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

Percentage Accurate: 99.4% → 99.8%

Time: 16.2s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% 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

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

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 99.0%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Final simplification 99.7%

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

Alternative 2: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2000000 \lor \neg \left(a \cdot 120 \leq -1 \cdot 10^{-7}\right) \land \left(a \cdot 120 \leq -2 \cdot 10^{-25} \lor \neg \left(a \cdot 120 \leq 10^{+49}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2000000.0)
         (and (not (<= (* a 120.0) -1e-7))
              (or (<= (* a 120.0) -2e-25) (not (<= (* a 120.0) 1e+49)))))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2000000.0) || (!((a * 120.0) <= -1e-7) && (((a * 120.0) <= -2e-25) || !((a * 120.0) <= 1e+49)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2000000.0d0)) .or. (.not. ((a * 120.0d0) <= (-1d-7))) .and. ((a * 120.0d0) <= (-2d-25)) .or. (.not. ((a * 120.0d0) <= 1d+49))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2000000.0) || (!((a * 120.0) <= -1e-7) && (((a * 120.0) <= -2e-25) || !((a * 120.0) <= 1e+49)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2000000.0) or (not ((a * 120.0) <= -1e-7) and (((a * 120.0) <= -2e-25) or not ((a * 120.0) <= 1e+49))):
		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(a * 120.0) <= -2000000.0) || (!(Float64(a * 120.0) <= -1e-7) && ((Float64(a * 120.0) <= -2e-25) || !(Float64(a * 120.0) <= 1e+49))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2000000.0) || (~(((a * 120.0) <= -1e-7)) && (((a * 120.0) <= -2e-25) || ~(((a * 120.0) <= 1e+49)))))
		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[(a * 120.0), $MachinePrecision], -2000000.0], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-7]], $MachinePrecision], Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-25], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+49]], $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 a 120) < -2e6 or -9.9999999999999995e-8 < (*.f64 a 120) < -2.00000000000000008e-25 or 9.99999999999999946e48 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.7%

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

   if -2e6 < (*.f64 a 120) < -9.9999999999999995e-8 or -2.00000000000000008e-25 < (*.f64 a 120) < 9.99999999999999946e48

   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* 99.6%

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

   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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 82.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2000000 \lor \neg \left(a \cdot 120 \leq -1 \cdot 10^{-7}\right) \land \left(a \cdot 120 \leq -2 \cdot 10^{-25} \lor \neg \left(a \cdot 120 \leq 10^{+49}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.1 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 150000:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= a -1.65e-28)
     (* a 120.0)
     (if (<= a -7.1e-228)
       t_1
       (if (<= a -2.8e-280)
         (* x (/ 60.0 (- z t)))
         (if (<= a 3.8e-306)
           t_1
           (if (<= a 150000.0) (* -60.0 (/ (- x y) t)) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.65e-28) {
		tmp = a * 120.0;
	} else if (a <= -7.1e-228) {
		tmp = t_1;
	} else if (a <= -2.8e-280) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 3.8e-306) {
		tmp = t_1;
	} else if (a <= 150000.0) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (a <= (-1.65d-28)) then
        tmp = a * 120.0d0
    else if (a <= (-7.1d-228)) then
        tmp = t_1
    else if (a <= (-2.8d-280)) then
        tmp = x * (60.0d0 / (z - t))
    else if (a <= 3.8d-306) then
        tmp = t_1
    else if (a <= 150000.0d0) then
        tmp = (-60.0d0) * ((x - y) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -1.65e-28) {
		tmp = a * 120.0;
	} else if (a <= -7.1e-228) {
		tmp = t_1;
	} else if (a <= -2.8e-280) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 3.8e-306) {
		tmp = t_1;
	} else if (a <= 150000.0) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -1.65e-28:
		tmp = a * 120.0
	elif a <= -7.1e-228:
		tmp = t_1
	elif a <= -2.8e-280:
		tmp = x * (60.0 / (z - t))
	elif a <= 3.8e-306:
		tmp = t_1
	elif a <= 150000.0:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.65e-28)
		tmp = Float64(a * 120.0);
	elseif (a <= -7.1e-228)
		tmp = t_1;
	elseif (a <= -2.8e-280)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (a <= 3.8e-306)
		tmp = t_1;
	elseif (a <= 150000.0)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (a <= -1.65e-28)
		tmp = a * 120.0;
	elseif (a <= -7.1e-228)
		tmp = t_1;
	elseif (a <= -2.8e-280)
		tmp = x * (60.0 / (z - t));
	elseif (a <= 3.8e-306)
		tmp = t_1;
	elseif (a <= 150000.0)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e-28], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -7.1e-228], t$95$1, If[LessEqual[a, -2.8e-280], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-306], t$95$1, If[LessEqual[a, 150000.0], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6500000000000001e-28 or 1.5e5 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.4%

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

   if -1.6500000000000001e-28 < a < -7.1000000000000005e-228 or -2.80000000000000017e-280 < a < 3.8e-306

   1. Initial program 97.9%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 80.3%

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

   8. Taylor expanded in x around 0 50.8%

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

   if -7.1000000000000005e-228 < a < -2.80000000000000017e-280

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 90.3%

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

   8. Taylor expanded in x around inf 78.4%

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

      1. associate-*r/ 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if 3.8e-306 < a < 1.5e5

   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* 99.6%

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

   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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 83.5%

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

   8. Taylor expanded in z around 0 52.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.1 \cdot 10^{-228}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-306}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 150000:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+49}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+111)
   (* a 120.0)
   (if (<= (* a 120.0) -4e-41)
     (+ (* a 120.0) (* y (/ 60.0 t)))
     (if (<= (* a 120.0) 1e+49) (* 60.0 (/ (- x y) (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+111) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-41) {
		tmp = (a * 120.0) + (y * (60.0 / t));
	} else if ((a * 120.0) <= 1e+49) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-4d+111)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-4d-41)) then
        tmp = (a * 120.0d0) + (y * (60.0d0 / t))
    else if ((a * 120.0d0) <= 1d+49) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+111) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-41) {
		tmp = (a * 120.0) + (y * (60.0 / t));
	} else if ((a * 120.0) <= 1e+49) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+111:
		tmp = a * 120.0
	elif (a * 120.0) <= -4e-41:
		tmp = (a * 120.0) + (y * (60.0 / t))
	elif (a * 120.0) <= 1e+49:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+111)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -4e-41)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(60.0 / t)));
	elseif (Float64(a * 120.0) <= 1e+49)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e+111)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -4e-41)
		tmp = (a * 120.0) + (y * (60.0 / t));
	elseif ((a * 120.0) <= 1e+49)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+111], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-41], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+49], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -3.99999999999999983e111 or 9.99999999999999946e48 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -3.99999999999999983e111 < (*.f64 a 120) < -4.00000000000000002e-41

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-*l/ 87.7%

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

      3. associate-/l* 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 78.9%

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

   if -4.00000000000000002e-41 < (*.f64 a 120) < 9.99999999999999946e48

   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* 99.6%

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

   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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 82.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+49}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + \frac{y}{t \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+49}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+111)
   (* a 120.0)
   (if (<= (* a 120.0) -4e-41)
     (+ (* a 120.0) (/ y (* t 0.016666666666666666)))
     (if (<= (* a 120.0) 1e+49) (* 60.0 (/ (- x y) (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+111) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-41) {
		tmp = (a * 120.0) + (y / (t * 0.016666666666666666));
	} else if ((a * 120.0) <= 1e+49) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-4d+111)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-4d-41)) then
        tmp = (a * 120.0d0) + (y / (t * 0.016666666666666666d0))
    else if ((a * 120.0d0) <= 1d+49) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+111) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e-41) {
		tmp = (a * 120.0) + (y / (t * 0.016666666666666666));
	} else if ((a * 120.0) <= 1e+49) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+111:
		tmp = a * 120.0
	elif (a * 120.0) <= -4e-41:
		tmp = (a * 120.0) + (y / (t * 0.016666666666666666))
	elif (a * 120.0) <= 1e+49:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+111)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -4e-41)
		tmp = Float64(Float64(a * 120.0) + Float64(y / Float64(t * 0.016666666666666666)));
	elseif (Float64(a * 120.0) <= 1e+49)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e+111)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -4e-41)
		tmp = (a * 120.0) + (y / (t * 0.016666666666666666));
	elseif ((a * 120.0) <= 1e+49)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+111], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-41], N[(N[(a * 120.0), $MachinePrecision] + N[(y / N[(t * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+49], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -3.99999999999999983e111 or 9.99999999999999946e48 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -3.99999999999999983e111 < (*.f64 a 120) < -4.00000000000000002e-41

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-*l/ 87.7%

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

      3. associate-/l* 87.7%

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

   7. Simplified 87.7%

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

      1. clear-num 87.7%

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

      2. un-div-inv 87.7%

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

      3. div-inv 87.7%

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

      4. metadata-eval 87.7%

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

   9. Applied egg-rr 87.7%

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

   10. Taylor expanded in z around 0 78.9%

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

       1. *-commutative 78.9%

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

   12. Simplified 78.9%

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

   if -4.00000000000000002e-41 < (*.f64 a 120) < 9.99999999999999946e48

   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* 99.6%

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

   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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 82.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + \frac{y}{t \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+49}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-228}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 106000:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e-28)
   (* a 120.0)
   (if (<= a -6.2e-228)
     (* -60.0 (/ y (- z t)))
     (if (<= a 106000.0) (* -60.0 (/ (- x y) t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-28) {
		tmp = a * 120.0;
	} else if (a <= -6.2e-228) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 106000.0) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.65d-28)) then
        tmp = a * 120.0d0
    else if (a <= (-6.2d-228)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 106000.0d0) then
        tmp = (-60.0d0) * ((x - y) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-28) {
		tmp = a * 120.0;
	} else if (a <= -6.2e-228) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 106000.0) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e-28:
		tmp = a * 120.0
	elif a <= -6.2e-228:
		tmp = -60.0 * (y / (z - t))
	elif a <= 106000.0:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e-28)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.2e-228)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 106000.0)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e-28)
		tmp = a * 120.0;
	elseif (a <= -6.2e-228)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 106000.0)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e-28], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.2e-228], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 106000.0], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6500000000000001e-28 or 106000 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.4%

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

   if -1.6500000000000001e-28 < a < -6.1999999999999996e-228

   1. Initial program 97.5%

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

      1. associate-/l* 99.6%

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

   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 99.4%

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

      2. un-div-inv 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 75.1%

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

   8. Taylor expanded in x around 0 45.5%

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

   if -6.1999999999999996e-228 < a < 106000

   1. Initial program 98.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 86.7%

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

   8. Taylor expanded in z around 0 51.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-228}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 106000:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.95 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-283}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 460000:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.95e-54)
   (* a 120.0)
   (if (<= a -9.5e-283)
     (* (- x y) (/ 60.0 z))
     (if (<= a 460000.0) (* -60.0 (/ (- x y) t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.95e-54) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-283) {
		tmp = (x - y) * (60.0 / z);
	} else if (a <= 460000.0) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.95d-54)) then
        tmp = a * 120.0d0
    else if (a <= (-9.5d-283)) then
        tmp = (x - y) * (60.0d0 / z)
    else if (a <= 460000.0d0) then
        tmp = (-60.0d0) * ((x - y) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.95e-54) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-283) {
		tmp = (x - y) * (60.0 / z);
	} else if (a <= 460000.0) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.95e-54:
		tmp = a * 120.0
	elif a <= -9.5e-283:
		tmp = (x - y) * (60.0 / z)
	elif a <= 460000.0:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.95e-54)
		tmp = Float64(a * 120.0);
	elseif (a <= -9.5e-283)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	elseif (a <= 460000.0)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.95e-54)
		tmp = a * 120.0;
	elseif (a <= -9.5e-283)
		tmp = (x - y) * (60.0 / z);
	elseif (a <= 460000.0)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.95e-54], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9.5e-283], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 460000.0], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.95000000000000018e-54 or 4.6e5 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 74.5%

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

   if -4.95000000000000018e-54 < a < -9.49999999999999979e-283

   1. Initial program 97.5%

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

      1. associate-/l* 99.6%

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

   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 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 78.8%

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

   8. Taylor expanded in z around inf 51.5%

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

      1. associate-*r/ 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-/l* 51.5%

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

   10. Simplified 51.5%

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

   if -9.49999999999999979e-283 < a < 4.6e5

   1. Initial program 98.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 86.2%

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

   8. Taylor expanded in z around 0 53.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.95 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-283}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 460000:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+34} \lor \neg \left(y \leq 2200000000\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.7e+34) (not (<= y 2200000000.0)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.7e+34) || !(y <= 2200000000.0)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (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 ((y <= (-3.7d+34)) .or. (.not. (y <= 2200000000.0d0))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = (a * 120.0d0) + (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 ((y <= -3.7e+34) || !(y <= 2200000000.0)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.7e+34) or not (y <= 2200000000.0):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.7e+34) || !(y <= 2200000000.0))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + 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 ((y <= -3.7e+34) || ~((y <= 2200000000.0)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.7e+34], N[Not[LessEqual[y, 2200000000.0]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000009e34 or 2.2e9 < y

   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 0 88.0%

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

   if -3.70000000000000009e34 < y < 2.2e9

   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 x around inf 94.4%

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

      1. associate-*r/ 38.9%

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

      2. *-commutative 38.9%

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

      3. associate-/l* 38.9%

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

   7. Simplified 94.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+34} \lor \neg \left(y \leq 2200000000\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+104}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.6e+130)
   (/ 60.0 (/ (- z t) (- x y)))
   (if (<= x 1.6e+104)
     (+ (* a 120.0) (* -60.0 (/ y (- z t))))
     (* 60.0 (/ (- x y) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.6e+130) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (x <= 1.6e+104) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} 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 (x <= (-2.6d+130)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (x <= 1.6d+104) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    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 (x <= -2.6e+130) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (x <= 1.6e+104) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.6e+130:
		tmp = 60.0 / ((z - t) / (x - y))
	elif x <= 1.6e+104:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.6e+130)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (x <= 1.6e+104)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	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 (x <= -2.6e+130)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (x <= 1.6e+104)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.6e+130], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+104], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999998e130

   1. Initial program 96.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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 99.7%

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

   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 81.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. 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 99.7%

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

   9. Applied egg-rr 81.8%

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

   if -2.5999999999999998e130 < x < 1.6e104

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   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%

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

   if 1.6e104 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   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 99.4%

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

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 87.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+104}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+33}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 250000000000:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9.2e+33)
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (if (<= y 250000000000.0)
     (+ (* a 120.0) (* x (/ 60.0 (- z t))))
     (+ (* a 120.0) (* y (/ -60.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.2e+33) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (y <= 250000000000.0) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-9.2d+33)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else if (y <= 250000000000.0d0) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    else
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.2e+33) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (y <= 250000000000.0) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.2e+33:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	elif y <= 250000000000.0:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.2e+33)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	elseif (y <= 250000000000.0)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.2e+33)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	elseif (y <= 250000000000.0)
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	else
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.2e+33], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 250000000000.0], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.20000000000000042e33

   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 x around 0 92.0%

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

   if -9.20000000000000042e33 < y < 2.5e11

   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 x around inf 94.4%

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

      1. associate-*r/ 38.9%

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

      2. *-commutative 38.9%

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

      3. associate-/l* 38.9%

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

   7. Simplified 94.5%

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

   if 2.5e11 < y

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in x around 0 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 83.0%

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

      3. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+33}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 250000000000:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+41}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.1e+34)
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (if (<= y 7.6e+41)
     (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
     (+ (* a 120.0) (* y (/ -60.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+34) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (y <= 7.6e+41) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.1d+34)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else if (y <= 7.6d+41) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+34) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (y <= 7.6e+41) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.1e+34:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	elif y <= 7.6e+41:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.1e+34)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	elseif (y <= 7.6e+41)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.1e+34)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	elseif (y <= 7.6e+41)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	else
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.1e+34], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e+41], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1000000000000001e34

   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 x around 0 92.0%

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

   if -1.1000000000000001e34 < y < 7.6000000000000003e41

   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 x around inf 94.0%

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

   if 7.6000000000000003e41 < y

   1. Initial program 96.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 83.0%

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

      3. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+41}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-29} \lor \neg \left(a \leq 106000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e-29) (not (<= a 106000.0)))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e-29) || !(a <= 106000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.9d-29)) .or. (.not. (a <= 106000.0d0))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e-29) || !(a <= 106000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e-29) or not (a <= 106000.0):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e-29) || !(a <= 106000.0))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e-29) || ~((a <= 106000.0)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e-29], N[Not[LessEqual[a, 106000.0]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999988e-29 or 106000 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.4%

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

   if -1.89999999999999988e-29 < a < 106000

   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* 99.6%

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

   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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 82.4%

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

   8. Taylor expanded in x around 0 46.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-29} \lor \neg \left(a \leq 106000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-86} \lor \neg \left(a \leq 8.8 \cdot 10^{-224}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.6e-86) (not (<= a 8.8e-224))) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e-86) || !(a <= 8.8e-224)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.6d-86)) .or. (.not. (a <= 8.8d-224))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e-86) || !(a <= 8.8e-224)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.6e-86) or not (a <= 8.8e-224):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.6e-86) || !(a <= 8.8e-224))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.6e-86) || ~((a <= 8.8e-224)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.6e-86], N[Not[LessEqual[a, 8.8e-224]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000001e-86 or 8.8000000000000004e-224 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   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 58.8%

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

   if -2.6000000000000001e-86 < a < 8.8000000000000004e-224

   1. Initial program 98.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 89.1%

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

   8. Taylor expanded in x around 0 50.8%

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

   9. Taylor expanded in z around inf 33.1%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-86} \lor \neg \left(a \leq 8.8 \cdot 10^{-224}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+163}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.45e+163)
   (* -60.0 (/ y z))
   (if (<= y 5e+190) (* a 120.0) (* 60.0 (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.45e+163) {
		tmp = -60.0 * (y / z);
	} else if (y <= 5e+190) {
		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 <= (-1.45d+163)) then
        tmp = (-60.0d0) * (y / z)
    else if (y <= 5d+190) 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 <= -1.45e+163) {
		tmp = -60.0 * (y / z);
	} else if (y <= 5e+190) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.45e+163:
		tmp = -60.0 * (y / z)
	elif y <= 5e+190:
		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 <= -1.45e+163)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (y <= 5e+190)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.45e+163)
		tmp = -60.0 * (y / z);
	elseif (y <= 5e+190)
		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, -1.45e+163], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+190], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.44999999999999999e163

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 79.7%

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

   8. Taylor expanded in x around 0 71.8%

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

   9. Taylor expanded in z around inf 56.0%

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

   if -1.44999999999999999e163 < y < 5.00000000000000036e190

   1. Initial program 99.2%

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

      1. associate-/l* 99.7%

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

   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 54.0%

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

   if 5.00000000000000036e190 < y

   1. Initial program 95.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.5%

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

      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 78.6%

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

   8. Taylor expanded in x around 0 67.3%

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

   9. Taylor expanded in z around 0 41.9%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+163}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+190}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.2% 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 99.0%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 46.9%

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

6. Final simplification 46.9%

   \[\leadsto a \cdot 120 \]
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 2024039 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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