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

Percentage Accurate: 99.4% → 99.8%

Time: 14.0s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

   2. fma-define 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -5e+67)
     (* a 120.0)
     (if (<= (* a 120.0) -5e-60)
       t_1
       (if (<= (* a 120.0) -1e-93)
         (+ (* a 120.0) (* -60.0 (/ y z)))
         (if (<= (* a 120.0) 2e-96)
           t_1
           (if (<= (* a 120.0) 1e-75)
             (* a 120.0)
             (if (<= (* a 120.0) 2e-39)
               t_1
               (+ (* a 120.0) (* x (/ -60.0 t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-60) {
		tmp = t_1;
	} else if ((a * 120.0) <= -1e-93) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e-96) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-75) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-39) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-5d+67)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-5d-60)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-1d-93)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 2d-96) then
        tmp = t_1
    else if ((a * 120.0d0) <= 1d-75) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-39) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e-60) {
		tmp = t_1;
	} else if ((a * 120.0) <= -1e-93) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 2e-96) {
		tmp = t_1;
	} else if ((a * 120.0) <= 1e-75) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-39) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -5e+67:
		tmp = a * 120.0
	elif (a * 120.0) <= -5e-60:
		tmp = t_1
	elif (a * 120.0) <= -1e-93:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 2e-96:
		tmp = t_1
	elif (a * 120.0) <= 1e-75:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-39:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+67)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -5e-60)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -1e-93)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 2e-96)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 1e-75)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-39)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+67)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -5e-60)
		tmp = t_1;
	elseif ((a * 120.0) <= -1e-93)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 2e-96)
		tmp = t_1;
	elseif ((a * 120.0) <= 1e-75)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-39)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (x * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+67], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-60], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-93], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-96], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-75], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-39], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.99999999999999976e67 or 1.9999999999999998e-96 < (*.f64 a #s(literal 120 binary64)) < 9.9999999999999996e-76

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.7%

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

   if -4.99999999999999976e67 < (*.f64 a #s(literal 120 binary64)) < -5.0000000000000001e-60 or -9.999999999999999e-94 < (*.f64 a #s(literal 120 binary64)) < 1.9999999999999998e-96 or 9.9999999999999996e-76 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999986e-39

   1. Initial program 98.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 84.0%

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

   if -5.0000000000000001e-60 < (*.f64 a #s(literal 120 binary64)) < -9.999999999999999e-94

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. +-commutative 84.8%

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

      2. fma-define 84.8%

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

      3. associate-*r/ 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in z around inf 84.8%

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

   if 1.99999999999999986e-39 < (*.f64 a #s(literal 120 binary64))

   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 x around inf 88.0%

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

      1. associate-*r/ 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-*r/ 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in z around 0 74.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-60}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-96}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-75}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-39}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+62} \lor \neg \left(a \leq -1.16 \cdot 10^{-64}\right) \land \left(a \leq -1.5 \cdot 10^{-95} \lor \neg \left(a \leq 2.5 \cdot 10^{-92} \lor \neg \left(a \leq 5.8 \cdot 10^{-78}\right) \land a \leq 1.2 \cdot 10^{-8}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e+62)
         (and (not (<= a -1.16e-64))
              (or (<= a -1.5e-95)
                  (not
                   (or (<= a 2.5e-92)
                       (and (not (<= a 5.8e-78)) (<= a 1.2e-8)))))))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e+62) || (!(a <= -1.16e-64) && ((a <= -1.5e-95) || !((a <= 2.5e-92) || (!(a <= 5.8e-78) && (a <= 1.2e-8)))))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.35d+62)) .or. (.not. (a <= (-1.16d-64))) .and. (a <= (-1.5d-95)) .or. (.not. (a <= 2.5d-92) .or. (.not. (a <= 5.8d-78)) .and. (a <= 1.2d-8))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e+62) || (!(a <= -1.16e-64) && ((a <= -1.5e-95) || !((a <= 2.5e-92) || (!(a <= 5.8e-78) && (a <= 1.2e-8)))))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.35e+62) or (not (a <= -1.16e-64) and ((a <= -1.5e-95) or not ((a <= 2.5e-92) or (not (a <= 5.8e-78) and (a <= 1.2e-8))))):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.35e+62) || (!(a <= -1.16e-64) && ((a <= -1.5e-95) || !((a <= 2.5e-92) || (!(a <= 5.8e-78) && (a <= 1.2e-8))))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.35e+62) || (~((a <= -1.16e-64)) && ((a <= -1.5e-95) || ~(((a <= 2.5e-92) || (~((a <= 5.8e-78)) && (a <= 1.2e-8)))))))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.35e+62], And[N[Not[LessEqual[a, -1.16e-64]], $MachinePrecision], Or[LessEqual[a, -1.5e-95], N[Not[Or[LessEqual[a, 2.5e-92], And[N[Not[LessEqual[a, 5.8e-78]], $MachinePrecision], LessEqual[a, 1.2e-8]]]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35e62 or -1.15999999999999992e-64 < a < -1.5e-95 or 2.50000000000000006e-92 < a < 5.8000000000000001e-78 or 1.19999999999999999e-8 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   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 77.0%

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

   if -1.35e62 < a < -1.15999999999999992e-64 or -1.5e-95 < a < 2.50000000000000006e-92 or 5.8000000000000001e-78 < a < 1.19999999999999999e-8

   1. Initial program 98.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 83.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+62} \lor \neg \left(a \leq -1.16 \cdot 10^{-64}\right) \land \left(a \leq -1.5 \cdot 10^{-95} \lor \neg \left(a \leq 2.5 \cdot 10^{-92} \lor \neg \left(a \leq 5.8 \cdot 10^{-78}\right) \land a \leq 1.2 \cdot 10^{-8}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-92} \lor \neg \left(a \leq 5.8 \cdot 10^{-78}\right) \land a \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= a -2.15e+60)
     (* a 120.0)
     (if (<= a -1.16e-64)
       t_1
       (if (<= a -1.55e-95)
         (+ (* a 120.0) (* -60.0 (/ y z)))
         (if (or (<= a 3.9e-92) (and (not (<= a 5.8e-78)) (<= a 1.15e-9)))
           t_1
           (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (a <= -2.15e+60) {
		tmp = a * 120.0;
	} else if (a <= -1.16e-64) {
		tmp = t_1;
	} else if (a <= -1.55e-95) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a <= 3.9e-92) || (!(a <= 5.8e-78) && (a <= 1.15e-9))) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (a <= (-2.15d+60)) then
        tmp = a * 120.0d0
    else if (a <= (-1.16d-64)) then
        tmp = t_1
    else if (a <= (-1.55d-95)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a <= 3.9d-92) .or. (.not. (a <= 5.8d-78)) .and. (a <= 1.15d-9)) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (a <= -2.15e+60) {
		tmp = a * 120.0;
	} else if (a <= -1.16e-64) {
		tmp = t_1;
	} else if (a <= -1.55e-95) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a <= 3.9e-92) || (!(a <= 5.8e-78) && (a <= 1.15e-9))) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if a <= -2.15e+60:
		tmp = a * 120.0
	elif a <= -1.16e-64:
		tmp = t_1
	elif a <= -1.55e-95:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a <= 3.9e-92) or (not (a <= 5.8e-78) and (a <= 1.15e-9)):
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (a <= -2.15e+60)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.16e-64)
		tmp = t_1;
	elseif (a <= -1.55e-95)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif ((a <= 3.9e-92) || (!(a <= 5.8e-78) && (a <= 1.15e-9)))
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if (a <= -2.15e+60)
		tmp = a * 120.0;
	elseif (a <= -1.16e-64)
		tmp = t_1;
	elseif (a <= -1.55e-95)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a <= 3.9e-92) || (~((a <= 5.8e-78)) && (a <= 1.15e-9)))
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e+60], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.16e-64], t$95$1, If[LessEqual[a, -1.55e-95], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3.9e-92], And[N[Not[LessEqual[a, 5.8e-78]], $MachinePrecision], LessEqual[a, 1.15e-9]]], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.14999999999999986e60 or 3.8999999999999997e-92 < a < 5.8000000000000001e-78 or 1.15e-9 < a

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   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 76.7%

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

   if -2.14999999999999986e60 < a < -1.15999999999999992e-64 or -1.54999999999999996e-95 < a < 3.8999999999999997e-92 or 5.8000000000000001e-78 < a < 1.15e-9

   1. Initial program 98.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 83.6%

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

   if -1.15999999999999992e-64 < a < -1.54999999999999996e-95

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. +-commutative 84.8%

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

      2. fma-define 84.8%

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

      3. associate-*r/ 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in z around inf 84.8%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-64}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-92} \lor \neg \left(a \leq 5.8 \cdot 10^{-78}\right) \land a \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -0.82:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-271}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-125}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))))
   (if (<= a -4.7e+60)
     (* a 120.0)
     (if (<= a -0.82)
       t_1
       (if (<= a -1.3e-112)
         (* a 120.0)
         (if (<= a -1.15e-237)
           t_1
           (if (<= a 2.1e-271)
             (* -60.0 (/ y (- z t)))
             (if (<= a 8e-125) (* 60.0 (/ (- x y) z)) (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -4.7e+60) {
		tmp = a * 120.0;
	} else if (a <= -0.82) {
		tmp = t_1;
	} else if (a <= -1.3e-112) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-237) {
		tmp = t_1;
	} else if (a <= 2.1e-271) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8e-125) {
		tmp = 60.0 * ((x - y) / 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) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * ((x - y) / t)
    if (a <= (-4.7d+60)) then
        tmp = a * 120.0d0
    else if (a <= (-0.82d0)) then
        tmp = t_1
    else if (a <= (-1.3d-112)) then
        tmp = a * 120.0d0
    else if (a <= (-1.15d-237)) then
        tmp = t_1
    else if (a <= 2.1d-271) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 8d-125) then
        tmp = 60.0d0 * ((x - y) / 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 t_1 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -4.7e+60) {
		tmp = a * 120.0;
	} else if (a <= -0.82) {
		tmp = t_1;
	} else if (a <= -1.3e-112) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-237) {
		tmp = t_1;
	} else if (a <= 2.1e-271) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8e-125) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	tmp = 0
	if a <= -4.7e+60:
		tmp = a * 120.0
	elif a <= -0.82:
		tmp = t_1
	elif a <= -1.3e-112:
		tmp = a * 120.0
	elif a <= -1.15e-237:
		tmp = t_1
	elif a <= 2.1e-271:
		tmp = -60.0 * (y / (z - t))
	elif a <= 8e-125:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -4.7e+60)
		tmp = Float64(a * 120.0);
	elseif (a <= -0.82)
		tmp = t_1;
	elseif (a <= -1.3e-112)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.15e-237)
		tmp = t_1;
	elseif (a <= 2.1e-271)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 8e-125)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * ((x - y) / t);
	tmp = 0.0;
	if (a <= -4.7e+60)
		tmp = a * 120.0;
	elseif (a <= -0.82)
		tmp = t_1;
	elseif (a <= -1.3e-112)
		tmp = a * 120.0;
	elseif (a <= -1.15e-237)
		tmp = t_1;
	elseif (a <= 2.1e-271)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 8e-125)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e+60], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -0.82], t$95$1, If[LessEqual[a, -1.3e-112], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.15e-237], t$95$1, If[LessEqual[a, 2.1e-271], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-125], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.6999999999999998e60 or -0.819999999999999951 < a < -1.29999999999999996e-112 or 8.0000000000000001e-125 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 70.2%

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

   if -4.6999999999999998e60 < a < -0.819999999999999951 or -1.29999999999999996e-112 < a < -1.15000000000000006e-237

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 84.7%

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

   6. Taylor expanded in z around 0 55.7%

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

   if -1.15000000000000006e-237 < a < 2.1000000000000001e-271

   1. Initial program 95.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 0 95.7%

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

   6. Taylor expanded in x around 0 74.8%

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

   if 2.1000000000000001e-271 < a < 8.0000000000000001e-125

   1. Initial program 99.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 89.9%

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

   6. Taylor expanded in z around inf 53.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -0.82:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-237}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-271}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-125}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -50000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+67)
   (* a 120.0)
   (if (<= (* a 120.0) -50000000.0)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) -1e-93)
       (+ (* a 120.0) (* x (/ 60.0 z)))
       (if (<= (* a 120.0) 5e-129)
         (/ 60.0 (/ (- z t) (- x y)))
         (+ (* a 120.0) (/ (* x -60.0) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -50000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= -1e-93) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if ((a * 120.0) <= 5e-129) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d+67)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-50000000.0d0)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= (-1d-93)) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / z))
    else if ((a * 120.0d0) <= 5d-129) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -50000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= -1e-93) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if ((a * 120.0) <= 5e-129) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+67:
		tmp = a * 120.0
	elif (a * 120.0) <= -50000000.0:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= -1e-93:
		tmp = (a * 120.0) + (x * (60.0 / z))
	elif (a * 120.0) <= 5e-129:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+67)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -50000000.0)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= -1e-93)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	elseif (Float64(a * 120.0) <= 5e-129)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e+67)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -50000000.0)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= -1e-93)
		tmp = (a * 120.0) + (x * (60.0 / z));
	elseif ((a * 120.0) <= 5e-129)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + ((x * -60.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+67], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -50000000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-93], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-129], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.99999999999999976e67

   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* 99.9%

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

   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 86.4%

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

   if -4.99999999999999976e67 < (*.f64 a #s(literal 120 binary64)) < -5e7

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 82.0%

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

   if -5e7 < (*.f64 a #s(literal 120 binary64)) < -9.999999999999999e-94

   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* 99.7%

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

   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 86.1%

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

      1. associate-*r/ 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*r/ 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in z around inf 79.3%

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

   if -9.999999999999999e-94 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000027e-129

   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. Taylor expanded in a around 0 89.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   6. 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%

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

   7. Applied egg-rr 89.5%

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

   if 5.00000000000000027e-129 < (*.f64 a #s(literal 120 binary64))

   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 x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in z around 0 71.5%

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

      1. associate-*r/ 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -50000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -50000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -5e+67)
     (* a 120.0)
     (if (<= (* a 120.0) -50000000.0)
       t_1
       (if (<= (* a 120.0) -2e-110)
         (+ (* a 120.0) (* x (/ 60.0 z)))
         (if (<= (* a 120.0) 5e-129)
           t_1
           (+ (* a 120.0) (/ (* x -60.0) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -50000000.0) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-110) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if ((a * 120.0) <= 5e-129) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-5d+67)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-50000000.0d0)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2d-110)) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / z))
    else if ((a * 120.0d0) <= 5d-129) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -50000000.0) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-110) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if ((a * 120.0) <= 5e-129) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -5e+67:
		tmp = a * 120.0
	elif (a * 120.0) <= -50000000.0:
		tmp = t_1
	elif (a * 120.0) <= -2e-110:
		tmp = (a * 120.0) + (x * (60.0 / z))
	elif (a * 120.0) <= 5e-129:
		tmp = t_1
	else:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+67)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -50000000.0)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2e-110)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	elseif (Float64(a * 120.0) <= 5e-129)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+67)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -50000000.0)
		tmp = t_1;
	elseif ((a * 120.0) <= -2e-110)
		tmp = (a * 120.0) + (x * (60.0 / z));
	elseif ((a * 120.0) <= 5e-129)
		tmp = t_1;
	else
		tmp = (a * 120.0) + ((x * -60.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+67], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -50000000.0], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-110], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-129], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.99999999999999976e67

   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* 99.9%

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

   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 86.4%

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

   if -4.99999999999999976e67 < (*.f64 a #s(literal 120 binary64)) < -5e7 or -2.0000000000000001e-110 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000027e-129

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 89.1%

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

   if -5e7 < (*.f64 a #s(literal 120 binary64)) < -2.0000000000000001e-110

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 84.8%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r/ 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in z around inf 77.3%

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

   if 5.00000000000000027e-129 < (*.f64 a #s(literal 120 binary64))

   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 x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in z around 0 71.5%

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

      1. associate-*r/ 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -50000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-129}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -50000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -5e+67)
     (* a 120.0)
     (if (<= (* a 120.0) -50000000.0)
       t_1
       (if (<= (* a 120.0) -2e-110)
         (+ (* a 120.0) (* x (/ 60.0 z)))
         (if (<= (* a 120.0) 5e-129)
           t_1
           (+ (* a 120.0) (* x (/ -60.0 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -50000000.0) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-110) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if ((a * 120.0) <= 5e-129) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-5d+67)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-50000000.0d0)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2d-110)) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / z))
    else if ((a * 120.0d0) <= 5d-129) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+67) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -50000000.0) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-110) {
		tmp = (a * 120.0) + (x * (60.0 / z));
	} else if ((a * 120.0) <= 5e-129) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -5e+67:
		tmp = a * 120.0
	elif (a * 120.0) <= -50000000.0:
		tmp = t_1
	elif (a * 120.0) <= -2e-110:
		tmp = (a * 120.0) + (x * (60.0 / z))
	elif (a * 120.0) <= 5e-129:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+67)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -50000000.0)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2e-110)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / z)));
	elseif (Float64(a * 120.0) <= 5e-129)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+67)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -50000000.0)
		tmp = t_1;
	elseif ((a * 120.0) <= -2e-110)
		tmp = (a * 120.0) + (x * (60.0 / z));
	elseif ((a * 120.0) <= 5e-129)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (x * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+67], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -50000000.0], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-110], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-129], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.99999999999999976e67

   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* 99.9%

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

   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 86.4%

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

   if -4.99999999999999976e67 < (*.f64 a #s(literal 120 binary64)) < -5e7 or -2.0000000000000001e-110 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000027e-129

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 89.1%

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

   if -5e7 < (*.f64 a #s(literal 120 binary64)) < -2.0000000000000001e-110

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 84.8%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r/ 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in z around inf 77.3%

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

   if 5.00000000000000027e-129 < (*.f64 a #s(literal 120 binary64))

   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 x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in z around 0 71.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -50000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-129}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -40000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-133}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))))
   (if (<= a -2.15e+60)
     (* a 120.0)
     (if (<= a -40000.0)
       t_1
       (if (<= a -2.1e-112)
         (* a 120.0)
         (if (<= a -8.5e-245)
           t_1
           (if (<= a 2.5e-133) (* -60.0 (/ y (- z t))) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -2.15e+60) {
		tmp = a * 120.0;
	} else if (a <= -40000.0) {
		tmp = t_1;
	} else if (a <= -2.1e-112) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-245) {
		tmp = t_1;
	} else if (a <= 2.5e-133) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * ((x - y) / t)
    if (a <= (-2.15d+60)) then
        tmp = a * 120.0d0
    else if (a <= (-40000.0d0)) then
        tmp = t_1
    else if (a <= (-2.1d-112)) then
        tmp = a * 120.0d0
    else if (a <= (-8.5d-245)) then
        tmp = t_1
    else if (a <= 2.5d-133) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -2.15e+60) {
		tmp = a * 120.0;
	} else if (a <= -40000.0) {
		tmp = t_1;
	} else if (a <= -2.1e-112) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-245) {
		tmp = t_1;
	} else if (a <= 2.5e-133) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	tmp = 0
	if a <= -2.15e+60:
		tmp = a * 120.0
	elif a <= -40000.0:
		tmp = t_1
	elif a <= -2.1e-112:
		tmp = a * 120.0
	elif a <= -8.5e-245:
		tmp = t_1
	elif a <= 2.5e-133:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -2.15e+60)
		tmp = Float64(a * 120.0);
	elseif (a <= -40000.0)
		tmp = t_1;
	elseif (a <= -2.1e-112)
		tmp = Float64(a * 120.0);
	elseif (a <= -8.5e-245)
		tmp = t_1;
	elseif (a <= 2.5e-133)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * ((x - y) / t);
	tmp = 0.0;
	if (a <= -2.15e+60)
		tmp = a * 120.0;
	elseif (a <= -40000.0)
		tmp = t_1;
	elseif (a <= -2.1e-112)
		tmp = a * 120.0;
	elseif (a <= -8.5e-245)
		tmp = t_1;
	elseif (a <= 2.5e-133)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e+60], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -40000.0], t$95$1, If[LessEqual[a, -2.1e-112], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8.5e-245], t$95$1, If[LessEqual[a, 2.5e-133], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.14999999999999986e60 or -4e4 < a < -2.1000000000000001e-112 or 2.5e-133 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.8%

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

   if -2.14999999999999986e60 < a < -4e4 or -2.1000000000000001e-112 < a < -8.50000000000000022e-245

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 84.7%

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

   6. Taylor expanded in z around 0 55.7%

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

   if -8.50000000000000022e-245 < a < 2.5e-133

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 92.3%

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

   6. Taylor expanded in x around 0 58.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -40000:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-245}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-133}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -280000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-289}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+131}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= x -280000000000.0)
     t_1
     (if (<= x -4.9e-200)
       (* a 120.0)
       (if (<= x -3.1e-289)
         (/ (* y -60.0) (- z t))
         (if (<= x 9.2e+131) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -280000000000.0) {
		tmp = t_1;
	} else if (x <= -4.9e-200) {
		tmp = a * 120.0;
	} else if (x <= -3.1e-289) {
		tmp = (y * -60.0) / (z - t);
	} else if (x <= 9.2e+131) {
		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 = x * (60.0d0 / (z - t))
    if (x <= (-280000000000.0d0)) then
        tmp = t_1
    else if (x <= (-4.9d-200)) then
        tmp = a * 120.0d0
    else if (x <= (-3.1d-289)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (x <= 9.2d+131) 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 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -280000000000.0) {
		tmp = t_1;
	} else if (x <= -4.9e-200) {
		tmp = a * 120.0;
	} else if (x <= -3.1e-289) {
		tmp = (y * -60.0) / (z - t);
	} else if (x <= 9.2e+131) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / (z - t))
	tmp = 0
	if x <= -280000000000.0:
		tmp = t_1
	elif x <= -4.9e-200:
		tmp = a * 120.0
	elif x <= -3.1e-289:
		tmp = (y * -60.0) / (z - t)
	elif x <= 9.2e+131:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (x <= -280000000000.0)
		tmp = t_1;
	elseif (x <= -4.9e-200)
		tmp = Float64(a * 120.0);
	elseif (x <= -3.1e-289)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (x <= 9.2e+131)
		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 = x * (60.0 / (z - t));
	tmp = 0.0;
	if (x <= -280000000000.0)
		tmp = t_1;
	elseif (x <= -4.9e-200)
		tmp = a * 120.0;
	elseif (x <= -3.1e-289)
		tmp = (y * -60.0) / (z - t);
	elseif (x <= 9.2e+131)
		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[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -280000000000.0], t$95$1, If[LessEqual[x, -4.9e-200], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -3.1e-289], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+131], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e11 or 9.19999999999999966e131 < x

   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* 99.7%

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

   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 0 73.4%

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

   6. Taylor expanded in x around inf 60.7%

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

      1. associate-*r/ 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r/ 86.0%

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

   8. Simplified 60.8%

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

   if -2.8e11 < x < -4.9e-200 or -3.1e-289 < x < 9.19999999999999966e131

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.3%

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

   if -4.9e-200 < x < -3.1e-289

   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* 99.7%

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

   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 0 67.3%

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

   6. Taylor expanded in x around 0 67.3%

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

      1. associate-*r/ 67.6%

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

   8. Simplified 67.6%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -280000000000:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-289}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+131}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -280000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+130}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= x -280000000000.0)
     t_1
     (if (<= x -4.5e-201)
       (* a 120.0)
       (if (<= x -1.8e-288)
         (* y (/ -60.0 (- z t)))
         (if (<= x 1.35e+130) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -280000000000.0) {
		tmp = t_1;
	} else if (x <= -4.5e-201) {
		tmp = a * 120.0;
	} else if (x <= -1.8e-288) {
		tmp = y * (-60.0 / (z - t));
	} else if (x <= 1.35e+130) {
		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 = x * (60.0d0 / (z - t))
    if (x <= (-280000000000.0d0)) then
        tmp = t_1
    else if (x <= (-4.5d-201)) then
        tmp = a * 120.0d0
    else if (x <= (-1.8d-288)) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (x <= 1.35d+130) 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 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -280000000000.0) {
		tmp = t_1;
	} else if (x <= -4.5e-201) {
		tmp = a * 120.0;
	} else if (x <= -1.8e-288) {
		tmp = y * (-60.0 / (z - t));
	} else if (x <= 1.35e+130) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / (z - t))
	tmp = 0
	if x <= -280000000000.0:
		tmp = t_1
	elif x <= -4.5e-201:
		tmp = a * 120.0
	elif x <= -1.8e-288:
		tmp = y * (-60.0 / (z - t))
	elif x <= 1.35e+130:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (x <= -280000000000.0)
		tmp = t_1;
	elseif (x <= -4.5e-201)
		tmp = Float64(a * 120.0);
	elseif (x <= -1.8e-288)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (x <= 1.35e+130)
		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 = x * (60.0 / (z - t));
	tmp = 0.0;
	if (x <= -280000000000.0)
		tmp = t_1;
	elseif (x <= -4.5e-201)
		tmp = a * 120.0;
	elseif (x <= -1.8e-288)
		tmp = y * (-60.0 / (z - t));
	elseif (x <= 1.35e+130)
		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[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -280000000000.0], t$95$1, If[LessEqual[x, -4.5e-201], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -1.8e-288], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+130], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e11 or 1.3499999999999999e130 < x

   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* 99.7%

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

   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 0 73.4%

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

   6. Taylor expanded in x around inf 60.7%

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

      1. associate-*r/ 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r/ 86.0%

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

   8. Simplified 60.8%

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

   if -2.8e11 < x < -4.5000000000000002e-201 or -1.8000000000000001e-288 < x < 1.3499999999999999e130

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.3%

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

   if -4.5000000000000002e-201 < x < -1.8000000000000001e-288

   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* 99.7%

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

   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 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 94.2%

      \[\leadsto \color{blue}{y \cdot \left(120 \cdot \frac{a}{y} - 60 \cdot \frac{1}{z - t}\right)} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv 94.2%

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

      2. metadata-eval 94.2%

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

      3. associate-*r/ 94.3%

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

      4. metadata-eval 94.3%

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

   10. Simplified 94.3%

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

   11. Taylor expanded in a around 0 67.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -280000000000:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+130}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -280000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-289}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= x -280000000000.0)
     t_1
     (if (<= x -4.5e-201)
       (* a 120.0)
       (if (<= x -3.9e-289)
         (* -60.0 (/ y (- z t)))
         (if (<= x 1.5e+129) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -280000000000.0) {
		tmp = t_1;
	} else if (x <= -4.5e-201) {
		tmp = a * 120.0;
	} else if (x <= -3.9e-289) {
		tmp = -60.0 * (y / (z - t));
	} else if (x <= 1.5e+129) {
		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 = x * (60.0d0 / (z - t))
    if (x <= (-280000000000.0d0)) then
        tmp = t_1
    else if (x <= (-4.5d-201)) then
        tmp = a * 120.0d0
    else if (x <= (-3.9d-289)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (x <= 1.5d+129) 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 = x * (60.0 / (z - t));
	double tmp;
	if (x <= -280000000000.0) {
		tmp = t_1;
	} else if (x <= -4.5e-201) {
		tmp = a * 120.0;
	} else if (x <= -3.9e-289) {
		tmp = -60.0 * (y / (z - t));
	} else if (x <= 1.5e+129) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / (z - t))
	tmp = 0
	if x <= -280000000000.0:
		tmp = t_1
	elif x <= -4.5e-201:
		tmp = a * 120.0
	elif x <= -3.9e-289:
		tmp = -60.0 * (y / (z - t))
	elif x <= 1.5e+129:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (x <= -280000000000.0)
		tmp = t_1;
	elseif (x <= -4.5e-201)
		tmp = Float64(a * 120.0);
	elseif (x <= -3.9e-289)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (x <= 1.5e+129)
		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 = x * (60.0 / (z - t));
	tmp = 0.0;
	if (x <= -280000000000.0)
		tmp = t_1;
	elseif (x <= -4.5e-201)
		tmp = a * 120.0;
	elseif (x <= -3.9e-289)
		tmp = -60.0 * (y / (z - t));
	elseif (x <= 1.5e+129)
		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[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -280000000000.0], t$95$1, If[LessEqual[x, -4.5e-201], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, -3.9e-289], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+129], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e11 or 1.50000000000000015e129 < x

   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* 99.7%

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

   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 0 73.4%

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

   6. Taylor expanded in x around inf 60.7%

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

      1. associate-*r/ 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r/ 86.0%

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

   8. Simplified 60.8%

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

   if -2.8e11 < x < -4.5000000000000002e-201 or -3.8999999999999998e-289 < x < 1.50000000000000015e129

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.3%

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

   if -4.5000000000000002e-201 < x < -3.8999999999999998e-289

   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* 99.7%

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

   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 0 67.3%

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

   6. Taylor expanded in x around 0 67.3%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -280000000000:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-289}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-60}{z - t} + a \cdot 120\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+74}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq 22000000:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* y (/ -60.0 (- z t))) (* a 120.0))))
   (if (<= y -1.42e+173)
     t_1
     (if (<= y -3.1e+74)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= y 22000000.0) (+ (* x (/ 60.0 (- z t))) (* a 120.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (-60.0 / (z - t))) + (a * 120.0);
	double tmp;
	if (y <= -1.42e+173) {
		tmp = t_1;
	} else if (y <= -3.1e+74) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (y <= 22000000.0) {
		tmp = (x * (60.0 / (z - t))) + (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 = (y * ((-60.0d0) / (z - t))) + (a * 120.0d0)
    if (y <= (-1.42d+173)) then
        tmp = t_1
    else if (y <= (-3.1d+74)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (y <= 22000000.0d0) then
        tmp = (x * (60.0d0 / (z - t))) + (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 = (y * (-60.0 / (z - t))) + (a * 120.0);
	double tmp;
	if (y <= -1.42e+173) {
		tmp = t_1;
	} else if (y <= -3.1e+74) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (y <= 22000000.0) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (-60.0 / (z - t))) + (a * 120.0)
	tmp = 0
	if y <= -1.42e+173:
		tmp = t_1
	elif y <= -3.1e+74:
		tmp = 60.0 * ((x - y) / (z - t))
	elif y <= 22000000.0:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(-60.0 / Float64(z - t))) + Float64(a * 120.0))
	tmp = 0.0
	if (y <= -1.42e+173)
		tmp = t_1;
	elseif (y <= -3.1e+74)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (y <= 22000000.0)
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (-60.0 / (z - t))) + (a * 120.0);
	tmp = 0.0;
	if (y <= -1.42e+173)
		tmp = t_1;
	elseif (y <= -3.1e+74)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (y <= 22000000.0)
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.42e+173], t$95$1, If[LessEqual[y, -3.1e+74], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 22000000.0], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4199999999999999e173 or 2.2e7 < y

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. 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 0 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*l/ 90.4%

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

      3. associate-*r/ 92.9%

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

   9. Simplified 92.9%

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

   if -1.4199999999999999e173 < y < -3.10000000000000021e74

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 94.1%

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

   if -3.10000000000000021e74 < y < 2.2e7

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 94.9%

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

      1. associate-*r/ 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r/ 95.0%

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

   7. Simplified 95.0%

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

Alternative 14: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-120} \lor \neg \left(a \cdot 120 \leq 10^{-136}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e-120) (not (<= (* a 120.0) 1e-136)))
   (+ (* x (/ 60.0 (- 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 (((a * 120.0) <= -4e-120) || !((a * 120.0) <= 1e-136)) {
		tmp = (x * (60.0 / (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 (((a * 120.0d0) <= (-4d-120)) .or. (.not. ((a * 120.0d0) <= 1d-136))) then
        tmp = (x * (60.0d0 / (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 (((a * 120.0) <= -4e-120) || !((a * 120.0) <= 1e-136)) {
		tmp = (x * (60.0 / (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 ((a * 120.0) <= -4e-120) or not ((a * 120.0) <= 1e-136):
		tmp = (x * (60.0 / (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(a * 120.0) <= -4e-120) || !(Float64(a * 120.0) <= 1e-136))
		tmp = Float64(Float64(x * Float64(60.0 / 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 (((a * 120.0) <= -4e-120) || ~(((a * 120.0) <= 1e-136)))
		tmp = (x * (60.0 / (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[(a * 120.0), $MachinePrecision], -4e-120], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-136]], $MachinePrecision]], N[(N[(x * N[(60.0 / 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 a #s(literal 120 binary64)) < -3.99999999999999991e-120 or 1e-136 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. *-commutative 86.8%

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

      3. associate-*r/ 86.8%

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

   7. Simplified 86.8%

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

   if -3.99999999999999991e-120 < (*.f64 a #s(literal 120 binary64)) < 1e-136

   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. Taylor expanded in a around 0 91.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   6. 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%

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

   7. Applied egg-rr 91.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-120} \lor \neg \left(a \cdot 120 \leq 10^{-136}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-136}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-215}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-133}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e-136)
   (* a 120.0)
   (if (<= a -5.8e-215)
     (* 60.0 (/ x z))
     (if (<= a 3.8e-133) (* -60.0 (/ y z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e-136) {
		tmp = a * 120.0;
	} else if (a <= -5.8e-215) {
		tmp = 60.0 * (x / z);
	} else if (a <= 3.8e-133) {
		tmp = -60.0 * (y / 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 (a <= (-1.25d-136)) then
        tmp = a * 120.0d0
    else if (a <= (-5.8d-215)) then
        tmp = 60.0d0 * (x / z)
    else if (a <= 3.8d-133) then
        tmp = (-60.0d0) * (y / 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 (a <= -1.25e-136) {
		tmp = a * 120.0;
	} else if (a <= -5.8e-215) {
		tmp = 60.0 * (x / z);
	} else if (a <= 3.8e-133) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e-136:
		tmp = a * 120.0
	elif a <= -5.8e-215:
		tmp = 60.0 * (x / z)
	elif a <= 3.8e-133:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e-136)
		tmp = Float64(a * 120.0);
	elseif (a <= -5.8e-215)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (a <= 3.8e-133)
		tmp = Float64(-60.0 * Float64(y / 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 (a <= -1.25e-136)
		tmp = a * 120.0;
	elseif (a <= -5.8e-215)
		tmp = 60.0 * (x / z);
	elseif (a <= 3.8e-133)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e-136], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -5.8e-215], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-133], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.25e-136 or 3.8000000000000003e-133 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.8%

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

   if -1.25e-136 < a < -5.8000000000000001e-215

   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* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0 83.3%

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

   6. Taylor expanded in z around inf 49.3%

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

   7. Taylor expanded in x around inf 43.7%

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

   if -5.8000000000000001e-215 < a < 3.8000000000000003e-133

   1. Initial program 97.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 93.0%

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

   6. Taylor expanded in z around inf 54.5%

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

   7. Taylor expanded in x around 0 37.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-136}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-215}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-133}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-123} \lor \neg \left(a \leq 1.4 \cdot 10^{-131}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9e-123) (not (<= a 1.4e-131)))
   (* 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 <= -9e-123) || !(a <= 1.4e-131)) {
		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 <= (-9d-123)) .or. (.not. (a <= 1.4d-131))) 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 <= -9e-123) || !(a <= 1.4e-131)) {
		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 <= -9e-123) or not (a <= 1.4e-131):
		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 <= -9e-123) || !(a <= 1.4e-131))
		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 <= -9e-123) || ~((a <= 1.4e-131)))
		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, -9e-123], N[Not[LessEqual[a, 1.4e-131]], $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 < -8.99999999999999986e-123 or 1.4e-131 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 65.8%

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

   if -8.99999999999999986e-123 < a < 1.4e-131

   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. Taylor expanded in a around 0 91.1%

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

   6. Taylor expanded in x around 0 49.2%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-123} \lor \neg \left(a \leq 1.4 \cdot 10^{-131}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-212} \lor \neg \left(a \leq 6.5 \cdot 10^{-139}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-212) (not (<= a 6.5e-139)))
   (* a 120.0)
   (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-212) || !(a <= 6.5e-139)) {
		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 <= (-4.7d-212)) .or. (.not. (a <= 6.5d-139))) 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 <= -4.7e-212) || !(a <= 6.5e-139)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-212) or not (a <= 6.5e-139):
		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 <= -4.7e-212) || !(a <= 6.5e-139))
		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 <= -4.7e-212) || ~((a <= 6.5e-139)))
		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, -4.7e-212], N[Not[LessEqual[a, 6.5e-139]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.69999999999999998e-212 or 6.5e-139 < 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 60.6%

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

   if -4.69999999999999998e-212 < a < 6.5e-139

   1. Initial program 97.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 93.0%

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

   6. Taylor expanded in z around inf 54.5%

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

   7. Taylor expanded in x around 0 37.6%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-212} \lor \neg \left(a \leq 6.5 \cdot 10^{-139}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 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* 99.8%

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

3. Simplified 99.8%

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

Alternative 19: 50.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 z around inf 49.5%

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

6. Final simplification 49.5%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024087 
(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)))