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

Percentage Accurate: 99.4% → 99.8%

Time: 17.6s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

   1. clear-num 99.7%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{-x}{t}\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+204}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+273}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x) t))))
   (if (<= x -8.2e+169)
     t_1
     (if (<= x 5.5e+161)
       (* a 120.0)
       (if (<= x 1.5e+204)
         (* 60.0 (/ x z))
         (if (<= x 1.3e+273) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (-x / t);
	double tmp;
	if (x <= -8.2e+169) {
		tmp = t_1;
	} else if (x <= 5.5e+161) {
		tmp = a * 120.0;
	} else if (x <= 1.5e+204) {
		tmp = 60.0 * (x / z);
	} else if (x <= 1.3e+273) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (-x / t)
    if (x <= (-8.2d+169)) then
        tmp = t_1
    else if (x <= 5.5d+161) then
        tmp = a * 120.0d0
    else if (x <= 1.5d+204) then
        tmp = 60.0d0 * (x / z)
    else if (x <= 1.3d+273) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (-x / t);
	double tmp;
	if (x <= -8.2e+169) {
		tmp = t_1;
	} else if (x <= 5.5e+161) {
		tmp = a * 120.0;
	} else if (x <= 1.5e+204) {
		tmp = 60.0 * (x / z);
	} else if (x <= 1.3e+273) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (-x / t)
	tmp = 0
	if x <= -8.2e+169:
		tmp = t_1
	elif x <= 5.5e+161:
		tmp = a * 120.0
	elif x <= 1.5e+204:
		tmp = 60.0 * (x / z)
	elif x <= 1.3e+273:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(-x) / t))
	tmp = 0.0
	if (x <= -8.2e+169)
		tmp = t_1;
	elseif (x <= 5.5e+161)
		tmp = Float64(a * 120.0);
	elseif (x <= 1.5e+204)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (x <= 1.3e+273)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (-x / t);
	tmp = 0.0;
	if (x <= -8.2e+169)
		tmp = t_1;
	elseif (x <= 5.5e+161)
		tmp = a * 120.0;
	elseif (x <= 1.5e+204)
		tmp = 60.0 * (x / z);
	elseif (x <= 1.3e+273)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[((-x) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+169], t$95$1, If[LessEqual[x, 5.5e+161], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 1.5e+204], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+273], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2000000000000006e169 or 1.29999999999999997e273 < x

   1. Initial program 97.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 82.0%

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

   8. Taylor expanded in x around inf 80.9%

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

   9. Taylor expanded in z around 0 54.2%

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

       1. associate-*r/ 54.2%

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

       2. neg-mul-1 54.2%

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

   11. Simplified 54.2%

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

   if -8.2000000000000006e169 < x < 5.5000000000000005e161 or 1.49999999999999991e204 < x < 1.29999999999999997e273

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 60.0%

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

   if 5.5000000000000005e161 < x < 1.49999999999999991e204

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.3%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 85.9%

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

   8. Taylor expanded in x around inf 85.4%

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

   9. Taylor expanded in z around inf 86.1%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+169}:\\ \;\;\;\;60 \cdot \frac{-x}{t}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+204}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+273}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{-x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{-58} \lor \neg \left(z - t \leq 20000000000\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -5e-58) (not (<= (- z t) 20000000000.0)))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
   (/ 60.0 (/ (- z t) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -5e-58) || !((z - t) <= 20000000000.0)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - t) <= (-5d-58)) .or. (.not. ((z - t) <= 20000000000.0d0))) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else
        tmp = 60.0d0 / ((z - t) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -5e-58) || !((z - t) <= 20000000000.0)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -5e-58) or not ((z - t) <= 20000000000.0):
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	else:
		tmp = 60.0 / ((z - t) / (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -5e-58) || !(Float64(z - t) <= 20000000000.0))
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	else
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) <= -5e-58) || ~(((z - t) <= 20000000000.0)))
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	else
		tmp = 60.0 / ((z - t) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -5e-58], N[Not[LessEqual[N[(z - t), $MachinePrecision], 20000000000.0]], $MachinePrecision]], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -4.99999999999999977e-58 or 2e10 < (-.f64 z t)

   1. Initial program 99.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 88.6%

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

   if -4.99999999999999977e-58 < (-.f64 z t) < 2e10

   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%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 90.5%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   9. Applied egg-rr 90.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{-58} \lor \neg \left(z - t \leq 20000000000\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{-58} \lor \neg \left(z - t \leq 5 \cdot 10^{+21}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -5e-58) (not (<= (- z t) 5e+21)))
   (+ (* 60.0 (/ x (- z t))) (* a 120.0))
   (/ 60.0 (/ (- z t) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -5e-58) || !((z - t) <= 5e+21)) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - t) <= (-5d-58)) .or. (.not. ((z - t) <= 5d+21))) then
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    else
        tmp = 60.0d0 / ((z - t) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -5e-58) || !((z - t) <= 5e+21)) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -5e-58) or not ((z - t) <= 5e+21):
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	else:
		tmp = 60.0 / ((z - t) / (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -5e-58) || !(Float64(z - t) <= 5e+21))
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) <= -5e-58) || ~(((z - t) <= 5e+21)))
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	else
		tmp = 60.0 / ((z - t) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -5e-58], N[Not[LessEqual[N[(z - t), $MachinePrecision], 5e+21]], $MachinePrecision]], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -4.99999999999999977e-58 or 5e21 < (-.f64 z t)

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.5%

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

   if -4.99999999999999977e-58 < (-.f64 z t) < 5e21

   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%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 90.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   9. Applied egg-rr 90.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{-58} \lor \neg \left(z - t \leq 5 \cdot 10^{+21}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-291}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* 60.0 (/ x z)) (* a 120.0))))
   (if (<= z -3.9e-17)
     t_1
     (if (<= z 1.4e-291)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (<= z 1.05e+22) (- (* a 120.0) (/ 60.0 (/ t x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x / z)) + (a * 120.0);
	double tmp;
	if (z <= -3.9e-17) {
		tmp = t_1;
	} else if (z <= 1.4e-291) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= 1.05e+22) {
		tmp = (a * 120.0) - (60.0 / (t / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x / z)) + (a * 120.0d0)
    if (z <= (-3.9d-17)) then
        tmp = t_1
    else if (z <= 1.4d-291) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (z <= 1.05d+22) then
        tmp = (a * 120.0d0) - (60.0d0 / (t / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x / z)) + (a * 120.0);
	double tmp;
	if (z <= -3.9e-17) {
		tmp = t_1;
	} else if (z <= 1.4e-291) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= 1.05e+22) {
		tmp = (a * 120.0) - (60.0 / (t / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x / z)) + (a * 120.0)
	tmp = 0
	if z <= -3.9e-17:
		tmp = t_1
	elif z <= 1.4e-291:
		tmp = 60.0 / ((z - t) / (x - y))
	elif z <= 1.05e+22:
		tmp = (a * 120.0) - (60.0 / (t / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x / z)) + Float64(a * 120.0))
	tmp = 0.0
	if (z <= -3.9e-17)
		tmp = t_1;
	elseif (z <= 1.4e-291)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (z <= 1.05e+22)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 / Float64(t / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x / z)) + (a * 120.0);
	tmp = 0.0;
	if (z <= -3.9e-17)
		tmp = t_1;
	elseif (z <= 1.4e-291)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (z <= 1.05e+22)
		tmp = (a * 120.0) - (60.0 / (t / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e-17], t$95$1, If[LessEqual[z, 1.4e-291], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+22], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.89999999999999989e-17 or 1.0499999999999999e22 < z

   1. Initial program 99.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 95.1%

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

      1. *-commutative 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in x around inf 86.7%

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

      1. associate-/r* 78.8%

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

   10. Simplified 78.8%

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

   11. Taylor expanded in z around inf 81.1%

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

   if -3.89999999999999989e-17 < z < 1.4e-291

   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%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 78.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   9. Applied egg-rr 78.8%

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

   if 1.4e-291 < z < 1.0499999999999999e22

   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%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 80.0%

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

   8. Taylor expanded in z around 0 78.3%

      \[\leadsto \frac{60}{\frac{\color{blue}{-1 \cdot t}}{x}} + a \cdot 120 \]
   9. Step-by-step derivation

      1. neg-mul-1 78.3%

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

   10. Simplified 78.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-17}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-291}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-295}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* 60.0 (/ x z)) (* a 120.0))))
   (if (<= z -3.8e-17)
     t_1
     (if (<= z 1.2e-295)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (<= z 1.02e+21) (+ (* a 120.0) (* -60.0 (/ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x / z)) + (a * 120.0);
	double tmp;
	if (z <= -3.8e-17) {
		tmp = t_1;
	} else if (z <= 1.2e-295) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= 1.02e+21) {
		tmp = (a * 120.0) + (-60.0 * (x / 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 = (60.0d0 * (x / z)) + (a * 120.0d0)
    if (z <= (-3.8d-17)) then
        tmp = t_1
    else if (z <= 1.2d-295) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (z <= 1.02d+21) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / 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 = (60.0 * (x / z)) + (a * 120.0);
	double tmp;
	if (z <= -3.8e-17) {
		tmp = t_1;
	} else if (z <= 1.2e-295) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= 1.02e+21) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x / z)) + (a * 120.0)
	tmp = 0
	if z <= -3.8e-17:
		tmp = t_1
	elif z <= 1.2e-295:
		tmp = 60.0 / ((z - t) / (x - y))
	elif z <= 1.02e+21:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x / z)) + Float64(a * 120.0))
	tmp = 0.0
	if (z <= -3.8e-17)
		tmp = t_1;
	elseif (z <= 1.2e-295)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (z <= 1.02e+21)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x / z)) + (a * 120.0);
	tmp = 0.0;
	if (z <= -3.8e-17)
		tmp = t_1;
	elseif (z <= 1.2e-295)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (z <= 1.02e+21)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-17], t$95$1, If[LessEqual[z, 1.2e-295], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+21], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000001e-17 or 1.02e21 < z

   1. Initial program 99.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 95.1%

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

      1. *-commutative 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in x around inf 86.7%

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

      1. associate-/r* 78.8%

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

   10. Simplified 78.8%

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

   11. Taylor expanded in z around inf 81.1%

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

   if -3.8000000000000001e-17 < z < 1.1999999999999999e-295

   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%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 78.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   9. Applied egg-rr 78.8%

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

   if 1.1999999999999999e-295 < z < 1.02e21

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 88.0%

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

      1. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around inf 73.6%

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

      1. associate-/r* 67.7%

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

   10. Simplified 67.7%

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

   11. Taylor expanded in t around inf 78.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-17}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-295}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-293}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* 60.0 (/ x z)) (* a 120.0))))
   (if (<= z -5.8e-17)
     t_1
     (if (<= z 1.15e-293)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= z 1.02e+27) (+ (* a 120.0) (* -60.0 (/ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x / z)) + (a * 120.0);
	double tmp;
	if (z <= -5.8e-17) {
		tmp = t_1;
	} else if (z <= 1.15e-293) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 1.02e+27) {
		tmp = (a * 120.0) + (-60.0 * (x / 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 = (60.0d0 * (x / z)) + (a * 120.0d0)
    if (z <= (-5.8d-17)) then
        tmp = t_1
    else if (z <= 1.15d-293) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (z <= 1.02d+27) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / 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 = (60.0 * (x / z)) + (a * 120.0);
	double tmp;
	if (z <= -5.8e-17) {
		tmp = t_1;
	} else if (z <= 1.15e-293) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 1.02e+27) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x / z)) + (a * 120.0)
	tmp = 0
	if z <= -5.8e-17:
		tmp = t_1
	elif z <= 1.15e-293:
		tmp = 60.0 * ((x - y) / (z - t))
	elif z <= 1.02e+27:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x / z)) + Float64(a * 120.0))
	tmp = 0.0
	if (z <= -5.8e-17)
		tmp = t_1;
	elseif (z <= 1.15e-293)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (z <= 1.02e+27)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x / z)) + (a * 120.0);
	tmp = 0.0;
	if (z <= -5.8e-17)
		tmp = t_1;
	elseif (z <= 1.15e-293)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (z <= 1.02e+27)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-17], t$95$1, If[LessEqual[z, 1.15e-293], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+27], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000006e-17 or 1.0199999999999999e27 < z

   1. Initial program 99.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 95.1%

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

      1. *-commutative 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in x around inf 86.7%

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

      1. associate-/r* 78.8%

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

   10. Simplified 78.8%

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

   11. Taylor expanded in z around inf 81.1%

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

   if -5.8000000000000006e-17 < z < 1.14999999999999998e-293

   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%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 78.8%

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

   if 1.14999999999999998e-293 < z < 1.0199999999999999e27

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 88.0%

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

      1. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in x around inf 73.6%

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

      1. associate-/r* 67.7%

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

   10. Simplified 67.7%

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

   11. Taylor expanded in t around inf 78.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-17}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-293}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+146} \lor \neg \left(z - t \leq 10^{+106}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -5e+146) (not (<= (- z t) 1e+106)))
   (* 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 (((z - t) <= -5e+146) || !((z - t) <= 1e+106)) {
		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 (((z - t) <= (-5d+146)) .or. (.not. ((z - t) <= 1d+106))) 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 (((z - t) <= -5e+146) || !((z - t) <= 1e+106)) {
		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 ((z - t) <= -5e+146) or not ((z - t) <= 1e+106):
		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 ((Float64(z - t) <= -5e+146) || !(Float64(z - t) <= 1e+106))
		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 (((z - t) <= -5e+146) || ~(((z - t) <= 1e+106)))
		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[N[(z - t), $MachinePrecision], -5e+146], N[Not[LessEqual[N[(z - t), $MachinePrecision], 1e+106]], $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 (-.f64 z t) < -4.9999999999999999e146 or 1.00000000000000009e106 < (-.f64 z t)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.1%

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

   if -4.9999999999999999e146 < (-.f64 z t) < 1.00000000000000009e106

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 76.9%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+146} \lor \neg \left(z - t \leq 10^{+106}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{elif}\;x \leq 48000000:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.2e+24)
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
   (if (<= x 48000000.0)
     (+ (/ 60.0 (/ (- t z) y)) (* a 120.0))
     (+ (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.2e+24) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else if (x <= 48000000.0) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4.2d+24)) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else if (x <= 48000000.0d0) then
        tmp = (60.0d0 / ((t - z) / y)) + (a * 120.0d0)
    else
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.2e+24) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else if (x <= 48000000.0) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.2e+24:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	elif x <= 48000000.0:
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0)
	else:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.2e+24)
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	elseif (x <= 48000000.0)
		tmp = Float64(Float64(60.0 / Float64(Float64(t - z) / y)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.2e+24)
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	elseif (x <= 48000000.0)
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	else
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.2e+24], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 48000000.0], N[(N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000003e24

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 94.2%

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

   if -4.2000000000000003e24 < x < 4.8e7

   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%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 94.6%

      \[\leadsto \frac{60}{\frac{z - t}{\color{blue}{-1 \cdot y}}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. neg-mul-1 94.6%

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

   9. Simplified 94.6%

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

   if 4.8e7 < x

   1. Initial program 98.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 88.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{elif}\;x \leq 48000000:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{elif}\;x \leq 20000000:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.15e+24)
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
   (if (<= x 20000000.0)
     (+ (/ (* y -60.0) (- z t)) (* a 120.0))
     (+ (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.15e+24) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else if (x <= 20000000.0) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.15d+24)) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else if (x <= 20000000.0d0) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.15e+24) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else if (x <= 20000000.0) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.15e+24:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	elif x <= 20000000.0:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.15e+24)
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	elseif (x <= 20000000.0)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.15e+24)
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	elseif (x <= 20000000.0)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.15e+24], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 20000000.0], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.14999999999999994e24

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 94.2%

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

   if -2.14999999999999994e24 < x < 2e7

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 94.7%

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

      1. associate-*r/ 94.6%

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

   7. Simplified 94.6%

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

   if 2e7 < x

   1. Initial program 98.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 88.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{elif}\;x \leq 20000000:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+169} \lor \neg \left(x \leq 8.5 \cdot 10^{+161}\right) \land x \leq 7.2 \cdot 10^{+203}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8e+169) (and (not (<= x 8.5e+161)) (<= x 7.2e+203)))
   (* 60.0 (/ x z))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8e+169) || (!(x <= 8.5e+161) && (x <= 7.2e+203))) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-8d+169)) .or. (.not. (x <= 8.5d+161)) .and. (x <= 7.2d+203)) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8e+169) || (!(x <= 8.5e+161) && (x <= 7.2e+203))) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -8e+169) or (not (x <= 8.5e+161) and (x <= 7.2e+203)):
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8e+169) || (!(x <= 8.5e+161) && (x <= 7.2e+203)))
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -8e+169) || (~((x <= 8.5e+161)) && (x <= 7.2e+203)))
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8e+169], And[N[Not[LessEqual[x, 8.5e+161]], $MachinePrecision], LessEqual[x, 7.2e+203]]], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999947e169 or 8.50000000000000007e161 < x < 7.19999999999999964e203

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 81.7%

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

   8. Taylor expanded in x around inf 81.6%

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

   9. Taylor expanded in z around inf 49.6%

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

   if -7.99999999999999947e169 < x < 8.50000000000000007e161 or 7.19999999999999964e203 < x

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 58.3%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+169} \lor \neg \left(x \leq 8.5 \cdot 10^{+161}\right) \land x \leq 7.2 \cdot 10^{+203}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+169} \lor \neg \left(x \leq 6 \cdot 10^{+29}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.3e+169) (not (<= x 6e+29)))
   (* 60.0 (/ x (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.3e+169) || !(x <= 6e+29)) {
		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 ((x <= (-4.3d+169)) .or. (.not. (x <= 6d+29))) 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 ((x <= -4.3e+169) || !(x <= 6e+29)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.3e+169) or not (x <= 6e+29):
		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 ((x <= -4.3e+169) || !(x <= 6e+29))
		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 ((x <= -4.3e+169) || ~((x <= 6e+29)))
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.3e+169], N[Not[LessEqual[x, 6e+29]], $MachinePrecision]], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3000000000000001e169 or 5.9999999999999998e29 < x

   1. Initial program 98.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 75.8%

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

   8. Taylor expanded in x around inf 69.0%

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

   if -4.3000000000000001e169 < x < 5.9999999999999998e29

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 66.1%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+169} \lor \neg \left(x \leq 6 \cdot 10^{+29}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{-60}{\frac{t - z}{x}}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.3e+170)
   (/ -60.0 (/ (- t z) x))
   (if (<= x 6e+29) (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+170) {
		tmp = -60.0 / ((t - z) / x);
	} else if (x <= 6e+29) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.3d+170)) then
        tmp = (-60.0d0) / ((t - z) / x)
    else if (x <= 6d+29) then
        tmp = a * 120.0d0
    else
        tmp = x * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+170) {
		tmp = -60.0 / ((t - z) / x);
	} else if (x <= 6e+29) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.3e+170:
		tmp = -60.0 / ((t - z) / x)
	elif x <= 6e+29:
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.3e+170)
		tmp = Float64(-60.0 / Float64(Float64(t - z) / x));
	elseif (x <= 6e+29)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.3e+170)
		tmp = -60.0 / ((t - z) / x);
	elseif (x <= 6e+29)
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.3e+170], N[(-60.0 / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+29], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2999999999999999e170

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 81.0%

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

   8. Taylor expanded in x around inf 81.0%

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

      1. clear-num 81.0%

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

      2. div-inv 81.2%

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

      3. frac-2neg 81.2%

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

      4. metadata-eval 81.2%

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

      5. distribute-neg-frac2 81.2%

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

   10. Applied egg-rr 81.2%

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

   if -1.2999999999999999e170 < x < 5.9999999999999998e29

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 66.1%

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

   if 5.9999999999999998e29 < x

   1. Initial program 98.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.4%

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

   6. Taylor expanded in x around inf 60.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{-60}{\frac{t - z}{x}}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+169}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.1e+169)
   (* 60.0 (/ x (- z t)))
   (if (<= x 6e+29) (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.1e+169) {
		tmp = 60.0 * (x / (z - t));
	} else if (x <= 6e+29) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.1d+169)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (x <= 6d+29) then
        tmp = a * 120.0d0
    else
        tmp = x * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.1e+169) {
		tmp = 60.0 * (x / (z - t));
	} else if (x <= 6e+29) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.1e+169:
		tmp = 60.0 * (x / (z - t))
	elif x <= 6e+29:
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.1e+169)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (x <= 6e+29)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.1e+169)
		tmp = 60.0 * (x / (z - t));
	elseif (x <= 6e+29)
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.1e+169], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+29], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0999999999999998e169

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 81.0%

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

   8. Taylor expanded in x around inf 81.0%

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

   if -6.0999999999999998e169 < x < 5.9999999999999998e29

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 66.1%

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

   if 5.9999999999999998e29 < x

   1. Initial program 98.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.4%

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

   6. Taylor expanded in x around inf 60.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+169}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+196} \lor \neg \left(y \leq 2.6 \cdot 10^{+247}\right):\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.8e+196) (not (<= y 2.6e+247))) (* 60.0 (/ y t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e+196) || !(y <= 2.6e+247)) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.8d+196)) .or. (.not. (y <= 2.6d+247))) then
        tmp = 60.0d0 * (y / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e+196) || !(y <= 2.6e+247)) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.8e+196) or not (y <= 2.6e+247):
		tmp = 60.0 * (y / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.8e+196) || !(y <= 2.6e+247))
		tmp = Float64(60.0 * Float64(y / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.8e+196) || ~((y <= 2.6e+247)))
		tmp = 60.0 * (y / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.8e+196], N[Not[LessEqual[y, 2.6e+247]], $MachinePrecision]], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000004e196 or 2.59999999999999991e247 < y

   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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.9%

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

      1. associate-*r/ 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in z around 0 61.5%

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

      1. associate-*r/ 61.5%

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

      2. *-commutative 61.5%

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

   10. Simplified 61.5%

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

   11. Taylor expanded in t around 0 58.2%

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

   12. Taylor expanded in y around inf 58.1%

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

   if -1.80000000000000004e196 < y < 2.59999999999999991e247

   1. Initial program 99.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.8%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+196} \lor \neg \left(y \leq 2.6 \cdot 10^{+247}\right):\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+194}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+250}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.5e+194)
   (* 60.0 (/ y t))
   (if (<= y 9.8e+250) (* a 120.0) (/ (* 60.0 y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.5e+194) {
		tmp = 60.0 * (y / t);
	} else if (y <= 9.8e+250) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 * 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 (y <= (-6.5d+194)) then
        tmp = 60.0d0 * (y / t)
    else if (y <= 9.8d+250) then
        tmp = a * 120.0d0
    else
        tmp = (60.0d0 * 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 (y <= -6.5e+194) {
		tmp = 60.0 * (y / t);
	} else if (y <= 9.8e+250) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.5e+194:
		tmp = 60.0 * (y / t)
	elif y <= 9.8e+250:
		tmp = a * 120.0
	else:
		tmp = (60.0 * y) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.5e+194)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (y <= 9.8e+250)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(60.0 * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.5e+194)
		tmp = 60.0 * (y / t);
	elseif (y <= 9.8e+250)
		tmp = a * 120.0;
	else
		tmp = (60.0 * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.5e+194], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+250], N[(a * 120.0), $MachinePrecision], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000005e194

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 84.3%

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

      1. associate-*r/ 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in z around 0 56.0%

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

      1. associate-*r/ 55.9%

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

      2. *-commutative 55.9%

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

   10. Simplified 55.9%

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

   11. Taylor expanded in t around 0 50.8%

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

   12. Taylor expanded in y around inf 50.7%

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

   if -6.50000000000000005e194 < y < 9.79999999999999986e250

   1. Initial program 99.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.8%

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

   if 9.79999999999999986e250 < y

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 71.4%

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

      1. associate-*r/ 71.6%

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

      2. *-commutative 71.6%

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

   10. Simplified 71.6%

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

   11. Taylor expanded in t around 0 71.6%

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

   12. Taylor expanded in y around inf 71.6%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+194}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+250}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 99.7% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

Alternative 18: 49.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around inf 50.6%

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

6. Final simplification 50.6%

   \[\leadsto a \cdot 120 \]
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 2024110 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))