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

Percentage Accurate: 99.3% → 99.4%

Time: 13.1s

Alternatives: 16

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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-223}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-148}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e-51)
   (* a 120.0)
   (if (<= a -1.5e-223)
     (* -60.0 (/ x (- t z)))
     (if (<= a 1.46e-297)
       (* -60.0 (/ (- y x) z))
       (if (<= a 3.9e-148) (* 60.0 (/ (- y x) t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-51) {
		tmp = a * 120.0;
	} else if (a <= -1.5e-223) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 1.46e-297) {
		tmp = -60.0 * ((y - x) / z);
	} else if (a <= 3.9e-148) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.3d-51)) then
        tmp = a * 120.0d0
    else if (a <= (-1.5d-223)) then
        tmp = (-60.0d0) * (x / (t - z))
    else if (a <= 1.46d-297) then
        tmp = (-60.0d0) * ((y - x) / z)
    else if (a <= 3.9d-148) then
        tmp = 60.0d0 * ((y - x) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-51) {
		tmp = a * 120.0;
	} else if (a <= -1.5e-223) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 1.46e-297) {
		tmp = -60.0 * ((y - x) / z);
	} else if (a <= 3.9e-148) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e-51:
		tmp = a * 120.0
	elif a <= -1.5e-223:
		tmp = -60.0 * (x / (t - z))
	elif a <= 1.46e-297:
		tmp = -60.0 * ((y - x) / z)
	elif a <= 3.9e-148:
		tmp = 60.0 * ((y - x) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e-51)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.5e-223)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	elseif (a <= 1.46e-297)
		tmp = Float64(-60.0 * Float64(Float64(y - x) / z));
	elseif (a <= 3.9e-148)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e-51)
		tmp = a * 120.0;
	elseif (a <= -1.5e-223)
		tmp = -60.0 * (x / (t - z));
	elseif (a <= 1.46e-297)
		tmp = -60.0 * ((y - x) / z);
	elseif (a <= 3.9e-148)
		tmp = 60.0 * ((y - x) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e-51], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.5e-223], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.46e-297], N[(-60.0 * N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-148], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.30000000000000002e-51 or 3.89999999999999994e-148 < a

   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 t around inf

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

      1. *-lowering-*.f64 72.5%

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

   7. Simplified 72.5%

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

   if -2.30000000000000002e-51 < a < -1.49999999999999996e-223

   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. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   8. 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 51.5%

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

   9. Simplified 51.5%

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

   if -1.49999999999999996e-223 < a < 1.4600000000000001e-297

   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 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 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 78.2%

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

   10. Simplified 78.2%

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

   if 1.4600000000000001e-297 < a < 3.89999999999999994e-148

   1. Initial program 99.6%

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t} + 120 \cdot a} \]
   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 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in a around 0

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

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

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

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

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

      3. --lowering--.f64 56.8%

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

   10. Simplified 56.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-223}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-148}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-217}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+151}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.2e+180)
   (* 60.0 (/ y (- t z)))
   (if (<= y -8e-217)
     (* a 120.0)
     (if (<= y 2.1e+151)
       (+ (* a 120.0) (* -60.0 (/ x t)))
       (* y (/ 60.0 (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+180) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= -8e-217) {
		tmp = a * 120.0;
	} else if (y <= 2.1e+151) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else {
		tmp = y * (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 (y <= (-3.2d+180)) then
        tmp = 60.0d0 * (y / (t - z))
    else if (y <= (-8d-217)) then
        tmp = a * 120.0d0
    else if (y <= 2.1d+151) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else
        tmp = y * (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 (y <= -3.2e+180) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= -8e-217) {
		tmp = a * 120.0;
	} else if (y <= 2.1e+151) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e+180:
		tmp = 60.0 * (y / (t - z))
	elif y <= -8e-217:
		tmp = a * 120.0
	elif y <= 2.1e+151:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	else:
		tmp = y * (60.0 / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.2e+180)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	elseif (y <= -8e-217)
		tmp = Float64(a * 120.0);
	elseif (y <= 2.1e+151)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	else
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.2e+180)
		tmp = 60.0 * (y / (t - z));
	elseif (y <= -8e-217)
		tmp = a * 120.0;
	elseif (y <= 2.1e+151)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	else
		tmp = y * (60.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.2e+180], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-217], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 2.1e+151], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.19999999999999994e180

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 81.8%

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

   7. Simplified 81.8%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

         \[\leadsto \frac{y}{t - z} \cdot \frac{1}{\frac{1}{60}} \]

      6. metadata-eval N/A

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

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

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

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

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

      9. --lowering--.f64 81.9%

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

   9. Applied egg-rr 81.9%

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

   if -3.19999999999999994e180 < y < -8.00000000000000066e-217

   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 t around inf

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

      1. *-lowering-*.f64 68.1%

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

   7. Simplified 68.1%

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

   if -8.00000000000000066e-217 < y < 2.1000000000000001e151

   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 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 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 68.8%

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

   10. Simplified 68.8%

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

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

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

       2. *-commutative N/A

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

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

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

       4. *-commutative N/A

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

       5. associate-/l* N/A

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

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

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

       7. /-lowering-/.f64 68.8%

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

   12. Applied egg-rr 68.8%

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

   if 2.1000000000000001e151 < y

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-217}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+151}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-218}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.2e+180)
   (* 60.0 (/ y (- t z)))
   (if (<= y -2.6e-218)
     (* a 120.0)
     (if (<= y 6.8e+152)
       (+ (* a 120.0) (/ (* x -60.0) t))
       (* y (/ 60.0 (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+180) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= -2.6e-218) {
		tmp = a * 120.0;
	} else if (y <= 6.8e+152) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else {
		tmp = y * (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 (y <= (-3.2d+180)) then
        tmp = 60.0d0 * (y / (t - z))
    else if (y <= (-2.6d-218)) then
        tmp = a * 120.0d0
    else if (y <= 6.8d+152) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else
        tmp = y * (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 (y <= -3.2e+180) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= -2.6e-218) {
		tmp = a * 120.0;
	} else if (y <= 6.8e+152) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e+180:
		tmp = 60.0 * (y / (t - z))
	elif y <= -2.6e-218:
		tmp = a * 120.0
	elif y <= 6.8e+152:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	else:
		tmp = y * (60.0 / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.2e+180)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	elseif (y <= -2.6e-218)
		tmp = Float64(a * 120.0);
	elseif (y <= 6.8e+152)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	else
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.2e+180)
		tmp = 60.0 * (y / (t - z));
	elseif (y <= -2.6e-218)
		tmp = a * 120.0;
	elseif (y <= 6.8e+152)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	else
		tmp = y * (60.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.2e+180], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-218], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 6.8e+152], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.19999999999999994e180

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 81.8%

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

   7. Simplified 81.8%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

         \[\leadsto \frac{y}{t - z} \cdot \frac{1}{\frac{1}{60}} \]

      6. metadata-eval N/A

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

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

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

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

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

      9. --lowering--.f64 81.9%

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

   9. Applied egg-rr 81.9%

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

   if -3.19999999999999994e180 < y < -2.59999999999999983e-218

   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 t around inf

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

      1. *-lowering-*.f64 68.1%

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

   7. Simplified 68.1%

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

   if -2.59999999999999983e-218 < y < 6.80000000000000041e152

   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 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 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 68.8%

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

   10. Simplified 68.8%

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

   if 6.80000000000000041e152 < y

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-218}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 100000:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e+53)
   (* a 120.0)
   (if (<= (* a 120.0) 100000.0) (/ (* 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 * 120.0) <= -1e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 100000.0) {
		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 * 120.0d0) <= (-1d+53)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 100000.0d0) 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 * 120.0) <= -1e+53) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 100000.0) {
		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 * 120.0) <= -1e+53:
		tmp = a * 120.0
	elif (a * 120.0) <= 100000.0:
		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 (Float64(a * 120.0) <= -1e+53)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 100000.0)
		tmp = Float64(Float64(60.0 * 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 * 120.0) <= -1e+53)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 100000.0)
		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[N[(a * 120.0), $MachinePrecision], -1e+53], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 100000.0], N[(N[(60.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.9999999999999999e52 or 1e5 < (*.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 t around inf

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

      1. *-lowering-*.f64 83.5%

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

   7. Simplified 83.5%

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

   if -9.9999999999999999e52 < (*.f64 a #s(literal 120 binary64)) < 1e5

   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 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 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 100000:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-227}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.22e-62)
   (* a 120.0)
   (if (<= a -3.7e-227)
     (* -60.0 (/ x (- t z)))
     (if (<= a 1.1e-147) (* y (/ 60.0 (- t z))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.22e-62) {
		tmp = a * 120.0;
	} else if (a <= -3.7e-227) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 1.1e-147) {
		tmp = y * (60.0 / (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 <= (-1.22d-62)) then
        tmp = a * 120.0d0
    else if (a <= (-3.7d-227)) then
        tmp = (-60.0d0) * (x / (t - z))
    else if (a <= 1.1d-147) then
        tmp = y * (60.0d0 / (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 <= -1.22e-62) {
		tmp = a * 120.0;
	} else if (a <= -3.7e-227) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 1.1e-147) {
		tmp = y * (60.0 / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.22e-62:
		tmp = a * 120.0
	elif a <= -3.7e-227:
		tmp = -60.0 * (x / (t - z))
	elif a <= 1.1e-147:
		tmp = y * (60.0 / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.22e-62)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.7e-227)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	elseif (a <= 1.1e-147)
		tmp = Float64(y * Float64(60.0 / 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 <= -1.22e-62)
		tmp = a * 120.0;
	elseif (a <= -3.7e-227)
		tmp = -60.0 * (x / (t - z));
	elseif (a <= 1.1e-147)
		tmp = y * (60.0 / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.22e-62], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.7e-227], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-147], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2199999999999999e-62 or 1.1000000000000001e-147 < a

   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 t around inf

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

      1. *-lowering-*.f64 72.5%

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

   7. Simplified 72.5%

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

   if -1.2199999999999999e-62 < a < -3.69999999999999978e-227

   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. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   8. 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 51.5%

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

   9. Simplified 51.5%

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

   if -3.69999999999999978e-227 < a < 1.1000000000000001e-147

   1. Initial program 99.7%

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 62.8%

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

   7. Simplified 62.8%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-227}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-220}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e-58)
   (* a 120.0)
   (if (<= a -1.25e-220)
     (* -60.0 (/ x (- t z)))
     (if (<= a 2.2e-175) (* -60.0 (/ (- y x) z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-58) {
		tmp = a * 120.0;
	} else if (a <= -1.25e-220) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 2.2e-175) {
		tmp = -60.0 * ((y - x) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3d-58)) then
        tmp = a * 120.0d0
    else if (a <= (-1.25d-220)) then
        tmp = (-60.0d0) * (x / (t - z))
    else if (a <= 2.2d-175) then
        tmp = (-60.0d0) * ((y - x) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-58) {
		tmp = a * 120.0;
	} else if (a <= -1.25e-220) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 2.2e-175) {
		tmp = -60.0 * ((y - x) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e-58:
		tmp = a * 120.0
	elif a <= -1.25e-220:
		tmp = -60.0 * (x / (t - z))
	elif a <= 2.2e-175:
		tmp = -60.0 * ((y - x) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e-58)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.25e-220)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	elseif (a <= 2.2e-175)
		tmp = Float64(-60.0 * Float64(Float64(y - x) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3e-58)
		tmp = a * 120.0;
	elseif (a <= -1.25e-220)
		tmp = -60.0 * (x / (t - z));
	elseif (a <= 2.2e-175)
		tmp = -60.0 * ((y - x) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e-58], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.25e-220], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-175], N[(-60.0 * N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.00000000000000008e-58 or 2.2e-175 < a

   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 t around inf

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

      1. *-lowering-*.f64 70.0%

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

   7. Simplified 70.0%

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

   if -3.00000000000000008e-58 < a < -1.25e-220

   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. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   8. 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 51.5%

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

   9. Simplified 51.5%

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

   if -1.25e-220 < a < 2.2e-175

   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 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 93.4%

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

   7. Simplified 93.4%

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

   8. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 60.2%

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

   10. Simplified 60.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-220}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot -60}{z} + a \cdot 120\\ \mathbf{if}\;z \leq -205000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* (- y x) -60.0) z) (* a 120.0))))
   (if (<= z -205000000.0)
     t_1
     (if (<= z 2.1e-20) (+ (* 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 = (((y - x) * -60.0) / z) + (a * 120.0);
	double tmp;
	if (z <= -205000000.0) {
		tmp = t_1;
	} else if (z <= 2.1e-20) {
		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 = (((y - x) * (-60.0d0)) / z) + (a * 120.0d0)
    if (z <= (-205000000.0d0)) then
        tmp = t_1
    else if (z <= 2.1d-20) 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 = (((y - x) * -60.0) / z) + (a * 120.0);
	double tmp;
	if (z <= -205000000.0) {
		tmp = t_1;
	} else if (z <= 2.1e-20) {
		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 = (((y - x) * -60.0) / z) + (a * 120.0)
	tmp = 0
	if z <= -205000000.0:
		tmp = t_1
	elif z <= 2.1e-20:
		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(Float64(Float64(y - x) * -60.0) / z) + Float64(a * 120.0))
	tmp = 0.0
	if (z <= -205000000.0)
		tmp = t_1;
	elseif (z <= 2.1e-20)
		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 = (((y - x) * -60.0) / z) + (a * 120.0);
	tmp = 0.0;
	if (z <= -205000000.0)
		tmp = t_1;
	elseif (z <= 2.1e-20)
		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[(N[(N[(y - x), $MachinePrecision] * -60.0), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -205000000.0], t$95$1, If[LessEqual[z, 2.1e-20], 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 < -2.05e8 or 2.0999999999999999e-20 < z

   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 t around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 88.6%

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

   7. Simplified 88.6%

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

   if -2.05e8 < z < 2.0999999999999999e-20

   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 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 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -205000000:\\ \;\;\;\;\frac{\left(y - x\right) \cdot -60}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot -60}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-65}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-300}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e-65)
   (* a 120.0)
   (if (<= a 1.35e-300)
     (* -60.0 (/ x (- t z)))
     (if (<= a 2.9e-148) (* y (/ 60.0 t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e-65) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-300) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 2.9e-148) {
		tmp = y * (60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5d-65)) then
        tmp = a * 120.0d0
    else if (a <= 1.35d-300) then
        tmp = (-60.0d0) * (x / (t - z))
    else if (a <= 2.9d-148) then
        tmp = y * (60.0d0 / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e-65) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-300) {
		tmp = -60.0 * (x / (t - z));
	} else if (a <= 2.9e-148) {
		tmp = y * (60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e-65:
		tmp = a * 120.0
	elif a <= 1.35e-300:
		tmp = -60.0 * (x / (t - z))
	elif a <= 2.9e-148:
		tmp = y * (60.0 / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e-65)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.35e-300)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	elseif (a <= 2.9e-148)
		tmp = Float64(y * Float64(60.0 / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e-65)
		tmp = a * 120.0;
	elseif (a <= 1.35e-300)
		tmp = -60.0 * (x / (t - z));
	elseif (a <= 2.9e-148)
		tmp = y * (60.0 / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e-65], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.35e-300], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-148], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.99999999999999983e-65 or 2.8999999999999998e-148 < a

   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 t around inf

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

      1. *-lowering-*.f64 72.5%

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

   7. Simplified 72.5%

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

   if -4.99999999999999983e-65 < a < 1.34999999999999998e-300

   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. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   8. 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 47.7%

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

   9. Simplified 47.7%

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

   if 1.34999999999999998e-300 < a < 2.8999999999999998e-148

   1. Initial program 99.6%

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

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 41.5%

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

   10. Simplified 41.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-65}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-300}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+243}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+158}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{-60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.6e+243)
   (* -60.0 (/ y z))
   (if (<= y -4.8e+180)
     (* 60.0 (/ y t))
     (if (<= y 1.95e+158) (* a 120.0) (/ y (/ z -60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.6e+243) {
		tmp = -60.0 * (y / z);
	} else if (y <= -4.8e+180) {
		tmp = 60.0 * (y / t);
	} else if (y <= 1.95e+158) {
		tmp = a * 120.0;
	} else {
		tmp = y / (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 (y <= (-1.6d+243)) then
        tmp = (-60.0d0) * (y / z)
    else if (y <= (-4.8d+180)) then
        tmp = 60.0d0 * (y / t)
    else if (y <= 1.95d+158) then
        tmp = a * 120.0d0
    else
        tmp = y / (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 (y <= -1.6e+243) {
		tmp = -60.0 * (y / z);
	} else if (y <= -4.8e+180) {
		tmp = 60.0 * (y / t);
	} else if (y <= 1.95e+158) {
		tmp = a * 120.0;
	} else {
		tmp = y / (z / -60.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.6e+243:
		tmp = -60.0 * (y / z)
	elif y <= -4.8e+180:
		tmp = 60.0 * (y / t)
	elif y <= 1.95e+158:
		tmp = a * 120.0
	else:
		tmp = y / (z / -60.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.6e+243)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (y <= -4.8e+180)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (y <= 1.95e+158)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y / Float64(z / -60.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.6e+243)
		tmp = -60.0 * (y / z);
	elseif (y <= -4.8e+180)
		tmp = 60.0 * (y / t);
	elseif (y <= 1.95e+158)
		tmp = a * 120.0;
	else
		tmp = y / (z / -60.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.6e+243], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e+180], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+158], N[(a * 120.0), $MachinePrecision], N[(y / N[(z / -60.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.60000000000000008e243

   1. Initial program 100.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 60.2%

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

   10. Simplified 60.2%

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

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

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

       5. /-lowering-/.f64 60.2%

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

   12. Applied egg-rr 60.2%

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

   if -1.60000000000000008e243 < y < -4.7999999999999997e180

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 87.1%

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

   7. Simplified 87.1%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

         \[\leadsto \frac{y}{t - z} \cdot \frac{1}{\frac{1}{60}} \]

      6. metadata-eval N/A

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

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

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

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

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

      9. --lowering--.f64 87.3%

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

   9. Applied egg-rr 87.3%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{t}\right)}, 60\right) \]
   11. Step-by-step derivation

       1. /-lowering-/.f64 75.1%

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

   12. Simplified 75.1%

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

   if -4.7999999999999997e180 < y < 1.95e158

   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 t around inf

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

      1. *-lowering-*.f64 60.6%

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

   7. Simplified 60.6%

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

   if 1.95e158 < y

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 46.8%

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

   10. Simplified 46.8%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

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

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

       4. /-lowering-/.f64 46.9%

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

   12. Applied egg-rr 46.9%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+243}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+158}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{-60}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+154}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y z))))
   (if (<= y -1.7e+245)
     t_1
     (if (<= y -5.8e+180)
       (* 60.0 (/ y t))
       (if (<= y 1.1e+154) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / z);
	double tmp;
	if (y <= -1.7e+245) {
		tmp = t_1;
	} else if (y <= -5.8e+180) {
		tmp = 60.0 * (y / t);
	} else if (y <= 1.1e+154) {
		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) * (y / z)
    if (y <= (-1.7d+245)) then
        tmp = t_1
    else if (y <= (-5.8d+180)) then
        tmp = 60.0d0 * (y / t)
    else if (y <= 1.1d+154) 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 * (y / z);
	double tmp;
	if (y <= -1.7e+245) {
		tmp = t_1;
	} else if (y <= -5.8e+180) {
		tmp = 60.0 * (y / t);
	} else if (y <= 1.1e+154) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / z)
	tmp = 0
	if y <= -1.7e+245:
		tmp = t_1
	elif y <= -5.8e+180:
		tmp = 60.0 * (y / t)
	elif y <= 1.1e+154:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / z))
	tmp = 0.0
	if (y <= -1.7e+245)
		tmp = t_1;
	elseif (y <= -5.8e+180)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (y <= 1.1e+154)
		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 * (y / z);
	tmp = 0.0;
	if (y <= -1.7e+245)
		tmp = t_1;
	elseif (y <= -5.8e+180)
		tmp = 60.0 * (y / t);
	elseif (y <= 1.1e+154)
		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[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+245], t$95$1, If[LessEqual[y, -5.8e+180], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+154], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999999e245 or 1.1000000000000001e154 < y

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 50.6%

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

   10. Simplified 50.6%

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

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

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

       5. /-lowering-/.f64 50.6%

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

   12. Applied egg-rr 50.6%

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

   if -1.69999999999999999e245 < y < -5.80000000000000015e180

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 87.1%

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

   7. Simplified 87.1%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

         \[\leadsto \frac{y}{t - z} \cdot \frac{1}{\frac{1}{60}} \]

      6. metadata-eval N/A

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

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

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

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

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

      9. --lowering--.f64 87.3%

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

   9. Applied egg-rr 87.3%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{t}\right)}, 60\right) \]
   11. Step-by-step derivation

       1. /-lowering-/.f64 75.1%

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

   12. Simplified 75.1%

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

   if -5.80000000000000015e180 < y < 1.1000000000000001e154

   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 t around inf

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

      1. *-lowering-*.f64 60.6%

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

   7. Simplified 60.6%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+245}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+180}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+154}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+156}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y z))))
   (if (<= y -1.35e+244)
     t_1
     (if (<= y -6.8e+180)
       (* y (/ 60.0 t))
       (if (<= y 8.2e+156) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / z);
	double tmp;
	if (y <= -1.35e+244) {
		tmp = t_1;
	} else if (y <= -6.8e+180) {
		tmp = y * (60.0 / t);
	} else if (y <= 8.2e+156) {
		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) * (y / z)
    if (y <= (-1.35d+244)) then
        tmp = t_1
    else if (y <= (-6.8d+180)) then
        tmp = y * (60.0d0 / t)
    else if (y <= 8.2d+156) 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 * (y / z);
	double tmp;
	if (y <= -1.35e+244) {
		tmp = t_1;
	} else if (y <= -6.8e+180) {
		tmp = y * (60.0 / t);
	} else if (y <= 8.2e+156) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / z)
	tmp = 0
	if y <= -1.35e+244:
		tmp = t_1
	elif y <= -6.8e+180:
		tmp = y * (60.0 / t)
	elif y <= 8.2e+156:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / z))
	tmp = 0.0
	if (y <= -1.35e+244)
		tmp = t_1;
	elseif (y <= -6.8e+180)
		tmp = Float64(y * Float64(60.0 / t));
	elseif (y <= 8.2e+156)
		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 * (y / z);
	tmp = 0.0;
	if (y <= -1.35e+244)
		tmp = t_1;
	elseif (y <= -6.8e+180)
		tmp = y * (60.0 / t);
	elseif (y <= 8.2e+156)
		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[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+244], t$95$1, If[LessEqual[y, -6.8e+180], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+156], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.34999999999999999e244 or 8.2000000000000003e156 < y

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 50.6%

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

   10. Simplified 50.6%

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

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

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

       5. /-lowering-/.f64 50.6%

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

   12. Applied egg-rr 50.6%

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

   if -1.34999999999999999e244 < y < -6.79999999999999969e180

   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 inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 75.0%

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

   10. Simplified 75.0%

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

   if -6.79999999999999969e180 < y < 8.2000000000000003e156

   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 t around inf

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

      1. *-lowering-*.f64 60.6%

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

   7. Simplified 60.6%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+244}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+156}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-176}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e-110)
   (* a 120.0)
   (if (<= a 9.5e-176) (* -60.0 (/ y z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-110) {
		tmp = a * 120.0;
	} else if (a <= 9.5e-176) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.3d-110)) then
        tmp = a * 120.0d0
    else if (a <= 9.5d-176) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-110) {
		tmp = a * 120.0;
	} else if (a <= 9.5e-176) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e-110:
		tmp = a * 120.0
	elif a <= 9.5e-176:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e-110)
		tmp = Float64(a * 120.0);
	elseif (a <= 9.5e-176)
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e-110)
		tmp = a * 120.0;
	elseif (a <= 9.5e-176)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e-110], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 9.5e-176], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3000000000000001e-110 or 9.5e-176 < a

   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 t around inf

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

      1. *-lowering-*.f64 65.9%

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

   7. Simplified 65.9%

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

   if -2.3000000000000001e-110 < a < 9.5e-176

   1. Initial program 99.7%

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

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 35.2%

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

   10. Simplified 35.2%

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

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

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

       5. /-lowering-/.f64 35.2%

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

   12. Applied egg-rr 35.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-176}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-169}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e-112)
   (* a 120.0)
   (if (<= a 2.8e-169) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e-112) {
		tmp = a * 120.0;
	} else if (a <= 2.8e-169) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.1d-112)) then
        tmp = a * 120.0d0
    else if (a <= 2.8d-169) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e-112) {
		tmp = a * 120.0;
	} else if (a <= 2.8e-169) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e-112:
		tmp = a * 120.0
	elif a <= 2.8e-169:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e-112)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.8e-169)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e-112)
		tmp = a * 120.0;
	elseif (a <= 2.8e-169)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e-112], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.8e-169], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1000000000000001e-112 or 2.79999999999999988e-169 < a

   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 t around inf

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

      1. *-lowering-*.f64 66.6%

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

   7. Simplified 66.6%

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

   if -2.1000000000000001e-112 < a < 2.79999999999999988e-169

   1. Initial program 99.7%

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

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   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 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in x 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 24.7%

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

   10. Simplified 24.7%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 24.8%

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

   12. Applied egg-rr 24.8%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-169}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 * ((y - x) / (t - z))) + (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 * ((y - x) / (t - z))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. 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 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 16: 51.0% 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 99.8%

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

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

   1. *-lowering-*.f64 51.2%

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

7. Simplified 51.2%

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

8. Final simplification 51.2%

   \[\leadsto a \cdot 120 \]
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 2024145 
(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)))