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

Percentage Accurate: 99.3% → 99.8%

Time: 12.8s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

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

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. neg-sub0 N/A

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

   5. associate-+l- N/A

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

   6. sub0-neg N/A

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

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

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

   8. distribute-frac-neg N/A

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

   9. distribute-frac-neg2 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. unsub-neg N/A

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

   14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

   19. *-lowering-*.f64 99.1%

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

3. Simplified 99.1%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

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

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

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

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

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

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

   6. --lowering--.f64 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{t}{y - x}}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ t (- y x)))))
   (if (<= z -5.2e-41)
     (* a 120.0)
     (if (<= z -1.1e-130)
       t_1
       (if (<= z -1.3e-178)
         (* a 120.0)
         (if (<= z 4.4e-44) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (t / (y - x));
	double tmp;
	if (z <= -5.2e-41) {
		tmp = a * 120.0;
	} else if (z <= -1.1e-130) {
		tmp = t_1;
	} else if (z <= -1.3e-178) {
		tmp = a * 120.0;
	} else if (z <= 4.4e-44) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / (t / (y - x))
    if (z <= (-5.2d-41)) then
        tmp = a * 120.0d0
    else if (z <= (-1.1d-130)) then
        tmp = t_1
    else if (z <= (-1.3d-178)) then
        tmp = a * 120.0d0
    else if (z <= 4.4d-44) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (t / (y - x));
	double tmp;
	if (z <= -5.2e-41) {
		tmp = a * 120.0;
	} else if (z <= -1.1e-130) {
		tmp = t_1;
	} else if (z <= -1.3e-178) {
		tmp = a * 120.0;
	} else if (z <= 4.4e-44) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (t / (y - x))
	tmp = 0
	if z <= -5.2e-41:
		tmp = a * 120.0
	elif z <= -1.1e-130:
		tmp = t_1
	elif z <= -1.3e-178:
		tmp = a * 120.0
	elif z <= 4.4e-44:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(t / Float64(y - x)))
	tmp = 0.0
	if (z <= -5.2e-41)
		tmp = Float64(a * 120.0);
	elseif (z <= -1.1e-130)
		tmp = t_1;
	elseif (z <= -1.3e-178)
		tmp = Float64(a * 120.0);
	elseif (z <= 4.4e-44)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (t / (y - x));
	tmp = 0.0;
	if (z <= -5.2e-41)
		tmp = a * 120.0;
	elseif (z <= -1.1e-130)
		tmp = t_1;
	elseif (z <= -1.3e-178)
		tmp = a * 120.0;
	elseif (z <= 4.4e-44)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-41], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, -1.1e-130], t$95$1, If[LessEqual[z, -1.3e-178], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 4.4e-44], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999999e-41 or -1.0999999999999999e-130 < z < -1.29999999999999999e-178 or 4.40000000000000024e-44 < z

   1. Initial program 98.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 62.4%

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

   7. Simplified 62.4%

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

   if -5.1999999999999999e-41 < z < -1.0999999999999999e-130 or -1.29999999999999999e-178 < z < 4.40000000000000024e-44

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 76.1%

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

   7. Simplified 76.1%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 76.1%

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

   9. Applied egg-rr 76.1%

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

   10. Taylor expanded in t around inf

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

   12. Simplified 64.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-44}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{y - x}{t}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-179}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- y x) t))))
   (if (<= z -2.3e-41)
     (* a 120.0)
     (if (<= z -1.7e-130)
       t_1
       (if (<= z -9e-179) (* a 120.0) (if (<= z 3.5e-46) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((y - x) / t);
	double tmp;
	if (z <= -2.3e-41) {
		tmp = a * 120.0;
	} else if (z <= -1.7e-130) {
		tmp = t_1;
	} else if (z <= -9e-179) {
		tmp = a * 120.0;
	} else if (z <= 3.5e-46) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((y - x) / t)
    if (z <= (-2.3d-41)) then
        tmp = a * 120.0d0
    else if (z <= (-1.7d-130)) then
        tmp = t_1
    else if (z <= (-9d-179)) then
        tmp = a * 120.0d0
    else if (z <= 3.5d-46) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((y - x) / t);
	double tmp;
	if (z <= -2.3e-41) {
		tmp = a * 120.0;
	} else if (z <= -1.7e-130) {
		tmp = t_1;
	} else if (z <= -9e-179) {
		tmp = a * 120.0;
	} else if (z <= 3.5e-46) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((y - x) / t)
	tmp = 0
	if z <= -2.3e-41:
		tmp = a * 120.0
	elif z <= -1.7e-130:
		tmp = t_1
	elif z <= -9e-179:
		tmp = a * 120.0
	elif z <= 3.5e-46:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (z <= -2.3e-41)
		tmp = Float64(a * 120.0);
	elseif (z <= -1.7e-130)
		tmp = t_1;
	elseif (z <= -9e-179)
		tmp = Float64(a * 120.0);
	elseif (z <= 3.5e-46)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((y - x) / t);
	tmp = 0.0;
	if (z <= -2.3e-41)
		tmp = a * 120.0;
	elseif (z <= -1.7e-130)
		tmp = t_1;
	elseif (z <= -9e-179)
		tmp = a * 120.0;
	elseif (z <= 3.5e-46)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e-41], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, -1.7e-130], t$95$1, If[LessEqual[z, -9e-179], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 3.5e-46], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-41 or -1.70000000000000003e-130 < z < -8.99999999999999984e-179 or 3.5000000000000002e-46 < z

   1. Initial program 98.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 62.4%

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

   7. Simplified 62.4%

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

   if -2.3000000000000001e-41 < z < -1.70000000000000003e-130 or -8.99999999999999984e-179 < z < 3.5000000000000002e-46

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t}} \]
   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 64.2%

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

   10. Simplified 64.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-179}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-46}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-265}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-44}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* y -60.0) z))))
   (if (<= z -1.7e-82)
     t_1
     (if (<= z -1.95e-265)
       (- (* a 120.0) (* -60.0 (/ y t)))
       (if (<= z 1.65e-44) (/ 60.0 (/ t (- y x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if (z <= -1.7e-82) {
		tmp = t_1;
	} else if (z <= -1.95e-265) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if (z <= 1.65e-44) {
		tmp = 60.0 / (t / (y - x));
	} 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) + ((y * (-60.0d0)) / z)
    if (z <= (-1.7d-82)) then
        tmp = t_1
    else if (z <= (-1.95d-265)) then
        tmp = (a * 120.0d0) - ((-60.0d0) * (y / t))
    else if (z <= 1.65d-44) then
        tmp = 60.0d0 / (t / (y - x))
    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) + ((y * -60.0) / z);
	double tmp;
	if (z <= -1.7e-82) {
		tmp = t_1;
	} else if (z <= -1.95e-265) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if (z <= 1.65e-44) {
		tmp = 60.0 / (t / (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((y * -60.0) / z)
	tmp = 0
	if z <= -1.7e-82:
		tmp = t_1
	elif z <= -1.95e-265:
		tmp = (a * 120.0) - (-60.0 * (y / t))
	elif z <= 1.65e-44:
		tmp = 60.0 / (t / (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z))
	tmp = 0.0
	if (z <= -1.7e-82)
		tmp = t_1;
	elseif (z <= -1.95e-265)
		tmp = Float64(Float64(a * 120.0) - Float64(-60.0 * Float64(y / t)));
	elseif (z <= 1.65e-44)
		tmp = Float64(60.0 / Float64(t / Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((y * -60.0) / z);
	tmp = 0.0;
	if (z <= -1.7e-82)
		tmp = t_1;
	elseif (z <= -1.95e-265)
		tmp = (a * 120.0) - (-60.0 * (y / t));
	elseif (z <= 1.65e-44)
		tmp = 60.0 / (t / (y - x));
	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[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e-82], t$95$1, If[LessEqual[z, -1.95e-265], N[(N[(a * 120.0), $MachinePrecision] - N[(-60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-44], N[(60.0 / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999988e-82 or 1.65000000000000003e-44 < z

   1. Initial program 98.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      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 71.2%

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

   10. Simplified 71.2%

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

   if -1.69999999999999988e-82 < z < -1.9499999999999999e-265

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 78.5%

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

   7. Simplified 78.5%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. frac-2neg N/A

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

      4. distribute-frac-neg N/A

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

      5. fmm-undef N/A

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

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

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

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

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

      8. neg-mul-1 N/A

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. --lowering--.f64 78.6%

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

   9. Applied egg-rr 78.6%

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

   10. Taylor expanded in t around inf

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

       1. /-lowering-/.f64 68.1%

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

   12. Simplified 68.1%

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

   if -1.9499999999999999e-265 < z < 1.65000000000000003e-44

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 76.4%

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

   7. Simplified 76.4%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 76.4%

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

   9. Applied egg-rr 76.4%

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

   10. Taylor expanded in t around inf

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

   12. Simplified 68.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-82}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-265}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-44}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-271}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-46}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* y -60.0) z))))
   (if (<= z -1.4e-82)
     t_1
     (if (<= z -3.3e-271)
       (+ (* a 120.0) (/ (* y 60.0) t))
       (if (<= z 5.4e-46) (* 60.0 (/ (- y x) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if (z <= -1.4e-82) {
		tmp = t_1;
	} else if (z <= -3.3e-271) {
		tmp = (a * 120.0) + ((y * 60.0) / t);
	} else if (z <= 5.4e-46) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    if (z <= (-1.4d-82)) then
        tmp = t_1
    else if (z <= (-3.3d-271)) then
        tmp = (a * 120.0d0) + ((y * 60.0d0) / t)
    else if (z <= 5.4d-46) then
        tmp = 60.0d0 * ((y - x) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if (z <= -1.4e-82) {
		tmp = t_1;
	} else if (z <= -3.3e-271) {
		tmp = (a * 120.0) + ((y * 60.0) / t);
	} else if (z <= 5.4e-46) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((y * -60.0) / z)
	tmp = 0
	if z <= -1.4e-82:
		tmp = t_1
	elif z <= -3.3e-271:
		tmp = (a * 120.0) + ((y * 60.0) / t)
	elif z <= 5.4e-46:
		tmp = 60.0 * ((y - x) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z))
	tmp = 0.0
	if (z <= -1.4e-82)
		tmp = t_1;
	elseif (z <= -3.3e-271)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * 60.0) / t));
	elseif (z <= 5.4e-46)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((y * -60.0) / z);
	tmp = 0.0;
	if (z <= -1.4e-82)
		tmp = t_1;
	elseif (z <= -3.3e-271)
		tmp = (a * 120.0) + ((y * 60.0) / t);
	elseif (z <= 5.4e-46)
		tmp = 60.0 * ((y - x) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-82], t$95$1, If[LessEqual[z, -3.3e-271], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-46], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000012e-82 or 5.4e-46 < z

   1. Initial program 98.6%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      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 71.2%

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

   10. Simplified 71.2%

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

   if -1.40000000000000012e-82 < z < -3.3000000000000002e-271

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 68.7%

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

   if -3.3000000000000002e-271 < z < 5.4e-46

   1. Initial program 99.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

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

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

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

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

      5. --lowering--.f64 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t}} \]
   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 67.8%

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

   10. Simplified 67.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-82}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-271}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot 60}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-46}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* y -60.0) z))))
   (if (<= z -4.8e-128)
     t_1
     (if (<= z -1.05e-264)
       (+ (* a 120.0) (/ (* x -60.0) t))
       (if (<= z 1.7e-45) (/ 60.0 (/ t (- y x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if (z <= -4.8e-128) {
		tmp = t_1;
	} else if (z <= -1.05e-264) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 1.7e-45) {
		tmp = 60.0 / (t / (y - x));
	} 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) + ((y * (-60.0d0)) / z)
    if (z <= (-4.8d-128)) then
        tmp = t_1
    else if (z <= (-1.05d-264)) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if (z <= 1.7d-45) then
        tmp = 60.0d0 / (t / (y - x))
    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) + ((y * -60.0) / z);
	double tmp;
	if (z <= -4.8e-128) {
		tmp = t_1;
	} else if (z <= -1.05e-264) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (z <= 1.7e-45) {
		tmp = 60.0 / (t / (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((y * -60.0) / z)
	tmp = 0
	if z <= -4.8e-128:
		tmp = t_1
	elif z <= -1.05e-264:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif z <= 1.7e-45:
		tmp = 60.0 / (t / (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z))
	tmp = 0.0
	if (z <= -4.8e-128)
		tmp = t_1;
	elseif (z <= -1.05e-264)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (z <= 1.7e-45)
		tmp = Float64(60.0 / Float64(t / Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((y * -60.0) / z);
	tmp = 0.0;
	if (z <= -4.8e-128)
		tmp = t_1;
	elseif (z <= -1.05e-264)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif (z <= 1.7e-45)
		tmp = 60.0 / (t / (y - x));
	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[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-128], t$95$1, If[LessEqual[z, -1.05e-264], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-45], N[(60.0 / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999996e-128 or 1.70000000000000002e-45 < z

   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 y around inf

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

      1. *-lowering-*.f64 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      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 69.4%

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

   10. Simplified 69.4%

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

   if -4.7999999999999996e-128 < z < -1.0500000000000001e-264

   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. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. associate-*l/ N/A

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

      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. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

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

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

       3. *-commutative N/A

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

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

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

       5. --lowering--.f64 85.5%

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

   11. Simplified 85.5%

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

   12. Taylor expanded in y around 0

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

       1. associate-*r/ N/A

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

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

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

       3. *-lowering-*.f64 68.5%

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

   14. Simplified 68.5%

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

   if -1.0500000000000001e-264 < z < 1.70000000000000002e-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. 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 76.4%

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

   7. Simplified 76.4%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 76.4%

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

   9. Applied egg-rr 76.4%

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

   10. Taylor expanded in t around inf

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

   12. Simplified 68.3%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-140}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-140)
   (- (* a 120.0) (* -60.0 (/ y t)))
   (if (<= (* a 120.0) 5e-42)
     (/ (* (- y x) 60.0) (- t z))
     (+ (* a 120.0) (/ (* y -60.0) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-140) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-42) {
		tmp = ((y - x) * 60.0) / (t - z);
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / 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) <= (-1d-140)) then
        tmp = (a * 120.0d0) - ((-60.0d0) * (y / t))
    else if ((a * 120.0d0) <= 5d-42) then
        tmp = ((y - x) * 60.0d0) / (t - z)
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / 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) <= -1e-140) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-42) {
		tmp = ((y - x) * 60.0) / (t - z);
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e-140:
		tmp = (a * 120.0) - (-60.0 * (y / t))
	elif (a * 120.0) <= 5e-42:
		tmp = ((y - x) * 60.0) / (t - z)
	else:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-140)
		tmp = Float64(Float64(a * 120.0) - Float64(-60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 5e-42)
		tmp = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e-140)
		tmp = (a * 120.0) - (-60.0 * (y / t));
	elseif ((a * 120.0) <= 5e-42)
		tmp = ((y - x) * 60.0) / (t - z);
	else
		tmp = (a * 120.0) + ((y * -60.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-140], N[(N[(a * 120.0), $MachinePrecision] - N[(-60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-42], N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.9999999999999998e-141

   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 y around inf

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

      1. *-lowering-*.f64 87.1%

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

   7. Simplified 87.1%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. frac-2neg N/A

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

      4. distribute-frac-neg N/A

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

      5. fmm-undef N/A

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

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

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

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

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

      8. neg-mul-1 N/A

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. --lowering--.f64 87.1%

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

   9. Applied egg-rr 87.1%

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

   10. Taylor expanded in t around inf

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

       1. /-lowering-/.f64 69.2%

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

   12. Simplified 69.2%

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

   if -9.9999999999999998e-141 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000003e-42

   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 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 84.4%

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

   7. Simplified 84.4%

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

   if 5.00000000000000003e-42 < (*.f64 a #s(literal 120 binary64))

   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 y around inf

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

      1. *-lowering-*.f64 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      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 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-140}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-140}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-140)
   (- (* a 120.0) (* -60.0 (/ y t)))
   (if (<= (* a 120.0) 5e-42)
     (/ 60.0 (/ (- t z) (- y x)))
     (+ (* a 120.0) (/ (* y -60.0) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-140) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-42) {
		tmp = 60.0 / ((t - z) / (y - x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / 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) <= (-1d-140)) then
        tmp = (a * 120.0d0) - ((-60.0d0) * (y / t))
    else if ((a * 120.0d0) <= 5d-42) then
        tmp = 60.0d0 / ((t - z) / (y - x))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / 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) <= -1e-140) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-42) {
		tmp = 60.0 / ((t - z) / (y - x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e-140:
		tmp = (a * 120.0) - (-60.0 * (y / t))
	elif (a * 120.0) <= 5e-42:
		tmp = 60.0 / ((t - z) / (y - x))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-140)
		tmp = Float64(Float64(a * 120.0) - Float64(-60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 5e-42)
		tmp = Float64(60.0 / Float64(Float64(t - z) / Float64(y - x)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e-140)
		tmp = (a * 120.0) - (-60.0 * (y / t));
	elseif ((a * 120.0) <= 5e-42)
		tmp = 60.0 / ((t - z) / (y - x));
	else
		tmp = (a * 120.0) + ((y * -60.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-140], N[(N[(a * 120.0), $MachinePrecision] - N[(-60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-42], N[(60.0 / N[(N[(t - z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.9999999999999998e-141

   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 y around inf

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

      1. *-lowering-*.f64 87.1%

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

   7. Simplified 87.1%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. frac-2neg N/A

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

      4. distribute-frac-neg N/A

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

      5. fmm-undef N/A

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

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

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

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

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

      8. neg-mul-1 N/A

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. --lowering--.f64 87.1%

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

   9. Applied egg-rr 87.1%

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

   10. Taylor expanded in t around inf

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

       1. /-lowering-/.f64 69.2%

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

   12. Simplified 69.2%

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

   if -9.9999999999999998e-141 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000003e-42

   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 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 84.4%

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

   7. Simplified 84.4%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 84.3%

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

   9. Applied egg-rr 84.3%

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

   if 5.00000000000000003e-42 < (*.f64 a #s(literal 120 binary64))

   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 y around inf

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

      1. *-lowering-*.f64 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      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 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-140}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-163}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-227}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-163)
   (* a 120.0)
   (if (<= a -2.45e-227)
     (/ (* y 60.0) t)
     (if (<= a 4.5e-43) (* -60.0 (/ x (- t z))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-163) {
		tmp = a * 120.0;
	} else if (a <= -2.45e-227) {
		tmp = (y * 60.0) / t;
	} else if (a <= 4.5e-43) {
		tmp = -60.0 * (x / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d-163)) then
        tmp = a * 120.0d0
    else if (a <= (-2.45d-227)) then
        tmp = (y * 60.0d0) / t
    else if (a <= 4.5d-43) then
        tmp = (-60.0d0) * (x / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-163) {
		tmp = a * 120.0;
	} else if (a <= -2.45e-227) {
		tmp = (y * 60.0) / t;
	} else if (a <= 4.5e-43) {
		tmp = -60.0 * (x / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-163:
		tmp = a * 120.0
	elif a <= -2.45e-227:
		tmp = (y * 60.0) / t
	elif a <= 4.5e-43:
		tmp = -60.0 * (x / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-163)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.45e-227)
		tmp = Float64(Float64(y * 60.0) / t);
	elseif (a <= 4.5e-43)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e-163)
		tmp = a * 120.0;
	elseif (a <= -2.45e-227)
		tmp = (y * 60.0) / t;
	elseif (a <= 4.5e-43)
		tmp = -60.0 * (x / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-163], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.45e-227], N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 4.5e-43], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e-163 or 4.50000000000000025e-43 < a

   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

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

      1. *-lowering-*.f64 65.7%

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

   7. Simplified 65.7%

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

   if -1.2e-163 < a < -2.4500000000000001e-227

   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 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 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in t around inf

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

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

   10. Simplified 51.5%

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

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{60 \cdot \frac{y}{t}} \]
   12. 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. *-lowering-*.f64 52.2%

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

   13. Simplified 52.2%

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

   if -2.4500000000000001e-227 < a < 4.50000000000000025e-43

   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. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf

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

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

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

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

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

      3. --lowering--.f64 50.7%

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

   9. Simplified 50.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-163}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-227}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+74}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ x (- t z))))))
   (if (<= x -1.3e+137)
     t_1
     (if (<= x 5.5e+74) (+ (* a 120.0) (* -60.0 (/ y (- z t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (x / (t - z)));
	double tmp;
	if (x <= -1.3e+137) {
		tmp = t_1;
	} else if (x <= 5.5e+74) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (x / (t - z)))
    if (x <= (-1.3d+137)) then
        tmp = t_1
    else if (x <= 5.5d+74) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (x / (t - z)));
	double tmp;
	if (x <= -1.3e+137) {
		tmp = t_1;
	} else if (x <= 5.5e+74) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (x / (t - z)))
	tmp = 0
	if x <= -1.3e+137:
		tmp = t_1
	elif x <= 5.5e+74:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / Float64(t - z))))
	tmp = 0.0
	if (x <= -1.3e+137)
		tmp = t_1;
	elseif (x <= 5.5e+74)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (x / (t - z)));
	tmp = 0.0;
	if (x <= -1.3e+137)
		tmp = t_1;
	elseif (x <= 5.5e+74)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+137], t$95$1, If[LessEqual[x, 5.5e+74], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e137 or 5.5000000000000003e74 < x

   1. Initial program 98.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 98.8%

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

   3. Simplified 98.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0

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

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

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

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

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

      3. --lowering--.f64 87.0%

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

   9. Simplified 87.0%

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

   if -1.3e137 < x < 5.5000000000000003e74

   1. Initial program 99.2%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 90.0%

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

   7. Simplified 90.0%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. frac-2neg N/A

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

      4. distribute-frac-neg N/A

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

      5. fmm-undef N/A

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

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

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

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

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

      8. neg-mul-1 N/A

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

      9. times-frac N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. --lowering--.f64 90.6%

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

   9. Applied egg-rr 90.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+74}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ x (- t z))))))
   (if (<= x -1.3e+137)
     t_1
     (if (<= x 1.7e+75) (+ (* a 120.0) (* y (/ 60.0 (- t z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (x / (t - z)));
	double tmp;
	if (x <= -1.3e+137) {
		tmp = t_1;
	} else if (x <= 1.7e+75) {
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (x / (t - z)))
    if (x <= (-1.3d+137)) then
        tmp = t_1
    else if (x <= 1.7d+75) then
        tmp = (a * 120.0d0) + (y * (60.0d0 / (t - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (x / (t - z)));
	double tmp;
	if (x <= -1.3e+137) {
		tmp = t_1;
	} else if (x <= 1.7e+75) {
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (x / (t - z)))
	tmp = 0
	if x <= -1.3e+137:
		tmp = t_1
	elif x <= 1.7e+75:
		tmp = (a * 120.0) + (y * (60.0 / (t - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / Float64(t - z))))
	tmp = 0.0
	if (x <= -1.3e+137)
		tmp = t_1;
	elseif (x <= 1.7e+75)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(60.0 / Float64(t - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (x / (t - z)));
	tmp = 0.0;
	if (x <= -1.3e+137)
		tmp = t_1;
	elseif (x <= 1.7e+75)
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+137], t$95$1, If[LessEqual[x, 1.7e+75], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e137 or 1.70000000000000006e75 < x

   1. Initial program 98.8%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 98.8%

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

   3. Simplified 98.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0

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

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

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

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

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

      3. --lowering--.f64 87.0%

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

   9. Simplified 87.0%

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

   if -1.3e137 < x < 1.70000000000000006e75

   1. Initial program 99.2%

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

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

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

      5. associate-+l- N/A

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

      6. sub0-neg N/A

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

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

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

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

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

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

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

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

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

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

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

      19. *-lowering-*.f64 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

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

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

      9. --lowering--.f64 90.6%

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

   7. Simplified 90.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{\frac{t - z}{y - x}}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+63}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (/ (- t z) (- y x)))))
   (if (<= y -9.5e+135)
     t_1
     (if (<= y 5e+63) (+ (* a 120.0) (* -60.0 (/ x (- t z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((t - z) / (y - x));
	double tmp;
	if (y <= -9.5e+135) {
		tmp = t_1;
	} else if (y <= 5e+63) {
		tmp = (a * 120.0) + (-60.0 * (x / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / ((t - z) / (y - x))
    if (y <= (-9.5d+135)) then
        tmp = t_1
    else if (y <= 5d+63) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / (t - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / ((t - z) / (y - x));
	double tmp;
	if (y <= -9.5e+135) {
		tmp = t_1;
	} else if (y <= 5e+63) {
		tmp = (a * 120.0) + (-60.0 * (x / (t - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / ((t - z) / (y - x))
	tmp = 0
	if y <= -9.5e+135:
		tmp = t_1
	elif y <= 5e+63:
		tmp = (a * 120.0) + (-60.0 * (x / (t - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(Float64(t - z) / Float64(y - x)))
	tmp = 0.0
	if (y <= -9.5e+135)
		tmp = t_1;
	elseif (y <= 5e+63)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / Float64(t - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / ((t - z) / (y - x));
	tmp = 0.0;
	if (y <= -9.5e+135)
		tmp = t_1;
	elseif (y <= 5e+63)
		tmp = (a * 120.0) + (-60.0 * (x / (t - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(N[(t - z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+135], t$95$1, If[LessEqual[y, 5e+63], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000036e135 or 5.00000000000000011e63 < y

   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 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 72.3%

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

   7. Simplified 72.3%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

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

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - x\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - x\right)\right)\right) \]

      6. --lowering--.f64 73.3%

         \[\leadsto \mathsf{/.f64}\left(60, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   9. Applied egg-rr 73.3%

      \[\leadsto \color{blue}{\frac{60}{\frac{t - z}{y - x}}} \]

   if -9.50000000000000036e135 < y < 5.00000000000000011e63

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{y - x}{t - z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{t - z} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{y - x}{t - z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(t, z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{t - z} \cdot 60} + a \cdot 120 \]

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-60 \cdot \frac{x}{t - z}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-60, \left(\frac{x}{t - z}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \left(t - z\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. --lowering--.f64 89.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   9. Simplified 89.5%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+63}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{60}{t - z}\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+81}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ 60.0 (- t z)))))
   (if (<= y -1.22e+147)
     t_1
     (if (<= y 1.26e+81) (+ (* a 120.0) (/ (* x -60.0) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (60.0 / (t - z));
	double tmp;
	if (y <= -1.22e+147) {
		tmp = t_1;
	} else if (y <= 1.26e+81) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (60.0d0 / (t - z))
    if (y <= (-1.22d+147)) then
        tmp = t_1
    else if (y <= 1.26d+81) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (60.0 / (t - z));
	double tmp;
	if (y <= -1.22e+147) {
		tmp = t_1;
	} else if (y <= 1.26e+81) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (60.0 / (t - z))
	tmp = 0
	if y <= -1.22e+147:
		tmp = t_1
	elif y <= 1.26e+81:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(60.0 / Float64(t - z)))
	tmp = 0.0
	if (y <= -1.22e+147)
		tmp = t_1;
	elseif (y <= 1.26e+81)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (60.0 / (t - z));
	tmp = 0.0;
	if (y <= -1.22e+147)
		tmp = t_1;
	elseif (y <= 1.26e+81)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+147], t$95$1, If[LessEqual[y, 1.26e+81], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.21999999999999996e147 or 1.25999999999999996e81 < y

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 61.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 61.8%

      \[\leadsto \color{blue}{y \cdot \frac{60}{t - z}} \]

   if -1.21999999999999996e147 < y < 1.25999999999999996e81

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{y - x}{t - z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{t - z} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{y - x}{t - z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(t, z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{t - z} \cdot 60} + a \cdot 120 \]
   7. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - x\right) \cdot 60}{t - z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      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. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60}{t - z} \cdot \left(y - x\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{60}{t - z}\right), \left(y - x\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \left(t - z\right)\right), \left(y - x\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(t, z\right)\right), \left(y - x\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. --lowering--.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   8. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{60}{t - z} \cdot \left(y - x\right)} + a \cdot 120 \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(60 \cdot \frac{y - x}{t}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), t\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(y - x\right) \cdot 60\right), t\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(y - x\right), 60\right), t\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

       5. --lowering--.f64 62.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), 60\right), t\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   11. Simplified 62.6%

       \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot 60}{t}} + a \cdot 120 \]

   12. Taylor expanded in y around 0

       \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-60 \cdot \frac{x}{t}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-60 \cdot x}{t}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-60 \cdot x\right), t\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

       3. *-lowering-*.f64 61.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, x\right), t\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   14. Simplified 61.3%

       \[\leadsto \color{blue}{\frac{-60 \cdot x}{t}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+147}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+81}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+65}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ y t))))
   (if (<= y -1.6e+251) t_1 (if (<= y 2.6e+65) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (y / t);
	double tmp;
	if (y <= -1.6e+251) {
		tmp = t_1;
	} else if (y <= 2.6e+65) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (y / t)
    if (y <= (-1.6d+251)) then
        tmp = t_1
    else if (y <= 2.6d+65) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (y / t);
	double tmp;
	if (y <= -1.6e+251) {
		tmp = t_1;
	} else if (y <= 2.6e+65) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (y / t)
	tmp = 0
	if y <= -1.6e+251:
		tmp = t_1
	elif y <= 2.6e+65:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(y / t))
	tmp = 0.0
	if (y <= -1.6e+251)
		tmp = t_1;
	elseif (y <= 2.6e+65)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (y / t);
	tmp = 0.0;
	if (y <= -1.6e+251)
		tmp = t_1;
	elseif (y <= 2.6e+65)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+251], t$95$1, If[LessEqual[y, 2.6e+65], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5999999999999999e251 or 2.60000000000000003e65 < y

   1. Initial program 98.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 98.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 77.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z}} \]

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t}} \]
   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%

       \[\leadsto \color{blue}{60 \cdot \frac{y - x}{t}} \]

   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 50.2%

          \[\leadsto \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(y, \color{blue}{t}\right)\right) \]

   13. Simplified 50.2%

       \[\leadsto 60 \cdot \color{blue}{\frac{y}{t}} \]

   if -1.5999999999999999e251 < y < 2.60000000000000003e65

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 57.0%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 57.0%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+251}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+65}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-251}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-170}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e-251)
   (* a 120.0)
   (if (<= a 1.5e-170) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e-251) {
		tmp = a * 120.0;
	} else if (a <= 1.5e-170) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6d-251)) then
        tmp = a * 120.0d0
    else if (a <= 1.5d-170) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e-251) {
		tmp = a * 120.0;
	} else if (a <= 1.5e-170) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e-251:
		tmp = a * 120.0
	elif a <= 1.5e-170:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e-251)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.5e-170)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e-251)
		tmp = a * 120.0;
	elseif (a <= 1.5e-170)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e-251], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.5e-170], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.9999999999999997e-251 or 1.50000000000000007e-170 < a

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 55.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 55.2%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -5.9999999999999997e-251 < a < 1.50000000000000007e-170

   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. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{y - x}{t - z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{t - z} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{y - x}{t - z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      6. --lowering--.f64 99.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(t, z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{y - x}{t - z} \cdot 60} + a \cdot 120 \]

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 46.1%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 46.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t - z}} \]

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{t}\right)\right) \]
   11. Step-by-step derivation

   12. Simplified 25.8%

       \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-251}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-170}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 + \left(y - x\right) \cdot \frac{60}{t - z} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* a 120.0) (* (- y x) (/ 60.0 (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((y - x) * (60.0 / (t - z)));
}

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) + ((y - x) * (60.0d0 / (t - z)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((y - x) * (60.0 / (t - z)));
}

Python

def code(x, y, z, t, a):
	return (a * 120.0) + ((y - x) * (60.0 / (t - z)))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(a * 120.0) + Float64(Float64(y - x) * Float64(60.0 / Float64(t - z))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (a * 120.0) + ((y - x) * (60.0 / (t - z)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   9. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

   14. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   17. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

   19. *-lowering-*.f64 99.1%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-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. Final simplification 99.8%

   \[\leadsto a \cdot 120 + \left(y - x\right) \cdot \frac{60}{t - z} \]
8. Add Preprocessing

Alternative 17: 52.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = a * 120.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = a * 120.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   9. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

   14. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   17. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

   19. *-lowering-*.f64 99.1%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{60 \cdot \left(y - x\right)}{t - z} + a \cdot 120} \]
4. Add Preprocessing

5. Taylor expanded in t around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 47.4%

      \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

7. Simplified 47.4%

   \[\leadsto \color{blue}{120 \cdot a} \]

8. Final simplification 47.4%

   \[\leadsto a \cdot 120 \]
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 2024152 
(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)))