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

Percentage Accurate: 99.4% → 99.8%

Time: 15.2s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 99.1%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. --lowering--.f64 99.8%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

4. Applied egg-rr 99.8%

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

Alternative 2: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{+47}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* 60.0 y) t))))
   (if (<= t -2.9e-115)
     t_1
     (if (<= t -9.5e-303)
       (+ (* a 120.0) (* -60.0 (/ y z)))
       (if (<= t 1.35e-180)
         (* 60.0 (/ (- x y) z))
         (if (<= t 3.55e+47) (+ (* a 120.0) (* y (/ -60.0 z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -2.9e-115) {
		tmp = t_1;
	} else if (t <= -9.5e-303) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 1.35e-180) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 3.55e+47) {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((60.0d0 * y) / t)
    if (t <= (-2.9d-115)) then
        tmp = t_1
    else if (t <= (-9.5d-303)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (t <= 1.35d-180) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (t <= 3.55d+47) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -2.9e-115) {
		tmp = t_1;
	} else if (t <= -9.5e-303) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 1.35e-180) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 3.55e+47) {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((60.0 * y) / t)
	tmp = 0
	if t <= -2.9e-115:
		tmp = t_1
	elif t <= -9.5e-303:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif t <= 1.35e-180:
		tmp = 60.0 * ((x - y) / z)
	elif t <= 3.55e+47:
		tmp = (a * 120.0) + (y * (-60.0 / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t))
	tmp = 0.0
	if (t <= -2.9e-115)
		tmp = t_1;
	elseif (t <= -9.5e-303)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (t <= 1.35e-180)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (t <= 3.55e+47)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((60.0 * y) / t);
	tmp = 0.0;
	if (t <= -2.9e-115)
		tmp = t_1;
	elseif (t <= -9.5e-303)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (t <= 1.35e-180)
		tmp = 60.0 * ((x - y) / z);
	elseif (t <= 3.55e+47)
		tmp = (a * 120.0) + (y * (-60.0 / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-115], t$95$1, If[LessEqual[t, -9.5e-303], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-180], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.55e+47], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.8999999999999998e-115 or 3.5500000000000001e47 < t

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 83.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 83.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(60 \cdot \frac{y}{t}\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\color{blue}{60} \cdot \frac{y}{t}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\frac{60 \cdot y}{\color{blue}{t}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\left(60 \cdot y\right), \color{blue}{t}\right)\right) \]

      6. *-lowering-*.f64 77.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), t\right)\right) \]

   8. Simplified 77.2%

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

   if -2.8999999999999998e-115 < t < -9.4999999999999999e-303

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 81.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 81.4%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 81.4%

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

   if -9.4999999999999999e-303 < t < 1.35000000000000007e-180

   1. Initial program 99.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 92.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{z \cdot \frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      10. --lowering--.f64 92.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   9. Applied egg-rr 92.6%

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

   10. Taylor expanded in z around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \color{blue}{\left(\frac{x - y}{z}\right)}\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{z}\right)\right) \]

       3. --lowering--.f64 81.2%

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right)\right) \]

   12. Simplified 81.2%

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

   if 1.35000000000000007e-180 < t < 3.5500000000000001e47

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 73.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 73.6%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(-60 \cdot \frac{y}{z}\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\color{blue}{-60} \cdot \frac{y}{z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\frac{-60 \cdot y}{\color{blue}{z}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\left(-60 \cdot y\right), \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), z\right)\right) \]

   8. Simplified 63.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\frac{y \cdot -60}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(y \cdot \color{blue}{\frac{-60}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-60}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 63.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 63.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-115}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{+47}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -980:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-299}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.78 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+47}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -980.0)
   (* a 120.0)
   (if (<= t -1.12e-299)
     (+ (* a 120.0) (* -60.0 (/ y z)))
     (if (<= t 1.78e-180)
       (* 60.0 (/ (- x y) z))
       (if (<= t 4e+47) (+ (* a 120.0) (* y (/ -60.0 z))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -980.0) {
		tmp = a * 120.0;
	} else if (t <= -1.12e-299) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 1.78e-180) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 4e+47) {
		tmp = (a * 120.0) + (y * (-60.0 / 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 (t <= (-980.0d0)) then
        tmp = a * 120.0d0
    else if (t <= (-1.12d-299)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (t <= 1.78d-180) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (t <= 4d+47) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / 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 (t <= -980.0) {
		tmp = a * 120.0;
	} else if (t <= -1.12e-299) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 1.78e-180) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 4e+47) {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -980.0:
		tmp = a * 120.0
	elif t <= -1.12e-299:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif t <= 1.78e-180:
		tmp = 60.0 * ((x - y) / z)
	elif t <= 4e+47:
		tmp = (a * 120.0) + (y * (-60.0 / z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -980.0)
		tmp = Float64(a * 120.0);
	elseif (t <= -1.12e-299)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (t <= 1.78e-180)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (t <= 4e+47)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / 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 (t <= -980.0)
		tmp = a * 120.0;
	elseif (t <= -1.12e-299)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (t <= 1.78e-180)
		tmp = 60.0 * ((x - y) / z);
	elseif (t <= 4e+47)
		tmp = (a * 120.0) + (y * (-60.0 / z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -980.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, -1.12e-299], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.78e-180], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+47], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -980 or 4.0000000000000002e47 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 69.0%

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

   if -980 < t < -1.11999999999999998e-299

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 79.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 79.2%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 67.8%

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

   if -1.11999999999999998e-299 < t < 1.7800000000000001e-180

   1. Initial program 99.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 92.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{z \cdot \frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      10. --lowering--.f64 92.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   9. Applied egg-rr 92.6%

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

   10. Taylor expanded in z around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \color{blue}{\left(\frac{x - y}{z}\right)}\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{z}\right)\right) \]

       3. --lowering--.f64 81.2%

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right)\right) \]

   12. Simplified 81.2%

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

   if 1.7800000000000001e-180 < t < 4.0000000000000002e47

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 73.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 73.6%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(-60 \cdot \frac{y}{z}\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\color{blue}{-60} \cdot \frac{y}{z}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\frac{-60 \cdot y}{\color{blue}{z}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\left(-60 \cdot y\right), \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, y\right), z\right)\right) \]

   8. Simplified 63.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\frac{y \cdot -60}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(y \cdot \color{blue}{\frac{-60}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-60}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 63.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 63.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -980:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-299}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.78 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+47}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -14000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.72 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-181}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= t -14000.0)
     (* a 120.0)
     (if (<= t -1.72e-302)
       t_1
       (if (<= t 6.4e-181)
         (* 60.0 (/ (- x y) z))
         (if (<= t 1.75e+49) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (t <= -14000.0) {
		tmp = a * 120.0;
	} else if (t <= -1.72e-302) {
		tmp = t_1;
	} else if (t <= 6.4e-181) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 1.75e+49) {
		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 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if (t <= (-14000.0d0)) then
        tmp = a * 120.0d0
    else if (t <= (-1.72d-302)) then
        tmp = t_1
    else if (t <= 6.4d-181) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (t <= 1.75d+49) 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 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (t <= -14000.0) {
		tmp = a * 120.0;
	} else if (t <= -1.72e-302) {
		tmp = t_1;
	} else if (t <= 6.4e-181) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 1.75e+49) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if t <= -14000.0:
		tmp = a * 120.0
	elif t <= -1.72e-302:
		tmp = t_1
	elif t <= 6.4e-181:
		tmp = 60.0 * ((x - y) / z)
	elif t <= 1.75e+49:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (t <= -14000.0)
		tmp = Float64(a * 120.0);
	elseif (t <= -1.72e-302)
		tmp = t_1;
	elseif (t <= 6.4e-181)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (t <= 1.75e+49)
		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 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if (t <= -14000.0)
		tmp = a * 120.0;
	elseif (t <= -1.72e-302)
		tmp = t_1;
	elseif (t <= 6.4e-181)
		tmp = 60.0 * ((x - y) / z);
	elseif (t <= 1.75e+49)
		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[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -14000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[t, -1.72e-302], t$95$1, If[LessEqual[t, 6.4e-181], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+49], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -14000 or 1.74999999999999987e49 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 69.0%

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

   if -14000 < t < -1.71999999999999993e-302 or 6.4000000000000003e-181 < t < 1.74999999999999987e49

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 76.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 76.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 65.8%

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

   if -1.71999999999999993e-302 < t < 6.4000000000000003e-181

   1. Initial program 99.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 92.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{z \cdot \frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      10. --lowering--.f64 92.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   9. Applied egg-rr 92.6%

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

   10. Taylor expanded in z around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \color{blue}{\left(\frac{x - y}{z}\right)}\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{z}\right)\right) \]

       3. --lowering--.f64 81.2%

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right)\right) \]

   12. Simplified 81.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -14000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -1.72 \cdot 10^{-302}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-181}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+49}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-243}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-233}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e-24)
   (* a 120.0)
   (if (<= a -4.7e-243)
     (/ (* 60.0 (- x y)) z)
     (if (<= a 1.05e-233)
       (* (/ 60.0 (- z t)) x)
       (if (<= a 1.24e-200) (* y (/ -60.0 (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-24) {
		tmp = a * 120.0;
	} else if (a <= -4.7e-243) {
		tmp = (60.0 * (x - y)) / z;
	} else if (a <= 1.05e-233) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 1.24e-200) {
		tmp = y * (-60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d-24)) then
        tmp = a * 120.0d0
    else if (a <= (-4.7d-243)) then
        tmp = (60.0d0 * (x - y)) / z
    else if (a <= 1.05d-233) then
        tmp = (60.0d0 / (z - t)) * x
    else if (a <= 1.24d-200) then
        tmp = y * ((-60.0d0) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-24) {
		tmp = a * 120.0;
	} else if (a <= -4.7e-243) {
		tmp = (60.0 * (x - y)) / z;
	} else if (a <= 1.05e-233) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 1.24e-200) {
		tmp = y * (-60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e-24:
		tmp = a * 120.0
	elif a <= -4.7e-243:
		tmp = (60.0 * (x - y)) / z
	elif a <= 1.05e-233:
		tmp = (60.0 / (z - t)) * x
	elif a <= 1.24e-200:
		tmp = y * (-60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e-24)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.7e-243)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / z);
	elseif (a <= 1.05e-233)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (a <= 1.24e-200)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e-24)
		tmp = a * 120.0;
	elseif (a <= -4.7e-243)
		tmp = (60.0 * (x - y)) / z;
	elseif (a <= 1.05e-233)
		tmp = (60.0 / (z - t)) * x;
	elseif (a <= 1.24e-200)
		tmp = y * (-60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e-24], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.7e-243], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.05e-233], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 1.24e-200], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.10000000000000001e-24 or 1.24e-200 < a

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 72.5%

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

   if -1.10000000000000001e-24 < a < -4.7000000000000004e-243

   1. Initial program 99.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 65.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 65.1%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), z\right) \]

      4. --lowering--.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), z\right) \]

   10. Simplified 54.1%

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

   if -4.7000000000000004e-243 < a < 1.0499999999999999e-233

   1. Initial program 99.5%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{x - y}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z - t} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z - t}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), \left(z - t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(z - t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 99.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{60 \cdot 1}{\color{blue}{z - t}}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{60}{\color{blue}{z} - t}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \color{blue}{\left(z - t\right)}\right)\right) \]

      10. --lowering--.f64 62.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Simplified 62.0%

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

   if 1.0499999999999999e-233 < a < 1.24e-200

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 85.9%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 85.9%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-60}{z - t}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \color{blue}{\left(z - t\right)}\right)\right) \]

      6. --lowering--.f64 85.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Applied egg-rr 85.9%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-243}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-233}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-240}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-234}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e-25)
   (* a 120.0)
   (if (<= a -2.1e-240)
     (* 60.0 (/ (- x y) z))
     (if (<= a 1.75e-234)
       (* (/ 60.0 (- z t)) x)
       (if (<= a 9e-201) (* y (/ -60.0 (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-25) {
		tmp = a * 120.0;
	} else if (a <= -2.1e-240) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.75e-234) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 9e-201) {
		tmp = y * (-60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d-25)) then
        tmp = a * 120.0d0
    else if (a <= (-2.1d-240)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 1.75d-234) then
        tmp = (60.0d0 / (z - t)) * x
    else if (a <= 9d-201) then
        tmp = y * ((-60.0d0) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-25) {
		tmp = a * 120.0;
	} else if (a <= -2.1e-240) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.75e-234) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 9e-201) {
		tmp = y * (-60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e-25:
		tmp = a * 120.0
	elif a <= -2.1e-240:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 1.75e-234:
		tmp = (60.0 / (z - t)) * x
	elif a <= 9e-201:
		tmp = y * (-60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e-25)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.1e-240)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 1.75e-234)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (a <= 9e-201)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e-25)
		tmp = a * 120.0;
	elseif (a <= -2.1e-240)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 1.75e-234)
		tmp = (60.0 / (z - t)) * x;
	elseif (a <= 9e-201)
		tmp = y * (-60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e-25], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.1e-240], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-234], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 9e-201], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.5e-25 or 9.0000000000000004e-201 < a

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 72.5%

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

   if -6.5e-25 < a < -2.09999999999999994e-240

   1. Initial program 99.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 65.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 65.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{z \cdot \frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      10. --lowering--.f64 65.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   9. Applied egg-rr 65.1%

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

   10. Taylor expanded in z around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \color{blue}{\left(\frac{x - y}{z}\right)}\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{z}\right)\right) \]

       3. --lowering--.f64 54.0%

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right)\right) \]

   12. Simplified 54.0%

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

   if -2.09999999999999994e-240 < a < 1.7500000000000001e-234

   1. Initial program 99.5%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{x - y}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z - t} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z - t}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), \left(z - t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(z - t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 99.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{60 \cdot 1}{\color{blue}{z - t}}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{60}{\color{blue}{z} - t}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \color{blue}{\left(z - t\right)}\right)\right) \]

      10. --lowering--.f64 62.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Simplified 62.0%

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

   if 1.7500000000000001e-234 < a < 9.0000000000000004e-201

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 85.9%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 85.9%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-60}{z - t}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \color{blue}{\left(z - t\right)}\right)\right) \]

      6. --lowering--.f64 85.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Applied egg-rr 85.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-240}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-234}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-244}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-233}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-207}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e-25)
   (* a 120.0)
   (if (<= a -9.8e-244)
     (* 60.0 (/ (- x y) z))
     (if (<= a 6.2e-233)
       (* (/ 60.0 (- z t)) x)
       (if (<= a 5.7e-207) (* -60.0 (/ y (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-25) {
		tmp = a * 120.0;
	} else if (a <= -9.8e-244) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 6.2e-233) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 5.7e-207) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d-25)) then
        tmp = a * 120.0d0
    else if (a <= (-9.8d-244)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 6.2d-233) then
        tmp = (60.0d0 / (z - t)) * x
    else if (a <= 5.7d-207) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-25) {
		tmp = a * 120.0;
	} else if (a <= -9.8e-244) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 6.2e-233) {
		tmp = (60.0 / (z - t)) * x;
	} else if (a <= 5.7e-207) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e-25:
		tmp = a * 120.0
	elif a <= -9.8e-244:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 6.2e-233:
		tmp = (60.0 / (z - t)) * x
	elif a <= 5.7e-207:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e-25)
		tmp = Float64(a * 120.0);
	elseif (a <= -9.8e-244)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 6.2e-233)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (a <= 5.7e-207)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e-25)
		tmp = a * 120.0;
	elseif (a <= -9.8e-244)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 6.2e-233)
		tmp = (60.0 / (z - t)) * x;
	elseif (a <= 5.7e-207)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e-25], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9.8e-244], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-233], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 5.7e-207], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.0000000000000004e-25 or 5.7e-207 < a

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 72.5%

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

   if -7.0000000000000004e-25 < a < -9.80000000000000029e-244

   1. Initial program 99.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 65.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 65.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{\frac{z}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 1}{z \cdot \frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot \frac{1}{\frac{1}{60}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z} \cdot 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      10. --lowering--.f64 65.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   9. Applied egg-rr 65.1%

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

   10. Taylor expanded in z around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \color{blue}{\left(\frac{x - y}{z}\right)}\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\left(x - y\right), \color{blue}{z}\right)\right) \]

       3. --lowering--.f64 54.0%

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right)\right) \]

   12. Simplified 54.0%

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

   if -9.80000000000000029e-244 < a < 6.2000000000000003e-233

   1. Initial program 99.5%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{x - y}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x - y}{z - t} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{x - y}{z - t}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), \left(z - t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(z - t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 99.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, t\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{60 \cdot 1}{\color{blue}{z - t}}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{60}{\color{blue}{z} - t}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \color{blue}{\left(z - t\right)}\right)\right) \]

      10. --lowering--.f64 62.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Simplified 62.0%

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

   if 6.2000000000000003e-233 < a < 5.7e-207

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 85.9%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 85.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-244}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-233}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-207}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-66}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* (- x y) (/ 60.0 z)))))
   (if (<= z -1.55e+195)
     t_1
     (if (<= z -7.2e-47)
       (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
       (if (<= z 2.8e-66) (+ (* a 120.0) (* (- x y) (/ -60.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((x - y) * (60.0 / z));
	double tmp;
	if (z <= -1.55e+195) {
		tmp = t_1;
	} else if (z <= -7.2e-47) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (z <= 2.8e-66) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    if (z <= (-1.55d+195)) then
        tmp = t_1
    else if (z <= (-7.2d-47)) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else if (z <= 2.8d-66) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((x - y) * (60.0 / z));
	double tmp;
	if (z <= -1.55e+195) {
		tmp = t_1;
	} else if (z <= -7.2e-47) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (z <= 2.8e-66) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((x - y) * (60.0 / z))
	tmp = 0
	if z <= -1.55e+195:
		tmp = t_1
	elif z <= -7.2e-47:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	elif z <= 2.8e-66:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)))
	tmp = 0.0
	if (z <= -1.55e+195)
		tmp = t_1;
	elseif (z <= -7.2e-47)
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	elseif (z <= 2.8e-66)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((x - y) * (60.0 / z));
	tmp = 0.0;
	if (z <= -1.55e+195)
		tmp = t_1;
	elseif (z <= -7.2e-47)
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	elseif (z <= 2.8e-66)
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+195], t$95$1, If[LessEqual[z, -7.2e-47], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-66], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e195 or 2.8e-66 < z

   1. Initial program 98.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 88.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 88.8%

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

   if -1.5500000000000001e195 < z < -7.19999999999999982e-47

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 81.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 81.8%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-60 \cdot \frac{y}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-60 \cdot \frac{1}{\frac{z - t}{y}}\right), \left(a \cdot 120\right)\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-60}{\frac{z - t}{y}}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \left(\frac{z - t}{y}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \mathsf{/.f64}\left(\left(z - t\right), y\right)\right), \left(a \cdot 120\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), y\right)\right), \left(a \cdot 120\right)\right) \]

      9. *-lowering-*.f64 81.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   7. Applied egg-rr 81.9%

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

   if -7.19999999999999982e-47 < z < 2.8e-66

   1. Initial program 99.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{-60}{t}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(-60, t\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 95.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+195}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-66}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-66}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* (- x y) (/ 60.0 z)))))
   (if (<= z -5.8e+194)
     t_1
     (if (<= z -5.5e-48)
       (+ (* a 120.0) (* -60.0 (/ y (- z t))))
       (if (<= z 3.5e-66) (+ (* a 120.0) (* (- x y) (/ -60.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((x - y) * (60.0 / z));
	double tmp;
	if (z <= -5.8e+194) {
		tmp = t_1;
	} else if (z <= -5.5e-48) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (z <= 3.5e-66) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    if (z <= (-5.8d+194)) then
        tmp = t_1
    else if (z <= (-5.5d-48)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else if (z <= 3.5d-66) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((x - y) * (60.0 / z));
	double tmp;
	if (z <= -5.8e+194) {
		tmp = t_1;
	} else if (z <= -5.5e-48) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (z <= 3.5e-66) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((x - y) * (60.0 / z))
	tmp = 0
	if z <= -5.8e+194:
		tmp = t_1
	elif z <= -5.5e-48:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	elif z <= 3.5e-66:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)))
	tmp = 0.0
	if (z <= -5.8e+194)
		tmp = t_1;
	elseif (z <= -5.5e-48)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	elseif (z <= 3.5e-66)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((x - y) * (60.0 / z));
	tmp = 0.0;
	if (z <= -5.8e+194)
		tmp = t_1;
	elseif (z <= -5.5e-48)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	elseif (z <= 3.5e-66)
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+194], t$95$1, If[LessEqual[z, -5.5e-48], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-66], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000001e194 or 3.5e-66 < z

   1. Initial program 98.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{60}{z}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 88.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, z\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 88.8%

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

   if -5.8000000000000001e194 < z < -5.50000000000000047e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 82.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 82.2%

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

   if -5.50000000000000047e-48 < z < 3.5e-66

   1. Initial program 99.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{-60}{t}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(-60, t\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 95.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+194}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-66}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-224}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ y (- z t))))))
   (if (<= (* a 120.0) -1e-43)
     t_1
     (if (<= (* a 120.0) 2e-224) (/ (* 60.0 (- x y)) (- z t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / (z - t)));
	double tmp;
	if ((a * 120.0) <= -1e-43) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-224) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    if ((a * 120.0d0) <= (-1d-43)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-224) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / (z - t)));
	double tmp;
	if ((a * 120.0) <= -1e-43) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-224) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (y / (z - t)))
	tmp = 0
	if (a * 120.0) <= -1e-43:
		tmp = t_1
	elif (a * 120.0) <= 2e-224:
		tmp = (60.0 * (x - y)) / (z - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))))
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-43)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-224)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (y / (z - t)));
	tmp = 0.0;
	if ((a * 120.0) <= -1e-43)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-224)
		tmp = (60.0 * (x - y)) / (z - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-43], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-224], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.00000000000000008e-43 or 2e-224 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 86.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 86.5%

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

   if -1.00000000000000008e-43 < (*.f64 a #s(literal 120 binary64)) < 2e-224

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 85.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 85.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-43}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-224}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-11}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000000:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-11)
   (+ (* a 120.0) (/ (* 60.0 y) t))
   (if (<= (* a 120.0) 200000000000.0)
     (/ (* 60.0 (- x y)) (- z t))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-11) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= 200000000000.0) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-11)) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else if ((a * 120.0d0) <= 200000000000.0d0) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-11) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= 200000000000.0) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-11:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	elif (a * 120.0) <= 200000000000.0:
		tmp = (60.0 * (x - y)) / (z - t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-11)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	elseif (Float64(a * 120.0) <= 200000000000.0)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-11)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	elseif ((a * 120.0) <= 200000000000.0)
		tmp = (60.0 * (x - y)) / (z - t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-11], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 200000000000.0], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999988e-11

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 91.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 91.9%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(60 \cdot \frac{y}{t}\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\color{blue}{60} \cdot \frac{y}{t}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\frac{60 \cdot y}{\color{blue}{t}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\left(60 \cdot y\right), \color{blue}{t}\right)\right) \]

      6. *-lowering-*.f64 82.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), t\right)\right) \]

   8. Simplified 82.4%

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

   if -1.99999999999999988e-11 < (*.f64 a #s(literal 120 binary64)) < 2e11

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(x - y\right)\right), \color{blue}{\left(z - t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(x - y\right)\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \left(z - t\right)\right) \]

      5. --lowering--.f64 75.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   5. Simplified 75.8%

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

   if 2e11 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 83.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-11}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 200000000000:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+138}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 1580000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.3e+138)
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (if (<= y 1580000.0)
     (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
     (+ (* a 120.0) (* -60.0 (/ y (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e+138) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 1580000.0) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-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 (y <= (-1.3d+138)) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else if (y <= 1580000.0d0) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else
        tmp = (a * 120.0d0) + ((-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 (y <= -1.3e+138) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 1580000.0) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.3e+138:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	elif y <= 1580000.0:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	else:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.3e+138)
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	elseif (y <= 1580000.0)
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(a * 120.0) + 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 (y <= -1.3e+138)
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	elseif (y <= 1580000.0)
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	else
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.3e+138], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1580000.0], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e138

   1. Initial program 94.2%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 88.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 88.9%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-60 \cdot \frac{y}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-60 \cdot \frac{1}{\frac{z - t}{y}}\right), \left(a \cdot 120\right)\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{-60}{\frac{z - t}{y}}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \left(\frac{z - t}{y}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \mathsf{/.f64}\left(\left(z - t\right), y\right)\right), \left(a \cdot 120\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), y\right)\right), \left(a \cdot 120\right)\right) \]

      9. *-lowering-*.f64 89.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(-60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   7. Applied egg-rr 89.0%

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

   if -1.3e138 < y < 1.58e6

   1. Initial program 99.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{x - y}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{1}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{\frac{z - t}{x - y}}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \left(\frac{z - t}{x - y}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(z - t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(x - y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(x, y\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \color{blue}{\left(\frac{z - t}{x}\right)}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(z - t\right), x\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. --lowering--.f64 93.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), x\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 93.1%

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

   if 1.58e6 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 92.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 92.9%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+138}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 1580000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-133}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ y (- z t))))))
   (if (<= z -3.2e-48)
     t_1
     (if (<= z 2.3e-133) (+ (* a 120.0) (* (- x y) (/ -60.0 t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / (z - t)));
	double tmp;
	if (z <= -3.2e-48) {
		tmp = t_1;
	} else if (z <= 2.3e-133) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    if (z <= (-3.2d-48)) then
        tmp = t_1
    else if (z <= 2.3d-133) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / (z - t)));
	double tmp;
	if (z <= -3.2e-48) {
		tmp = t_1;
	} else if (z <= 2.3e-133) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (y / (z - t)))
	tmp = 0
	if z <= -3.2e-48:
		tmp = t_1
	elif z <= 2.3e-133:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))))
	tmp = 0.0
	if (z <= -3.2e-48)
		tmp = t_1;
	elseif (z <= 2.3e-133)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (y / (z - t)));
	tmp = 0.0;
	if (z <= -3.2e-48)
		tmp = t_1;
	elseif (z <= 2.3e-133)
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-48], t$95$1, If[LessEqual[z, 2.3e-133], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999998e-48 or 2.3e-133 < z

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. distribute-lft-neg-in N/A

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

      6. associate-*l* N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(120 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\left(60 \cdot \frac{1}{z - t}\right) \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(60 \cdot \frac{1}{z - t}\right) \cdot y}\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\mathsf{neg}\left(60 \cdot \left(\frac{1}{z - t} \cdot y\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \color{blue}{\left(\frac{1}{z - t} \cdot y\right)}\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{1 \cdot y}{\color{blue}{z - t}}\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{y}{\color{blue}{z} - t}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \left(-60 \cdot \frac{\color{blue}{y}}{z - t}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right)\right) \]

      16. --lowering--.f64 81.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(120, a\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 81.2%

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

   if -3.1999999999999998e-48 < z < 2.3e-133

   1. Initial program 99.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(x - y\right) \cdot 60}{z - t}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(x - y\right) \cdot \frac{60}{z - t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{z - t} \cdot \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{z - t}\right), \left(x - y\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(z - t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \left(x - y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(\frac{-60}{t}\right)}, \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 96.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(-60, t\right), \mathsf{\_.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 96.4%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-133}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-205}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e-23)
   (* a 120.0)
   (if (<= a 1.85e-205) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e-23) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-205) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.3d-23)) then
        tmp = a * 120.0d0
    else if (a <= 1.85d-205) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e-23) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-205) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e-23:
		tmp = a * 120.0
	elif a <= 1.85e-205:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e-23)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.85e-205)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e-23)
		tmp = a * 120.0;
	elseif (a <= 1.85e-205)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e-23], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.85e-205], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.30000000000000002e-23 or 1.85e-205 < a

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 72.8%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 72.8%

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

   if -4.30000000000000002e-23 < a < 1.85e-205

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 46.9%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 46.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-205}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.95e+174) (* y (/ 60.0 t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.95e+174) {
		tmp = y * (60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.95d+174)) then
        tmp = y * (60.0d0 / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.95e+174) {
		tmp = y * (60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.95e+174:
		tmp = y * (60.0 / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.95e+174)
		tmp = Float64(y * Float64(60.0 / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.95e+174)
		tmp = y * (60.0 / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.95e+174], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9499999999999999e174

   1. Initial program 93.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 72.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 72.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-60}{z - t}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \color{blue}{\left(z - t\right)}\right)\right) \]

      6. --lowering--.f64 72.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Applied egg-rr 72.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{60}{t}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 45.2%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \color{blue}{t}\right)\right) \]

   10. Simplified 45.2%

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

   if -1.9499999999999999e174 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 59.5%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 59.5%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+167}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.22e+167) (* y (/ -60.0 z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.22e+167) {
		tmp = y * (-60.0 / 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 (y <= (-1.22d+167)) then
        tmp = y * ((-60.0d0) / 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 (y <= -1.22e+167) {
		tmp = y * (-60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.22e+167:
		tmp = y * (-60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.22e+167)
		tmp = Float64(y * Float64(-60.0 / 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 (y <= -1.22e+167)
		tmp = y * (-60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.22e+167], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.21999999999999996e167

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 70.7%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 70.7%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-60}{z - t}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \color{blue}{\left(z - t\right)}\right)\right) \]

      6. --lowering--.f64 70.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Applied egg-rr 70.7%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{-60}{z}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 41.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(-60, \color{blue}{z}\right)\right) \]

   10. Simplified 41.8%

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

   if -1.21999999999999996e167 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 59.8%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 59.8%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+167}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+167}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.2e+167) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+167) {
		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 (y <= (-1.2d+167)) 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 (y <= -1.2e+167) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.2e+167:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.2e+167)
		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 (y <= -1.2e+167)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.2e+167], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999999e167

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      3. --lowering--.f64 70.7%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 70.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 41.7%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 41.7%

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

   if -1.19999999999999999e167 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 59.8%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   5. Simplified 59.8%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+167}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 55.3%

      \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

5. Simplified 55.3%

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

6. Final simplification 55.3%

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

Developer Target 1: 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 2024185 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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