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

Percentage Accurate: 99.3% → 99.4%

Time: 12.3s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

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

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

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

   7. distribute-rgt-neg-out N/A

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

   8. distribute-frac-neg N/A

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

   9. distribute-frac-neg2 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. unsub-neg N/A

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

   14. remove-double-neg N/A

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

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

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

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

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

   17. --lowering--.f64 N/A

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

   18. --lowering--.f64 N/A

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

   19. *-lowering-*.f64 99.1%

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

3. Simplified 99.1%

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

   1. +-commutative N/A

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

   2. fma-define N/A

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

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

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

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

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

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

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

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

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

   7. --lowering--.f64 99.5%

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

6. Applied egg-rr 99.5%

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

Alternative 2: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+65}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-28)
   (* a 120.0)
   (if (<= (* a 120.0) 5e+65)
     (* 60.0 (/ (- y x) (- t z)))
     (+ (* a 120.0) (* x (/ -60.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-28) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+65) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d-28)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d+65) then
        tmp = 60.0d0 * ((y - x) / (t - z))
    else
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-28) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e+65) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-28:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e+65:
		tmp = 60.0 * ((y - x) / (t - z))
	else:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-28)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e+65)
		tmp = Float64(60.0 * Float64(Float64(y - x) / Float64(t - z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e-28)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e+65)
		tmp = 60.0 * ((y - x) / (t - z));
	else
		tmp = (a * 120.0) + (x * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-28], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+65], N[(60.0 * N[(N[(y - x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-28

   1. Initial program 98.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 76.0%

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

   7. Simplified 76.0%

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

   if -5.0000000000000002e-28 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999973e65

   1. Initial program 99.0%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 73.6%

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

   7. Simplified 73.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 74.5%

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

   9. Applied egg-rr 74.5%

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

   if 4.99999999999999973e65 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

      14. --lowering--.f64 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 84.5%

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

   10. Simplified 84.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+65}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -5 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ x (- z t))))))
   (if (<= x -5e+48)
     t_1
     (if (<= x 3.5e+107) (+ (* a 120.0) (/ (* 60.0 y) (- t z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (x / (z - t)));
	double tmp;
	if (x <= -5e+48) {
		tmp = t_1;
	} else if (x <= 3.5e+107) {
		tmp = (a * 120.0) + ((60.0 * y) / (t - 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 * (x / (z - t)))
    if (x <= (-5d+48)) then
        tmp = t_1
    else if (x <= 3.5d+107) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / (t - 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 * (x / (z - t)));
	double tmp;
	if (x <= -5e+48) {
		tmp = t_1;
	} else if (x <= 3.5e+107) {
		tmp = (a * 120.0) + ((60.0 * y) / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (x / (z - t)))
	tmp = 0
	if x <= -5e+48:
		tmp = t_1
	elif x <= 3.5e+107:
		tmp = (a * 120.0) + ((60.0 * y) / (t - z))
	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(x / Float64(z - t))))
	tmp = 0.0
	if (x <= -5e+48)
		tmp = t_1;
	elseif (x <= 3.5e+107)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / Float64(t - 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 * (x / (z - t)));
	tmp = 0.0;
	if (x <= -5e+48)
		tmp = t_1;
	elseif (x <= 3.5e+107)
		tmp = (a * 120.0) + ((60.0 * y) / (t - 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[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+48], t$95$1, If[LessEqual[x, 3.5e+107], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999973e48 or 3.4999999999999997e107 < x

   1. Initial program 98.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 98.8%

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

   3. Simplified 98.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. fma-define N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg N/A

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

      4. fmm-undef N/A

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

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

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

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

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

      7. neg-mul-1 N/A

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

      8. times-frac N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

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

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

      15. --lowering--.f64 98.8%

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

   8. Applied egg-rr 98.8%

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

   9. Taylor expanded in y around 0

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

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

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

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

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

       3. --lowering--.f64 90.2%

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

   11. Simplified 90.2%

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

   if -4.99999999999999973e48 < x < 3.4999999999999997e107

   1. Initial program 99.2%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 92.5%

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

   7. Simplified 92.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+48}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* x (/ -60.0 (- t z))))))
   (if (<= x -4.6e+48)
     t_1
     (if (<= x 4.2e+107) (+ (* a 120.0) (/ (* 60.0 y) (- t z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / (t - z)));
	double tmp;
	if (x <= -4.6e+48) {
		tmp = t_1;
	} else if (x <= 4.2e+107) {
		tmp = (a * 120.0) + ((60.0 * y) / (t - 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) + (x * ((-60.0d0) / (t - z)))
    if (x <= (-4.6d+48)) then
        tmp = t_1
    else if (x <= 4.2d+107) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / (t - 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) + (x * (-60.0 / (t - z)));
	double tmp;
	if (x <= -4.6e+48) {
		tmp = t_1;
	} else if (x <= 4.2e+107) {
		tmp = (a * 120.0) + ((60.0 * y) / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x * (-60.0 / (t - z)))
	tmp = 0
	if x <= -4.6e+48:
		tmp = t_1
	elif x <= 4.2e+107:
		tmp = (a * 120.0) + ((60.0 * y) / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / Float64(t - z))))
	tmp = 0.0
	if (x <= -4.6e+48)
		tmp = t_1;
	elseif (x <= 4.2e+107)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x * (-60.0 / (t - z)));
	tmp = 0.0;
	if (x <= -4.6e+48)
		tmp = t_1;
	elseif (x <= 4.2e+107)
		tmp = (a * 120.0) + ((60.0 * y) / (t - 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[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e+48], t$95$1, If[LessEqual[x, 4.2e+107], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6e48 or 4.1999999999999999e107 < x

   1. Initial program 98.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

      14. --lowering--.f64 90.1%

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

   7. Simplified 90.1%

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

   if -4.6e48 < x < 4.1999999999999999e107

   1. Initial program 99.2%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 92.5%

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

   7. Simplified 92.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+48}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* x (/ -60.0 (- t z))))))
   (if (<= z -1.22e-50)
     t_1
     (if (<= z 1.1e-95) (+ (* a 120.0) (* 60.0 (/ (- y x) t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / (t - z)));
	double tmp;
	if (z <= -1.22e-50) {
		tmp = t_1;
	} else if (z <= 1.1e-95) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x * ((-60.0d0) / (t - z)))
    if (z <= (-1.22d-50)) then
        tmp = t_1
    else if (z <= 1.1d-95) then
        tmp = (a * 120.0d0) + (60.0d0 * ((y - x) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (-60.0 / (t - z)));
	double tmp;
	if (z <= -1.22e-50) {
		tmp = t_1;
	} else if (z <= 1.1e-95) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x * (-60.0 / (t - z)))
	tmp = 0
	if z <= -1.22e-50:
		tmp = t_1
	elif z <= 1.1e-95:
		tmp = (a * 120.0) + (60.0 * ((y - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / Float64(t - z))))
	tmp = 0.0
	if (z <= -1.22e-50)
		tmp = t_1;
	elseif (z <= 1.1e-95)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(y - x) / 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 * (-60.0 / (t - z)));
	tmp = 0.0;
	if (z <= -1.22e-50)
		tmp = t_1;
	elseif (z <= 1.1e-95)
		tmp = (a * 120.0) + (60.0 * ((y - x) / 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[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e-50], t$95$1, If[LessEqual[z, 1.1e-95], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22000000000000007e-50 or 1.0999999999999999e-95 < z

   1. Initial program 99.2%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

      14. --lowering--.f64 83.3%

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

   7. Simplified 83.3%

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

   if -1.22000000000000007e-50 < z < 1.0999999999999999e-95

   1. Initial program 98.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

      6. --lowering--.f64 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-95}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.105:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* 60.0 x) z))))
   (if (<= z -7.5e+101)
     t_1
     (if (<= z 0.105) (+ (* a 120.0) (* 60.0 (/ (- y x) t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * x) / z);
	double tmp;
	if (z <= -7.5e+101) {
		tmp = t_1;
	} else if (z <= 0.105) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((60.0d0 * x) / z)
    if (z <= (-7.5d+101)) then
        tmp = t_1
    else if (z <= 0.105d0) then
        tmp = (a * 120.0d0) + (60.0d0 * ((y - x) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * x) / z);
	double tmp;
	if (z <= -7.5e+101) {
		tmp = t_1;
	} else if (z <= 0.105) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((60.0 * x) / z)
	tmp = 0
	if z <= -7.5e+101:
		tmp = t_1
	elif z <= 0.105:
		tmp = (a * 120.0) + (60.0 * ((y - x) / t))
	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 * x) / z))
	tmp = 0.0
	if (z <= -7.5e+101)
		tmp = t_1;
	elseif (z <= 0.105)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(y - x) / 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 * x) / z);
	tmp = 0.0;
	if (z <= -7.5e+101)
		tmp = t_1;
	elseif (z <= 0.105)
		tmp = (a * 120.0) + (60.0 * ((y - x) / 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[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+101], t$95$1, If[LessEqual[z, 0.105], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999995e101 or 0.104999999999999996 < z

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

      14. --lowering--.f64 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 81.1%

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

   10. Simplified 81.1%

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

   if -7.4999999999999995e101 < z < 0.104999999999999996

   1. Initial program 98.4%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

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

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

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

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

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

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

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

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

      6. --lowering--.f64 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+101}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;z \leq 0.105:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+63}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e-32)
   (* a 120.0)
   (if (<= a 3.9e+63) (* 60.0 (/ (- y x) (- t z))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e-32) {
		tmp = a * 120.0;
	} else if (a <= 3.9e+63) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.2d-32)) then
        tmp = a * 120.0d0
    else if (a <= 3.9d+63) then
        tmp = 60.0d0 * ((y - x) / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e-32) {
		tmp = a * 120.0;
	} else if (a <= 3.9e+63) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e-32:
		tmp = a * 120.0
	elif a <= 3.9e+63:
		tmp = 60.0 * ((y - x) / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e-32)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.9e+63)
		tmp = Float64(60.0 * Float64(Float64(y - x) / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.2e-32)
		tmp = a * 120.0;
	elseif (a <= 3.9e+63)
		tmp = 60.0 * ((y - x) / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e-32], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.9e+63], N[(60.0 * N[(N[(y - x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.19999999999999986e-32 or 3.9e63 < a

   1. Initial program 99.1%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 79.6%

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

   7. Simplified 79.6%

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

   if -7.19999999999999986e-32 < a < 3.9e63

   1. Initial program 99.0%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 73.6%

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

   7. Simplified 73.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 74.5%

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

   9. Applied egg-rr 74.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+63}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{t - z} \cdot -60\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+139)
   (* (/ x (- t z)) -60.0)
   (if (<= x 4.2e+133) (* a 120.0) (/ x (/ (- t z) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+139) {
		tmp = (x / (t - z)) * -60.0;
	} else if (x <= 4.2e+133) {
		tmp = a * 120.0;
	} else {
		tmp = x / ((t - z) / -60.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.8d+139)) then
        tmp = (x / (t - z)) * (-60.0d0)
    else if (x <= 4.2d+133) then
        tmp = a * 120.0d0
    else
        tmp = x / ((t - z) / (-60.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+139) {
		tmp = (x / (t - z)) * -60.0;
	} else if (x <= 4.2e+133) {
		tmp = a * 120.0;
	} else {
		tmp = x / ((t - z) / -60.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+139:
		tmp = (x / (t - z)) * -60.0
	elif x <= 4.2e+133:
		tmp = a * 120.0
	else:
		tmp = x / ((t - z) / -60.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+139)
		tmp = Float64(Float64(x / Float64(t - z)) * -60.0);
	elseif (x <= 4.2e+133)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x / Float64(Float64(t - z) / -60.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+139)
		tmp = (x / (t - z)) * -60.0;
	elseif (x <= 4.2e+133)
		tmp = a * 120.0;
	else
		tmp = x / ((t - z) / -60.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+139], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[x, 4.2e+133], N[(a * 120.0), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] / -60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8000000000000005e139

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. fma-define N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg N/A

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

      4. fmm-undef N/A

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

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

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

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

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

      7. neg-mul-1 N/A

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

      8. times-frac N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

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

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

      15. --lowering--.f64 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in x around inf

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

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

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

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

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

       3. --lowering--.f64 72.6%

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

   11. Simplified 72.6%

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

   if -6.8000000000000005e139 < x < 4.2e133

   1. Initial program 99.3%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 66.1%

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

   7. Simplified 66.1%

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

   if 4.2e133 < x

   1. Initial program 96.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

      14. --lowering--.f64 77.7%

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

   7. Simplified 77.7%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

      5. --lowering--.f64 77.8%

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

   9. Applied egg-rr 77.8%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{t - z} \cdot -60\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{t - z} \cdot -60\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.25e+140)
   (* (/ x (- t z)) -60.0)
   (if (<= x 1.5e+134) (* a 120.0) (* x (/ -60.0 (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.25e+140) {
		tmp = (x / (t - z)) * -60.0;
	} else if (x <= 1.5e+134) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.25d+140)) then
        tmp = (x / (t - z)) * (-60.0d0)
    else if (x <= 1.5d+134) then
        tmp = a * 120.0d0
    else
        tmp = x * ((-60.0d0) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.25e+140) {
		tmp = (x / (t - z)) * -60.0;
	} else if (x <= 1.5e+134) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.25e+140:
		tmp = (x / (t - z)) * -60.0
	elif x <= 1.5e+134:
		tmp = a * 120.0
	else:
		tmp = x * (-60.0 / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.25e+140)
		tmp = Float64(Float64(x / Float64(t - z)) * -60.0);
	elseif (x <= 1.5e+134)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(-60.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.25e+140)
		tmp = (x / (t - z)) * -60.0;
	elseif (x <= 1.5e+134)
		tmp = a * 120.0;
	else
		tmp = x * (-60.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.25e+140], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[x, 1.5e+134], N[(a * 120.0), $MachinePrecision], N[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2499999999999999e140

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

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

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. fma-define N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg N/A

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

      4. fmm-undef N/A

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

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

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

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

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

      7. neg-mul-1 N/A

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

      8. times-frac N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

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

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

      15. --lowering--.f64 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in x around inf

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

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

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

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

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

       3. --lowering--.f64 72.6%

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

   11. Simplified 72.6%

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

   if -3.2499999999999999e140 < x < 1.49999999999999998e134

   1. Initial program 99.3%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 66.1%

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

   7. Simplified 66.1%

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

   if 1.49999999999999998e134 < x

   1. Initial program 96.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

      17. --lowering--.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

      14. --lowering--.f64 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{t - z} \cdot -60\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z} \cdot -60\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x (- t z)) -60.0)))
   (if (<= x -1.7e+140) t_1 (if (<= x 1.35e+133) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / (t - z)) * -60.0;
	double tmp;
	if (x <= -1.7e+140) {
		tmp = t_1;
	} else if (x <= 1.35e+133) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (t - z)) * (-60.0d0)
    if (x <= (-1.7d+140)) then
        tmp = t_1
    else if (x <= 1.35d+133) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / (t - z)) * -60.0;
	double tmp;
	if (x <= -1.7e+140) {
		tmp = t_1;
	} else if (x <= 1.35e+133) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / (t - z)) * -60.0
	tmp = 0
	if x <= -1.7e+140:
		tmp = t_1
	elif x <= 1.35e+133:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / Float64(t - z)) * -60.0)
	tmp = 0.0
	if (x <= -1.7e+140)
		tmp = t_1;
	elseif (x <= 1.35e+133)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / (t - z)) * -60.0;
	tmp = 0.0;
	if (x <= -1.7e+140)
		tmp = t_1;
	elseif (x <= 1.35e+133)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]}, If[LessEqual[x, -1.7e+140], t$95$1, If[LessEqual[x, 1.35e+133], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e140 or 1.3500000000000001e133 < x

   1. Initial program 98.3%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z}} \]

      2. fma-define N/A

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{120}, \frac{60 \cdot \left(y - x\right)}{t - z}\right) \]

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(y - x\right)}{t - z}\right)} \]
   7. Step-by-step derivation

      1. fma-define N/A

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{120}, \frac{60 \cdot \left(y - x\right)}{t - z}\right) \]

      2. frac-2neg N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{\mathsf{neg}\left(\left(t - z\right)\right)}\right) \]

      3. distribute-frac-neg N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)\right) \]

      4. fmm-undef N/A

         \[\leadsto a \cdot 120 - \color{blue}{\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(t - z\right)\right)}} \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a \cdot 120\right), \color{blue}{\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \left(\frac{\color{blue}{60 \cdot \left(y - x\right)}}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \left(\frac{60 \cdot \left(y - x\right)}{-1 \cdot \color{blue}{\left(t - z\right)}}\right)\right) \]

      8. times-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \left(\frac{60}{-1} \cdot \color{blue}{\frac{y - x}{t - z}}\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \left(-60 \cdot \frac{\color{blue}{y - x}}{t - z}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \left(\left(\mathsf{neg}\left(60\right)\right) \cdot \frac{\color{blue}{y - x}}{t - z}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \mathsf{*.f64}\left(\left(\mathsf{neg}\left(60\right)\right), \color{blue}{\left(\frac{y - x}{t - z}\right)}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \mathsf{*.f64}\left(-60, \left(\frac{\color{blue}{y - x}}{t - z}\right)\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(t - z\right)}\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{t} - z\right)\right)\right)\right) \]

      15. --lowering--.f64 98.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, 120\right), \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{a \cdot 120 - -60 \cdot \frac{y - x}{t - z}} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

       3. --lowering--.f64 75.1%

          \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 75.1%

       \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]

   if -1.7e140 < x < 1.3500000000000001e133

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 66.1%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 66.1%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{t - z} \cdot -60\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+136}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7e+136)
   (* -60.0 (/ x t))
   (if (<= x 1.6e+134) (* a 120.0) (/ (* x -60.0) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7e+136) {
		tmp = -60.0 * (x / t);
	} else if (x <= 1.6e+134) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-7d+136)) then
        tmp = (-60.0d0) * (x / t)
    else if (x <= 1.6d+134) then
        tmp = a * 120.0d0
    else
        tmp = (x * (-60.0d0)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7e+136) {
		tmp = -60.0 * (x / t);
	} else if (x <= 1.6e+134) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7e+136:
		tmp = -60.0 * (x / t)
	elif x <= 1.6e+134:
		tmp = a * 120.0
	else:
		tmp = (x * -60.0) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7e+136)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (x <= 1.6e+134)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x * -60.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7e+136)
		tmp = -60.0 * (x / t);
	elseif (x <= 1.6e+134)
		tmp = a * 120.0;
	else
		tmp = (x * -60.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7e+136], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+134], N[(a * 120.0), $MachinePrecision], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.00000000000000002e136

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{t - z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x \cdot -60}{\color{blue}{t} - z} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{-60}{t - z}} \]

      4. metadata-eval N/A

         \[\leadsto x \cdot \frac{\mathsf{neg}\left(60\right)}{\color{blue}{t} - z} \]

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\mathsf{neg}\left(60\right)}{\color{blue}{t - z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{-60}{\color{blue}{t} - z}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \color{blue}{\left(t - z\right)}\right)\right) \]

      14. --lowering--.f64 71.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 71.3%

      \[\leadsto \color{blue}{x \cdot \frac{-60}{t - z}} \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-60}{t}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 47.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \color{blue}{t}\right)\right) \]

   10. Simplified 47.5%

       \[\leadsto x \cdot \color{blue}{\frac{-60}{t}} \]
   11. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{t}{-60}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{x \cdot 1}{\color{blue}{\frac{t}{-60}}} \]

       3. div-inv N/A

          \[\leadsto \frac{x \cdot 1}{t \cdot \color{blue}{\frac{1}{-60}}} \]

       4. times-frac N/A

          \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{\frac{1}{-60}}} \]

       5. metadata-eval N/A

          \[\leadsto \frac{x}{t} \cdot \frac{1}{\frac{-1}{60}} \]

       6. metadata-eval N/A

          \[\leadsto \frac{x}{t} \cdot -60 \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{-60}\right) \]

       8. /-lowering-/.f64 47.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), -60\right) \]

   12. Applied egg-rr 47.6%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot -60} \]

   if -7.00000000000000002e136 < x < 1.6e134

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 66.2%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 1.6e134 < x

   1. Initial program 96.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 96.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{t - z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x \cdot -60}{\color{blue}{t} - z} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{-60}{t - z}} \]

      4. metadata-eval N/A

         \[\leadsto x \cdot \frac{\mathsf{neg}\left(60\right)}{\color{blue}{t} - z} \]

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\mathsf{neg}\left(60\right)}{\color{blue}{t - z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{-60}{\color{blue}{t} - z}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \color{blue}{\left(t - z\right)}\right)\right) \]

      14. --lowering--.f64 77.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \frac{-60}{t - z}} \]

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{t}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-60 \cdot x\right), \color{blue}{t}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot -60\right), t\right) \]

      4. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, -60\right), t\right) \]

   10. Simplified 51.2%

       \[\leadsto \color{blue}{\frac{x \cdot -60}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+136}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))))
   (if (<= x -3.5e+131) t_1 (if (<= x 7.5e+133) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (x <= -3.5e+131) {
		tmp = t_1;
	} else if (x <= 7.5e+133) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    if (x <= (-3.5d+131)) then
        tmp = t_1
    else if (x <= 7.5d+133) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (x <= -3.5e+131) {
		tmp = t_1;
	} else if (x <= 7.5e+133) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	tmp = 0
	if x <= -3.5e+131:
		tmp = t_1
	elif x <= 7.5e+133:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	tmp = 0.0
	if (x <= -3.5e+131)
		tmp = t_1;
	elseif (x <= 7.5e+133)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	tmp = 0.0;
	if (x <= -3.5e+131)
		tmp = t_1;
	elseif (x <= 7.5e+133)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+131], t$95$1, If[LessEqual[x, 7.5e+133], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4999999999999999e131 or 7.49999999999999992e133 < x

   1. Initial program 98.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 98.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{t - z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x \cdot -60}{\color{blue}{t} - z} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{-60}{t - z}} \]

      4. metadata-eval N/A

         \[\leadsto x \cdot \frac{\mathsf{neg}\left(60\right)}{\color{blue}{t} - z} \]

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\mathsf{neg}\left(60\right)}{\color{blue}{t - z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{-60}{\color{blue}{t} - z}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \color{blue}{\left(t - z\right)}\right)\right) \]

      14. --lowering--.f64 74.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{-60}{t - z}} \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-60}{t}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 49.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \color{blue}{t}\right)\right) \]

   10. Simplified 49.2%

       \[\leadsto x \cdot \color{blue}{\frac{-60}{t}} \]
   11. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{t}{-60}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{x \cdot 1}{\color{blue}{\frac{t}{-60}}} \]

       3. div-inv N/A

          \[\leadsto \frac{x \cdot 1}{t \cdot \color{blue}{\frac{1}{-60}}} \]

       4. times-frac N/A

          \[\leadsto \frac{x}{t} \cdot \color{blue}{\frac{1}{\frac{1}{-60}}} \]

       5. metadata-eval N/A

          \[\leadsto \frac{x}{t} \cdot \frac{1}{\frac{-1}{60}} \]

       6. metadata-eval N/A

          \[\leadsto \frac{x}{t} \cdot -60 \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{-60}\right) \]

       8. /-lowering-/.f64 49.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), -60\right) \]

   12. Applied egg-rr 49.3%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot -60} \]

   if -3.4999999999999999e131 < x < 7.49999999999999992e133

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 66.2%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-60}{t}\\ \mathbf{if}\;x \leq -3.25 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ -60.0 t))))
   (if (<= x -3.25e+136) t_1 (if (<= x 1.6e+134) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-60.0 / t);
	double tmp;
	if (x <= -3.25e+136) {
		tmp = t_1;
	} else if (x <= 1.6e+134) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((-60.0d0) / t)
    if (x <= (-3.25d+136)) then
        tmp = t_1
    else if (x <= 1.6d+134) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-60.0 / t);
	double tmp;
	if (x <= -3.25e+136) {
		tmp = t_1;
	} else if (x <= 1.6e+134) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-60.0 / t)
	tmp = 0
	if x <= -3.25e+136:
		tmp = t_1
	elif x <= 1.6e+134:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(-60.0 / t))
	tmp = 0.0
	if (x <= -3.25e+136)
		tmp = t_1;
	elseif (x <= 1.6e+134)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (-60.0 / t);
	tmp = 0.0;
	if (x <= -3.25e+136)
		tmp = t_1;
	elseif (x <= 1.6e+134)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.25e+136], t$95$1, If[LessEqual[x, 1.6e+134], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2499999999999999e136 or 1.6e134 < x

   1. Initial program 98.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 98.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot x}{\color{blue}{t - z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x \cdot -60}{\color{blue}{t} - z} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{-60}{t - z}} \]

      4. metadata-eval N/A

         \[\leadsto x \cdot \frac{\mathsf{neg}\left(60\right)}{\color{blue}{t} - z} \]

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)}\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\mathsf{neg}\left(60\right)}{\color{blue}{t - z}}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{-60}{\color{blue}{t} - z}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \color{blue}{\left(t - z\right)}\right)\right) \]

      14. --lowering--.f64 74.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{-60}{t - z}} \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{-60}{t}\right)}\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 49.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(-60, \color{blue}{t}\right)\right) \]

   10. Simplified 49.2%

       \[\leadsto x \cdot \color{blue}{\frac{-60}{t}} \]

   if -3.2499999999999999e136 < x < 1.6e134

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 66.2%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 - 60 \cdot \frac{y - x}{z - t} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- (* a 120.0) (* 60.0 (/ (- y x) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) - (60.0 * ((y - x) / (z - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (a * 120.0d0) - (60.0d0 * ((y - x) / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) - (60.0 * ((y - x) / (z - t)));
}

Python

def code(x, y, z, t, a):
	return (a * 120.0) - (60.0 * ((y - x) / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(a * 120.0) - Float64(60.0 * Float64(Float64(y - x) / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (a * 120.0) - (60.0 * ((y - x) / (z - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 * N[(N[(y - x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   9. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

   14. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   17. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

   19. *-lowering-*.f64 99.1%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{y - x}{t - z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{t - z} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{y - x}{t - z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. --lowering--.f64 99.5%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(t, z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

6. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\frac{y - x}{t - z} \cdot 60} + a \cdot 120 \]

7. Final simplification 99.5%

   \[\leadsto a \cdot 120 - 60 \cdot \frac{y - x}{z - t} \]
8. Add Preprocessing

Alternative 15: 50.7% 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. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   9. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

   14. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   17. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

   19. *-lowering-*.f64 99.1%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
4. Add Preprocessing

5. Taylor expanded in t around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 53.2%

      \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

7. Simplified 53.2%

   \[\leadsto \color{blue}{120 \cdot a} \]

8. Final simplification 53.2%

   \[\leadsto a \cdot 120 \]
9. 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 2024138 
(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)))