-23)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 4e-39)
		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[N[(a * 120.0), $MachinePrecision], -1e-23], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-39], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -9.9999999999999996e-24

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 76.5%

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

   6. Taylor expanded in x around 0 77.9%

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

   if -9.9999999999999996e-24 < (*.f64 a 120) < 3.99999999999999972e-39

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 82.3%

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

   if 3.99999999999999972e-39 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 71.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-39}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-62}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-23)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (<= (* a 120.0) 5e-62)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* x (/ 60.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-23) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e-62) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-1d-23)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 5d-62) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-23) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e-62) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e-23:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 5e-62:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (60.0 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-23)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 5e-62)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e-23)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 5e-62)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (x * (60.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-23], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-62], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -9.9999999999999996e-24

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 76.5%

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

   6. Taylor expanded in x around 0 77.9%

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

   if -9.9999999999999996e-24 < (*.f64 a 120) < 5.0000000000000002e-62

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 82.9%

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

   if 5.0000000000000002e-62 < (*.f64 a 120)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 87.8%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-/l* 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

   10. Simplified 71.6%

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

   11. Taylor expanded in x around 0 71.5%

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

       1. associate-*r/ 71.5%

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

       2. associate-*l/ 71.5%

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

       3. *-commutative 71.5%

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

   13. Simplified 71.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-62}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+53} \lor \neg \left(y \leq 1.35 \cdot 10^{+101}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.7e+53) (not (<= y 1.35e+101)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (/ x (/ (- z t) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e+53) || !(y <= 1.35e+101)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.7d+53)) .or. (.not. (y <= 1.35d+101))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x / ((z - t) / 60.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e+53) || !(y <= 1.35e+101)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.7e+53) or not (y <= 1.35e+101):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x / ((z - t) / 60.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.7e+53) || !(y <= 1.35e+101))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) / 60.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.7e+53) || ~((y <= 1.35e+101)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x / ((z - t) / 60.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.7e+53], N[Not[LessEqual[y, 1.35e+101]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000019e53 or 1.35000000000000003e101 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 88.1%

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

   if -2.70000000000000019e53 < y < 1.35000000000000003e101

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 94.0%

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

      1. associate-*r/ 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-/l* 94.0%

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

   7. Simplified 94.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+53} \lor \neg \left(y \leq 1.35 \cdot 10^{+101}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\frac{z - t}{60}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-20} \lor \neg \left(a \leq 8.2 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.85e-20) (not (<= a 8.2e-36)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-20) || !(a <= 8.2e-36)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.85d-20)) .or. (.not. (a <= 8.2d-36))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-20) || !(a <= 8.2e-36)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.85e-20) or not (a <= 8.2e-36):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.85e-20) || !(a <= 8.2e-36))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.85e-20) || ~((a <= 8.2e-36)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.85e-20], N[Not[LessEqual[a, 8.2e-36]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85e-20 or 8.20000000000000025e-36 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 73.1%

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

   if -1.85e-20 < a < 8.20000000000000025e-36

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 81.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-20} \lor \neg \left(a \leq 8.2 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-30} \lor \neg \left(a \leq 5.6 \cdot 10^{-73}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.8e-30) (not (<= a 5.6e-73)))
   (* a 120.0)
   (* -60.0 (/ (- x y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e-30) || !(a <= 5.6e-73)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.8d-30)) .or. (.not. (a <= 5.6d-73))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e-30) || !(a <= 5.6e-73)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.8e-30) or not (a <= 5.6e-73):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.8e-30) || !(a <= 5.6e-73))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.8e-30) || ~((a <= 5.6e-73)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.8e-30], N[Not[LessEqual[a, 5.6e-73]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.79999999999999978e-30 or 5.60000000000000023e-73 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 71.2%

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

   if -5.79999999999999978e-30 < a < 5.60000000000000023e-73

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 83.3%

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

   6. Taylor expanded in z around 0 41.9%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-30} \lor \neg \left(a \leq 5.6 \cdot 10^{-73}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-142} \lor \neg \left(a \leq 6 \cdot 10^{-176}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.2e-142) (not (<= a 6e-176))) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.2e-142) || !(a <= 6e-176)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-9.2d-142)) .or. (.not. (a <= 6d-176))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.2e-142) || !(a <= 6e-176)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.2e-142) or not (a <= 6e-176):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.2e-142) || !(a <= 6e-176))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.2e-142) || ~((a <= 6e-176)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.2e-142], N[Not[LessEqual[a, 6e-176]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.20000000000000009e-142 or 6e-176 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.1%

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

   if -9.20000000000000009e-142 < a < 6e-176

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 88.5%

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

   6. Taylor expanded in z around 0 46.2%

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

   7. Taylor expanded in x around inf 34.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-142} \lor \neg \left(a \leq 6 \cdot 10^{-176}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 18: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 19: 50.8% 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. Add Preprocessing

5. Taylor expanded in z around inf 47.5%

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

6. Final simplification 47.5%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024031 
(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)))