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

Percentage Accurate: 99.4% → 99.8%

Time: 14.0s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

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

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. neg-sub0 N/A

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

   5. associate-+l- N/A

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

   6. sub0-neg N/A

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

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

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

   8. distribute-frac-neg N/A

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

   9. distribute-frac-neg2 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. unsub-neg N/A

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

   14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

   19. *-lowering-*.f64 99.4%

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

3. Simplified 99.4%

   \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
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. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+174}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-257}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.7e+174)
   (* a 120.0)
   (if (<= a -6.5e-257)
     (+ (* a 120.0) (/ (* 60.0 y) t))
     (if (<= a 7.5e-199)
       (* x (/ -60.0 (- t z)))
       (if (<= a 5.8e-78) (* 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 <= -4.7e+174) {
		tmp = a * 120.0;
	} else if (a <= -6.5e-257) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if (a <= 7.5e-199) {
		tmp = x * (-60.0 / (t - z));
	} else if (a <= 5.8e-78) {
		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 <= (-4.7d+174)) then
        tmp = a * 120.0d0
    else if (a <= (-6.5d-257)) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else if (a <= 7.5d-199) then
        tmp = x * ((-60.0d0) / (t - z))
    else if (a <= 5.8d-78) 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 <= -4.7e+174) {
		tmp = a * 120.0;
	} else if (a <= -6.5e-257) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if (a <= 7.5e-199) {
		tmp = x * (-60.0 / (t - z));
	} else if (a <= 5.8e-78) {
		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 <= -4.7e+174:
		tmp = a * 120.0
	elif a <= -6.5e-257:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	elif a <= 7.5e-199:
		tmp = x * (-60.0 / (t - z))
	elif a <= 5.8e-78:
		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 <= -4.7e+174)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.5e-257)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	elseif (a <= 7.5e-199)
		tmp = Float64(x * Float64(-60.0 / Float64(t - z)));
	elseif (a <= 5.8e-78)
		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 <= -4.7e+174)
		tmp = a * 120.0;
	elseif (a <= -6.5e-257)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	elseif (a <= 7.5e-199)
		tmp = x * (-60.0 / (t - z));
	elseif (a <= 5.8e-78)
		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, -4.7e+174], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.5e-257], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-199], N[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-78], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.6999999999999996e174 or 5.8000000000000001e-78 < 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 78.8%

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

   7. Simplified 78.8%

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

   if -4.6999999999999996e174 < a < -6.5000000000000002e-257

   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 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 64.4%

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

   10. Simplified 64.4%

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

   if -6.5000000000000002e-257 < a < 7.5000000000000003e-199

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

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

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

      14. --lowering--.f64 68.3%

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

   7. Simplified 68.3%

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

   if 7.5000000000000003e-199 < a < 5.8000000000000001e-78

   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 62.5%

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

   7. Simplified 62.5%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+174}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-257}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8500:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-258}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8500.0)
   (* a 120.0)
   (if (<= a -2.1e-258)
     (* 60.0 (/ (- y x) t))
     (if (<= a 2.8e-201)
       (* x (/ -60.0 (- t z)))
       (if (<= a 1.2e-78) (* 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 <= -8500.0) {
		tmp = a * 120.0;
	} else if (a <= -2.1e-258) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 2.8e-201) {
		tmp = x * (-60.0 / (t - z));
	} else if (a <= 1.2e-78) {
		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 <= (-8500.0d0)) then
        tmp = a * 120.0d0
    else if (a <= (-2.1d-258)) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 2.8d-201) then
        tmp = x * ((-60.0d0) / (t - z))
    else if (a <= 1.2d-78) 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 <= -8500.0) {
		tmp = a * 120.0;
	} else if (a <= -2.1e-258) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 2.8e-201) {
		tmp = x * (-60.0 / (t - z));
	} else if (a <= 1.2e-78) {
		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 <= -8500.0:
		tmp = a * 120.0
	elif a <= -2.1e-258:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 2.8e-201:
		tmp = x * (-60.0 / (t - z))
	elif a <= 1.2e-78:
		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 <= -8500.0)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.1e-258)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 2.8e-201)
		tmp = Float64(x * Float64(-60.0 / Float64(t - z)));
	elseif (a <= 1.2e-78)
		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 <= -8500.0)
		tmp = a * 120.0;
	elseif (a <= -2.1e-258)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 2.8e-201)
		tmp = x * (-60.0 / (t - z));
	elseif (a <= 1.2e-78)
		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, -8500.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.1e-258], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-201], N[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-78], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8500 or 1.2e-78 < 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 76.8%

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

   7. Simplified 76.8%

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

   if -8500 < a < -2.0999999999999999e-258

   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 69.6%

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

   7. Simplified 69.6%

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

   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 55.2%

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

   10. Simplified 55.2%

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

   if -2.0999999999999999e-258 < a < 2.7999999999999999e-201

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

         \[\leadsto x \cdot \left(\mathsf{neg}\left(\frac{60}{t - z}\right)\right) \]

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

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

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

      14. --lowering--.f64 68.3%

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

   7. Simplified 68.3%

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

   if 2.7999999999999999e-201 < a < 1.2e-78

   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 62.5%

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

   7. Simplified 62.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8500:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-258}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{-60}{t - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-76}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -20000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-76)
     (/ (* 60.0 (- y x)) (- t z))
     (+ (* a 120.0) (/ (* 60.0 x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-76) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-20000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-76) then
        tmp = (60.0d0 * (y - x)) / (t - z)
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-76) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -20000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-76:
		tmp = (60.0 * (y - x)) / (t - z)
	else:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -20000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-76)
		tmp = Float64(Float64(60.0 * Float64(y - x)) / Float64(t - z));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -20000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-76)
		tmp = (60.0 * (y - x)) / (t - z);
	else
		tmp = (a * 120.0) + ((60.0 * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -20000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-76], N[(N[(60.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e7

   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 78.3%

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

   7. Simplified 78.3%

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

   if -2e7 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999927e-77

   1. Initial program 98.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in 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 83.2%

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

   7. Simplified 83.2%

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

   if 9.99999999999999927e-77 < (*.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. 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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 80.6%

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

   9. Simplified 80.6%

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

   10. Taylor expanded in y around 0

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

       1. associate-*r/ N/A

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

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

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

       3. *-lowering-*.f64 82.7%

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

   12. Simplified 82.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-76}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -390:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-277}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -390.0)
   (* a 120.0)
   (if (<= a -3.1e-277)
     (* 60.0 (/ (- y x) t))
     (if (<= a 5.5e-78) (* -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 <= -390.0) {
		tmp = a * 120.0;
	} else if (a <= -3.1e-277) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 5.5e-78) {
		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 <= (-390.0d0)) then
        tmp = a * 120.0d0
    else if (a <= (-3.1d-277)) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 5.5d-78) 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 <= -390.0) {
		tmp = a * 120.0;
	} else if (a <= -3.1e-277) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 5.5e-78) {
		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 <= -390.0:
		tmp = a * 120.0
	elif a <= -3.1e-277:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 5.5e-78:
		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 <= -390.0)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.1e-277)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 5.5e-78)
		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 <= -390.0)
		tmp = a * 120.0;
	elseif (a <= -3.1e-277)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 5.5e-78)
		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, -390.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.1e-277], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-78], 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 < -390 or 5.50000000000000017e-78 < 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 76.8%

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

   7. Simplified 76.8%

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

   if -390 < a < -3.09999999999999979e-277

   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 68.9%

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

   7. Simplified 68.9%

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

   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 55.6%

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

   10. Simplified 55.6%

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

   if -3.09999999999999979e-277 < a < 5.50000000000000017e-78

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 97.6%

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

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 58.8%

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

   9. Simplified 58.8%

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

   10. Taylor expanded in z around 0

       \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z}} \]
   11. 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 56.8%

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

   12. Simplified 56.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -390:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-277}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-255}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e-50)
   (* a 120.0)
   (if (<= a -8.5e-255)
     (/ (* 60.0 y) t)
     (if (<= a 6.5e-78) (* -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 <= -1.9e-50) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-255) {
		tmp = (60.0 * y) / t;
	} else if (a <= 6.5e-78) {
		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 <= (-1.9d-50)) then
        tmp = a * 120.0d0
    else if (a <= (-8.5d-255)) then
        tmp = (60.0d0 * y) / t
    else if (a <= 6.5d-78) 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 <= -1.9e-50) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-255) {
		tmp = (60.0 * y) / t;
	} else if (a <= 6.5e-78) {
		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 <= -1.9e-50:
		tmp = a * 120.0
	elif a <= -8.5e-255:
		tmp = (60.0 * y) / t
	elif a <= 6.5e-78:
		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 <= -1.9e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= -8.5e-255)
		tmp = Float64(Float64(60.0 * y) / t);
	elseif (a <= 6.5e-78)
		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 <= -1.9e-50)
		tmp = a * 120.0;
	elseif (a <= -8.5e-255)
		tmp = (60.0 * y) / t;
	elseif (a <= 6.5e-78)
		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, -1.9e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8.5e-255], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 6.5e-78], 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 < -1.9e-50 or 6.5000000000000003e-78 < 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 74.1%

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

   7. Simplified 74.1%

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

   if -1.9e-50 < a < -8.49999999999999982e-255

   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 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 41.7%

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

   10. Simplified 41.7%

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

   if -8.49999999999999982e-255 < a < 6.5000000000000003e-78

   1. Initial program 97.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 59.7%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in z around 0

       \[\leadsto \color{blue}{-60 \cdot \frac{y - x}{z}} \]
   11. 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 56.2%

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

   12. Simplified 56.2%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-255}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-33}:\\ \;\;\;\;a \cdot 120 + \frac{\left(y - x\right) \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ (- y x) t)))))
   (if (<= t -7.2e-31)
     t_1
     (if (<= t 6.1e-33) (+ (* a 120.0) (/ (* (- y x) -60.0) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((y - x) / t));
	double tmp;
	if (t <= -7.2e-31) {
		tmp = t_1;
	} else if (t <= 6.1e-33) {
		tmp = (a * 120.0) + (((y - x) * -60.0) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 * ((y - x) / t))
    if (t <= (-7.2d-31)) then
        tmp = t_1
    else if (t <= 6.1d-33) then
        tmp = (a * 120.0d0) + (((y - x) * (-60.0d0)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((y - x) / t));
	double tmp;
	if (t <= -7.2e-31) {
		tmp = t_1;
	} else if (t <= 6.1e-33) {
		tmp = (a * 120.0) + (((y - x) * -60.0) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * ((y - x) / t))
	tmp = 0
	if t <= -7.2e-31:
		tmp = t_1
	elif t <= 6.1e-33:
		tmp = (a * 120.0) + (((y - x) * -60.0) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(y - x) / t)))
	tmp = 0.0
	if (t <= -7.2e-31)
		tmp = t_1;
	elseif (t <= 6.1e-33)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(Float64(y - x) * -60.0) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * ((y - x) / t));
	tmp = 0.0;
	if (t <= -7.2e-31)
		tmp = t_1;
	elseif (t <= 6.1e-33)
		tmp = (a * 120.0) + (((y - x) * -60.0) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e-31], t$95$1, If[LessEqual[t, 6.1e-33], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(N[(y - x), $MachinePrecision] * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.20000000000000007e-31 or 6.1000000000000001e-33 < t

   1. Initial program 99.1%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t} + 120 \cdot a} \]
   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 87.7%

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

   7. Simplified 87.7%

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

   if -7.20000000000000007e-31 < t < 6.1000000000000001e-33

   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 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 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-31}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-33}:\\ \;\;\;\;a \cdot 120 + \frac{\left(y - x\right) \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ (- y x) t)))))
   (if (<= t -1.5e-31)
     t_1
     (if (<= t 2e-34) (+ (* a 120.0) (* -60.0 (/ (- y x) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((y - x) / t));
	double tmp;
	if (t <= -1.5e-31) {
		tmp = t_1;
	} else if (t <= 2e-34) {
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (60.0d0 * ((y - x) / t))
    if (t <= (-1.5d-31)) then
        tmp = t_1
    else if (t <= 2d-34) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((y - x) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((y - x) / t));
	double tmp;
	if (t <= -1.5e-31) {
		tmp = t_1;
	} else if (t <= 2e-34) {
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * ((y - x) / t))
	tmp = 0
	if t <= -1.5e-31:
		tmp = t_1
	elif t <= 2e-34:
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(y - x) / t)))
	tmp = 0.0
	if (t <= -1.5e-31)
		tmp = t_1;
	elseif (t <= 2e-34)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(y - x) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * ((y - x) / t));
	tmp = 0.0;
	if (t <= -1.5e-31)
		tmp = t_1;
	elseif (t <= 2e-34)
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e-31], t$95$1, If[LessEqual[t, 2e-34], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999991e-31 or 1.99999999999999986e-34 < t

   1. Initial program 99.1%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t} + 120 \cdot a} \]
   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 87.7%

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

   7. Simplified 87.7%

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

   if -1.49999999999999991e-31 < t < 1.99999999999999986e-34

   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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 90.1%

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

   9. Simplified 90.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-31}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{if}\;t \leq -3 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* 60.0 y) t))))
   (if (<= t -3e-34)
     t_1
     (if (<= t 1.14e-29) (+ (* a 120.0) (* -60.0 (/ (- y x) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -3e-34) {
		tmp = t_1;
	} else if (t <= 1.14e-29) {
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((60.0d0 * y) / t)
    if (t <= (-3d-34)) then
        tmp = t_1
    else if (t <= 1.14d-29) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((y - x) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -3e-34) {
		tmp = t_1;
	} else if (t <= 1.14e-29) {
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((60.0 * y) / t)
	tmp = 0
	if t <= -3e-34:
		tmp = t_1
	elif t <= 1.14e-29:
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t))
	tmp = 0.0
	if (t <= -3e-34)
		tmp = t_1;
	elseif (t <= 1.14e-29)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(y - x) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((60.0 * y) / t);
	tmp = 0.0;
	if (t <= -3e-34)
		tmp = t_1;
	elseif (t <= 1.14e-29)
		tmp = (a * 120.0) + (-60.0 * ((y - x) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e-34], t$95$1, If[LessEqual[t, 1.14e-29], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3e-34 or 1.13999999999999995e-29 < t

   1. Initial program 99.1%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t} + 120 \cdot a} \]
   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 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 76.7%

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

   10. Simplified 76.7%

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

   if -3e-34 < t < 1.13999999999999995e-29

   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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 89.4%

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

   9. Simplified 89.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-257}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-180}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e-50)
   (* a 120.0)
   (if (<= a -6.6e-257)
     (/ (* 60.0 y) t)
     (if (<= a 1.85e-180) (/ (* 60.0 x) z) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e-50) {
		tmp = a * 120.0;
	} else if (a <= -6.6e-257) {
		tmp = (60.0 * y) / t;
	} else if (a <= 1.85e-180) {
		tmp = (60.0 * 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 <= (-4.3d-50)) then
        tmp = a * 120.0d0
    else if (a <= (-6.6d-257)) then
        tmp = (60.0d0 * y) / t
    else if (a <= 1.85d-180) then
        tmp = (60.0d0 * 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 <= -4.3e-50) {
		tmp = a * 120.0;
	} else if (a <= -6.6e-257) {
		tmp = (60.0 * y) / t;
	} else if (a <= 1.85e-180) {
		tmp = (60.0 * x) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e-50:
		tmp = a * 120.0
	elif a <= -6.6e-257:
		tmp = (60.0 * y) / t
	elif a <= 1.85e-180:
		tmp = (60.0 * x) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.6e-257)
		tmp = Float64(Float64(60.0 * y) / t);
	elseif (a <= 1.85e-180)
		tmp = Float64(Float64(60.0 * 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 <= -4.3e-50)
		tmp = a * 120.0;
	elseif (a <= -6.6e-257)
		tmp = (60.0 * y) / t;
	elseif (a <= 1.85e-180)
		tmp = (60.0 * x) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.6e-257], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.85e-180], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.29999999999999997e-50 or 1.85000000000000008e-180 < 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 69.9%

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

   7. Simplified 69.9%

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

   if -4.29999999999999997e-50 < a < -6.6e-257

   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 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 41.0%

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

   10. Simplified 41.0%

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

   if -6.6e-257 < a < 1.85000000000000008e-180

   1. Initial program 97.3%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 97.3%

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

   3. Simplified 97.3%

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

      1. 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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 62.8%

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

   9. Simplified 62.8%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

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

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

       3. *-lowering-*.f64 37.9%

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

   12. Simplified 37.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-257}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-180}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-258}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e-50)
   (* a 120.0)
   (if (<= a -4.8e-258)
     (* 60.0 (/ y t))
     (if (<= a 2.8e-181) (/ (* 60.0 x) z) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-50) {
		tmp = a * 120.0;
	} else if (a <= -4.8e-258) {
		tmp = 60.0 * (y / t);
	} else if (a <= 2.8e-181) {
		tmp = (60.0 * 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 <= (-5.6d-50)) then
        tmp = a * 120.0d0
    else if (a <= (-4.8d-258)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 2.8d-181) then
        tmp = (60.0d0 * 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 <= -5.6e-50) {
		tmp = a * 120.0;
	} else if (a <= -4.8e-258) {
		tmp = 60.0 * (y / t);
	} else if (a <= 2.8e-181) {
		tmp = (60.0 * x) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e-50:
		tmp = a * 120.0
	elif a <= -4.8e-258:
		tmp = 60.0 * (y / t)
	elif a <= 2.8e-181:
		tmp = (60.0 * x) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.8e-258)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 2.8e-181)
		tmp = Float64(Float64(60.0 * 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 <= -5.6e-50)
		tmp = a * 120.0;
	elseif (a <= -4.8e-258)
		tmp = 60.0 * (y / t);
	elseif (a <= 2.8e-181)
		tmp = (60.0 * x) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.8e-258], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-181], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.5999999999999996e-50 or 2.79999999999999986e-181 < 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 69.9%

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

   7. Simplified 69.9%

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

   if -5.5999999999999996e-50 < a < -4.8000000000000003e-258

   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 68.8%

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

   7. Simplified 68.8%

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

   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 57.1%

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

   10. Simplified 57.1%

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

   11. Taylor expanded in y around inf

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

       1. /-lowering-/.f64 40.9%

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

   13. Simplified 40.9%

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

   if -4.8000000000000003e-258 < a < 2.79999999999999986e-181

   1. Initial program 97.3%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 97.3%

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

   3. Simplified 97.3%

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

      1. 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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 62.8%

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

   9. Simplified 62.8%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

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

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

       3. *-lowering-*.f64 37.9%

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

   12. Simplified 37.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-258}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-255}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e-50)
   (* a 120.0)
   (if (<= a -6.8e-255)
     (* 60.0 (/ y t))
     (if (<= a 1.9e-121) (/ -60.0 (/ z y)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e-50) {
		tmp = a * 120.0;
	} else if (a <= -6.8e-255) {
		tmp = 60.0 * (y / t);
	} else if (a <= 1.9e-121) {
		tmp = -60.0 / (z / y);
	} 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-50)) then
        tmp = a * 120.0d0
    else if (a <= (-6.8d-255)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 1.9d-121) then
        tmp = (-60.0d0) / (z / y)
    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-50) {
		tmp = a * 120.0;
	} else if (a <= -6.8e-255) {
		tmp = 60.0 * (y / t);
	} else if (a <= 1.9e-121) {
		tmp = -60.0 / (z / y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e-50:
		tmp = a * 120.0
	elif a <= -6.8e-255:
		tmp = 60.0 * (y / t)
	elif a <= 1.9e-121:
		tmp = -60.0 / (z / y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.8e-255)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 1.9e-121)
		tmp = Float64(-60.0 / Float64(z / y));
	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-50)
		tmp = a * 120.0;
	elseif (a <= -6.8e-255)
		tmp = 60.0 * (y / t);
	elseif (a <= 1.9e-121)
		tmp = -60.0 / (z / y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.8e-255], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-121], N[(-60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1000000000000001e-50 or 1.9e-121 < 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 71.7%

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

   7. Simplified 71.7%

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

   if -2.1000000000000001e-50 < a < -6.79999999999999967e-255

   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 70.1%

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

   7. Simplified 70.1%

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

   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 58.2%

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

   10. Simplified 58.2%

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

   11. Taylor expanded in y around inf

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

       1. /-lowering-/.f64 41.6%

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

   13. Simplified 41.6%

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

   if -6.79999999999999967e-255 < a < 1.9e-121

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 97.6%

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

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   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 41.2%

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

   7. Simplified 41.2%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 28.7%

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

   10. Simplified 28.7%

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

       1. associate-/l* N/A

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

       2. clear-num N/A

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

       3. un-div-inv N/A

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

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

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

       5. /-lowering-/.f64 28.7%

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

   12. Applied egg-rr 28.7%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-255}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{-255}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e-47)
   (* a 120.0)
   (if (<= a -8.4e-255)
     (* 60.0 (/ y t))
     (if (<= a 7.4e-119) (* y (/ -60.0 z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-47) {
		tmp = a * 120.0;
	} else if (a <= -8.4e-255) {
		tmp = 60.0 * (y / t);
	} else if (a <= 7.4e-119) {
		tmp = y * (-60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8d-47)) then
        tmp = a * 120.0d0
    else if (a <= (-8.4d-255)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 7.4d-119) then
        tmp = y * ((-60.0d0) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-47) {
		tmp = a * 120.0;
	} else if (a <= -8.4e-255) {
		tmp = 60.0 * (y / t);
	} else if (a <= 7.4e-119) {
		tmp = y * (-60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e-47:
		tmp = a * 120.0
	elif a <= -8.4e-255:
		tmp = 60.0 * (y / t)
	elif a <= 7.4e-119:
		tmp = y * (-60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e-47)
		tmp = Float64(a * 120.0);
	elseif (a <= -8.4e-255)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 7.4e-119)
		tmp = Float64(y * Float64(-60.0 / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e-47)
		tmp = a * 120.0;
	elseif (a <= -8.4e-255)
		tmp = 60.0 * (y / t);
	elseif (a <= 7.4e-119)
		tmp = y * (-60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e-47], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8.4e-255], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.4e-119], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.9999999999999998e-47 or 7.4000000000000003e-119 < 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 71.7%

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

   7. Simplified 71.7%

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

   if -7.9999999999999998e-47 < a < -8.3999999999999999e-255

   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 70.1%

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

   7. Simplified 70.1%

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

   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 58.2%

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

   10. Simplified 58.2%

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

   11. Taylor expanded in y around inf

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

       1. /-lowering-/.f64 41.6%

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

   13. Simplified 41.6%

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

   if -8.3999999999999999e-255 < a < 7.4000000000000003e-119

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 97.6%

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

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   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 41.2%

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

   7. Simplified 41.2%

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

   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 28.7%

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

   10. Simplified 28.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{-255}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.85 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-265}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.85e-50)
   (* a 120.0)
   (if (<= a -2.3e-265)
     (* 60.0 (/ y t))
     (if (<= a 2.9e-195) (* x (/ -60.0 t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.85e-50) {
		tmp = a * 120.0;
	} else if (a <= -2.3e-265) {
		tmp = 60.0 * (y / t);
	} else if (a <= 2.9e-195) {
		tmp = x * (-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 <= (-3.85d-50)) then
        tmp = a * 120.0d0
    else if (a <= (-2.3d-265)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 2.9d-195) then
        tmp = x * ((-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 <= -3.85e-50) {
		tmp = a * 120.0;
	} else if (a <= -2.3e-265) {
		tmp = 60.0 * (y / t);
	} else if (a <= 2.9e-195) {
		tmp = x * (-60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.85e-50:
		tmp = a * 120.0
	elif a <= -2.3e-265:
		tmp = 60.0 * (y / t)
	elif a <= 2.9e-195:
		tmp = x * (-60.0 / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.85e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.3e-265)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 2.9e-195)
		tmp = Float64(x * 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 <= -3.85e-50)
		tmp = a * 120.0;
	elseif (a <= -2.3e-265)
		tmp = 60.0 * (y / t);
	elseif (a <= 2.9e-195)
		tmp = x * (-60.0 / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.85e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.3e-265], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-195], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.84999999999999982e-50 or 2.9000000000000002e-195 < 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 68.7%

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

   7. Simplified 68.7%

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

   if -3.84999999999999982e-50 < a < -2.2999999999999999e-265

   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 66.1%

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

   7. Simplified 66.1%

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

   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 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in y around inf

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

       1. /-lowering-/.f64 39.3%

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

   13. Simplified 39.3%

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

   if -2.2999999999999999e-265 < a < 2.9000000000000002e-195

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t} + 120 \cdot a} \]
   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 44.9%

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

   7. Simplified 44.9%

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

   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. *-lowering-*.f64 33.6%

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

   10. Simplified 33.6%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

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

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

       4. /-lowering-/.f64 33.6%

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

   12. Applied egg-rr 33.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.85 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-265}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* 60.0 y) t))))
   (if (<= t -1.25e-30)
     t_1
     (if (<= t 3.8e-28) (+ (* a 120.0) (/ (* 60.0 x) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -1.25e-30) {
		tmp = t_1;
	} else if (t <= 3.8e-28) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((60.0d0 * y) / t)
    if (t <= (-1.25d-30)) then
        tmp = t_1
    else if (t <= 3.8d-28) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -1.25e-30) {
		tmp = t_1;
	} else if (t <= 3.8e-28) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((60.0 * y) / t)
	tmp = 0
	if t <= -1.25e-30:
		tmp = t_1
	elif t <= 3.8e-28:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t))
	tmp = 0.0
	if (t <= -1.25e-30)
		tmp = t_1;
	elseif (t <= 3.8e-28)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((60.0 * y) / t);
	tmp = 0.0;
	if (t <= -1.25e-30)
		tmp = t_1;
	elseif (t <= 3.8e-28)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-30], t$95$1, If[LessEqual[t, 3.8e-28], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999993e-30 or 3.80000000000000009e-28 < t

   1. Initial program 99.1%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t} + 120 \cdot a} \]
   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 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 76.7%

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

   10. Simplified 76.7%

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

   if -1.24999999999999993e-30 < t < 3.80000000000000009e-28

   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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 89.4%

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

   9. Simplified 89.4%

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

   10. Taylor expanded in y around 0

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

       1. associate-*r/ N/A

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

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

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

       3. *-lowering-*.f64 70.1%

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

   12. Simplified 70.1%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* 60.0 y) t))))
   (if (<= t -6.4e-31)
     t_1
     (if (<= t 5.3e-45) (+ (* a 120.0) (/ (* y -60.0) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -6.4e-31) {
		tmp = t_1;
	} else if (t <= 5.3e-45) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((60.0d0 * y) / t)
    if (t <= (-6.4d-31)) then
        tmp = t_1
    else if (t <= 5.3d-45) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((60.0 * y) / t);
	double tmp;
	if (t <= -6.4e-31) {
		tmp = t_1;
	} else if (t <= 5.3e-45) {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((60.0 * y) / t)
	tmp = 0
	if t <= -6.4e-31:
		tmp = t_1
	elif t <= 5.3e-45:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t))
	tmp = 0.0
	if (t <= -6.4e-31)
		tmp = t_1;
	elseif (t <= 5.3e-45)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((60.0 * y) / t);
	tmp = 0.0;
	if (t <= -6.4e-31)
		tmp = t_1;
	elseif (t <= 5.3e-45)
		tmp = (a * 120.0) + ((y * -60.0) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e-31], t$95$1, If[LessEqual[t, 5.3e-45], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.40000000000000036e-31 or 5.2999999999999997e-45 < t

   1. Initial program 99.1%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t} + 120 \cdot a} \]
   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 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. associate-*r/ N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 76.1%

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

   10. Simplified 76.1%

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

   if -6.40000000000000036e-31 < t < 5.2999999999999997e-45

   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. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 89.9%

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

   9. Simplified 89.9%

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

   10. Taylor expanded in y around inf

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

       1. associate-*r/ N/A

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

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

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

       3. *-lowering-*.f64 64.1%

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

   12. Simplified 64.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{-31}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-89}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e-50)
   (* a 120.0)
   (if (<= a 6.6e-89) (* 60.0 (/ y t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e-50) {
		tmp = a * 120.0;
	} else if (a <= 6.6e-89) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d-50)) then
        tmp = a * 120.0d0
    else if (a <= 6.6d-89) then
        tmp = 60.0d0 * (y / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e-50) {
		tmp = a * 120.0;
	} else if (a <= 6.6e-89) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e-50:
		tmp = a * 120.0
	elif a <= 6.6e-89:
		tmp = 60.0 * (y / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= 6.6e-89)
		tmp = Float64(60.0 * Float64(y / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e-50)
		tmp = a * 120.0;
	elseif (a <= 6.6e-89)
		tmp = 60.0 * (y / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 6.6e-89], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e-50 or 6.5999999999999993e-89 < 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 73.7%

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

   7. Simplified 73.7%

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

   if -1.9e-50 < a < 6.5999999999999993e-89

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 98.7%

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

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   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 56.9%

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

   7. Simplified 56.9%

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

   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 49.4%

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

   10. Simplified 49.4%

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

   11. Taylor expanded in y around inf

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

       1. /-lowering-/.f64 29.2%

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

   13. Simplified 29.2%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-89}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

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

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. neg-sub0 N/A

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

   5. associate-+l- N/A

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

   6. sub0-neg N/A

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

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

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

   8. distribute-frac-neg N/A

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

   9. distribute-frac-neg2 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. unsub-neg N/A

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

   14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

   19. *-lowering-*.f64 99.4%

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

3. Simplified 99.4%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

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

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

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

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

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

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

   6. --lowering--.f64 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 19: 51.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

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

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. neg-sub0 N/A

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

   5. associate-+l- N/A

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

   6. sub0-neg N/A

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

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

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

   8. distribute-frac-neg N/A

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

   9. distribute-frac-neg2 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. unsub-neg N/A

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

   14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

   19. *-lowering-*.f64 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in t around inf

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

   1. *-lowering-*.f64 51.6%

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

7. Simplified 51.6%

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

8. Final simplification 51.6%

   \[\leadsto a \cdot 120 \]
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 2024150 
(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)))