Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 76.6% → 91.1%

Time: 12.1s

Alternatives: 16

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(\frac{t}{a - t} + 1\right)}{z}\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-165}:\\ \;\;\;\;x + y \cdot \left(\frac{-1}{a - t} \cdot \left(z - t\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ (/ y (- t a)) (/ (* y (+ (/ t (- a t)) 1.0)) z))))))
   (if (<= z -3.4e-113)
     t_1
     (if (<= z 2.1e-165)
       (+ x (* y (+ (* (/ -1.0 (- a t)) (- z t)) 1.0)))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)));
	double tmp;
	if (z <= -3.4e-113) {
		tmp = t_1;
	} else if (z <= 2.1e-165) {
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0d0)) / z)))
    if (z <= (-3.4d-113)) then
        tmp = t_1
    else if (z <= 2.1d-165) then
        tmp = x + (y * ((((-1.0d0) / (a - t)) * (z - t)) + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)));
	double tmp;
	if (z <= -3.4e-113) {
		tmp = t_1;
	} else if (z <= 2.1e-165) {
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)))
	tmp = 0
	if z <= -3.4e-113:
		tmp = t_1
	elif z <= 2.1e-165:
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y / Float64(t - a)) + Float64(Float64(y * Float64(Float64(t / Float64(a - t)) + 1.0)) / z))))
	tmp = 0.0
	if (z <= -3.4e-113)
		tmp = t_1;
	elseif (z <= 2.1e-165)
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(-1.0 / Float64(a - t)) * Float64(z - t)) + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)));
	tmp = 0.0;
	if (z <= -3.4e-113)
		tmp = t_1;
	elseif (z <= 2.1e-165)
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-113], t$95$1, If[LessEqual[z, 2.1e-165], N[(x + N[(y * N[(N[(N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000002e-113 or 2.09999999999999995e-165 < z

   1. Initial program 74.5%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 85.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(1 - \frac{t}{t - a}\right)}{z}\right)\right)}\right) \]
   6. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(t, a\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \left(t - a\right)\right)\right)\right), z\right)\right)\right)\right) \]

      9. --lowering--.f64 96.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(t, a\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(t, a\right)\right)\right)\right), z\right)\right)\right)\right) \]

   7. Simplified 96.1%

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

   if -3.4000000000000002e-113 < z < 2.09999999999999995e-165

   1. Initial program 79.4%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 93.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, a\right)\right), \left(z - t\right)\right), 1\right)\right)\right) \]

      6. --lowering--.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, a\right)\right), \mathsf{\_.f64}\left(z, t\right)\right), 1\right)\right)\right) \]

   6. Applied egg-rr 93.0%

      \[\leadsto x + y \cdot \left(\color{blue}{\frac{1}{t - a} \cdot \left(z - t\right)} + 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-113}:\\ \;\;\;\;x + z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(\frac{t}{a - t} + 1\right)}{z}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-165}:\\ \;\;\;\;x + y \cdot \left(\frac{-1}{a - t} \cdot \left(z - t\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(\frac{t}{a - t} + 1\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{-1}{a - t} \cdot \left(z - t\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e-10)
   (+ x (* y (+ (/ (- z t) (- t a)) 1.0)))
   (if (<= a 2.3e+57)
     (+ x (* y (/ z (- t a))))
     (+ x (* y (+ (* (/ -1.0 (- a t)) (- z t)) 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-10) {
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	} else if (a <= 2.3e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d-10)) then
        tmp = x + (y * (((z - t) / (t - a)) + 1.0d0))
    else if (a <= 2.3d+57) then
        tmp = x + (y * (z / (t - a)))
    else
        tmp = x + (y * ((((-1.0d0) / (a - t)) * (z - t)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-10) {
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	} else if (a <= 2.3e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e-10:
		tmp = x + (y * (((z - t) / (t - a)) + 1.0))
	elif a <= 2.3e+57:
		tmp = x + (y * (z / (t - a)))
	else:
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e-10)
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0)));
	elseif (a <= 2.3e+57)
		tmp = Float64(x + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(-1.0 / Float64(a - t)) * Float64(z - t)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e-10)
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	elseif (a <= 2.3e+57)
		tmp = x + (y * (z / (t - a)));
	else
		tmp = x + (y * (((-1.0 / (a - t)) * (z - t)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e-10], N[(x + N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+57], N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.99999999999999961e-10

   1. Initial program 79.9%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   if -6.99999999999999961e-10 < a < 2.2999999999999999e57

   1. Initial program 73.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 94.1%

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

   7. Simplified 94.1%

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

   if 2.2999999999999999e57 < a

   1. Initial program 77.4%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 95.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, a\right)\right), \left(z - t\right)\right), 1\right)\right)\right) \]

      6. --lowering--.f64 95.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, a\right)\right), \mathsf{\_.f64}\left(z, t\right)\right), 1\right)\right)\right) \]

   6. Applied egg-rr 95.3%

      \[\leadsto x + y \cdot \left(\color{blue}{\frac{1}{t - a} \cdot \left(z - t\right)} + 1\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{-1}{a - t} \cdot \left(z - t\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{if}\;a \leq -5.3 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+56}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (+ (/ (- z t) (- t a)) 1.0)))))
   (if (<= a -5.3e-11) t_1 (if (<= a 7e+56) (+ x (* y (/ z (- t a)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (((z - t) / (t - a)) + 1.0));
	double tmp;
	if (a <= -5.3e-11) {
		tmp = t_1;
	} else if (a <= 7e+56) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (((z - t) / (t - a)) + 1.0d0))
    if (a <= (-5.3d-11)) then
        tmp = t_1
    else if (a <= 7d+56) then
        tmp = x + (y * (z / (t - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (((z - t) / (t - a)) + 1.0));
	double tmp;
	if (a <= -5.3e-11) {
		tmp = t_1;
	} else if (a <= 7e+56) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (((z - t) / (t - a)) + 1.0))
	tmp = 0
	if a <= -5.3e-11:
		tmp = t_1
	elif a <= 7e+56:
		tmp = x + (y * (z / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0)))
	tmp = 0.0
	if (a <= -5.3e-11)
		tmp = t_1;
	elseif (a <= 7e+56)
		tmp = Float64(x + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (((z - t) / (t - a)) + 1.0));
	tmp = 0.0;
	if (a <= -5.3e-11)
		tmp = t_1;
	elseif (a <= 7e+56)
		tmp = x + (y * (z / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.3e-11], t$95$1, If[LessEqual[a, 7e+56], N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.2999999999999998e-11 or 6.99999999999999999e56 < a

   1. Initial program 78.5%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 92.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   if -5.2999999999999998e-11 < a < 6.99999999999999999e56

   1. Initial program 73.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 94.1%

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

   7. Simplified 94.1%

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

Alternative 4: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+85}:\\ \;\;\;\;x + \left(y + t \cdot \frac{y}{a - t}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.7e+85)
   (+ x (+ y (* t (/ y (- a t)))))
   (if (<= a 9.5e+57) (+ x (* y (/ z (- t a)))) (- (+ x y) (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.7e+85) {
		tmp = x + (y + (t * (y / (a - t))));
	} else if (a <= 9.5e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = (x + y) - (y / (a / 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 <= (-5.7d+85)) then
        tmp = x + (y + (t * (y / (a - t))))
    else if (a <= 9.5d+57) then
        tmp = x + (y * (z / (t - a)))
    else
        tmp = (x + y) - (y / (a / 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 <= -5.7e+85) {
		tmp = x + (y + (t * (y / (a - t))));
	} else if (a <= 9.5e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = (x + y) - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.7e+85:
		tmp = x + (y + (t * (y / (a - t))))
	elif a <= 9.5e+57:
		tmp = x + (y * (z / (t - a)))
	else:
		tmp = (x + y) - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.7e+85)
		tmp = Float64(x + Float64(y + Float64(t * Float64(y / Float64(a - t)))));
	elseif (a <= 9.5e+57)
		tmp = Float64(x + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.7e+85)
		tmp = x + (y + (t * (y / (a - t))));
	elseif (a <= 9.5e+57)
		tmp = x + (y * (z / (t - a)));
	else
		tmp = (x + y) - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.7e+85], N[(x + N[(y + N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+57], N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.7000000000000002e85

   1. Initial program 81.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. --lowering--.f64 81.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   4. Applied egg-rr 81.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + y\right) - -1 \cdot \frac{t \cdot y}{a - t}} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(y - -1 \cdot \frac{t \cdot y}{a - t}\right)} \]

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

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

      3. sub-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-/l* N/A

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

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

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

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

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

      10. --lowering--.f64 90.6%

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

   7. Simplified 90.6%

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

   if -5.7000000000000002e85 < a < 9.4999999999999997e57

   1. Initial program 74.0%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 91.2%

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

   7. Simplified 91.2%

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

   if 9.4999999999999997e57 < a

   1. Initial program 77.4%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 91.4%

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

   5. Simplified 91.4%

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

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

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

      6. /-lowering-/.f64 91.5%

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

   7. Applied egg-rr 91.5%

      \[\leadsto \color{blue}{\left(x + y\right) - \frac{y}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+79)
   (+ x (* y (+ (/ t (- a t)) 1.0)))
   (if (<= a 6.5e+58) (+ x (* y (/ z (- t a)))) (- (+ x y) (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+79) {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	} else if (a <= 6.5e+58) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = (x + y) - (y / (a / 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 <= (-1.35d+79)) then
        tmp = x + (y * ((t / (a - t)) + 1.0d0))
    else if (a <= 6.5d+58) then
        tmp = x + (y * (z / (t - a)))
    else
        tmp = (x + y) - (y / (a / 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 <= -1.35e+79) {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	} else if (a <= 6.5e+58) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = (x + y) - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+79:
		tmp = x + (y * ((t / (a - t)) + 1.0))
	elif a <= 6.5e+58:
		tmp = x + (y * (z / (t - a)))
	else:
		tmp = (x + y) - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+79)
		tmp = Float64(x + Float64(y * Float64(Float64(t / Float64(a - t)) + 1.0)));
	elseif (a <= 6.5e+58)
		tmp = Float64(x + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e+79)
		tmp = x + (y * ((t / (a - t)) + 1.0));
	elseif (a <= 6.5e+58)
		tmp = x + (y * (z / (t - a)));
	else
		tmp = (x + y) - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+79], N[(x + N[(y * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+58], N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.35e79

   1. Initial program 81.8%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 93.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(1 - \frac{t}{t - a}\right)} \]
   6. Step-by-step derivation

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

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

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

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

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

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \color{blue}{\left(t - a\right)}\right)\right)\right)\right) \]

      5. --lowering--.f64 90.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(t, \color{blue}{a}\right)\right)\right)\right)\right) \]

   7. Simplified 90.5%

      \[\leadsto \color{blue}{x + y \cdot \left(1 - \frac{t}{t - a}\right)} \]

   if -1.35e79 < a < 6.49999999999999998e58

   1. Initial program 74.0%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 91.2%

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

   7. Simplified 91.2%

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

   if 6.49999999999999998e58 < a

   1. Initial program 77.4%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 91.4%

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

   5. Simplified 91.4%

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

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

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

      6. /-lowering-/.f64 91.5%

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

   7. Applied egg-rr 91.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ y (/ a z)))))
   (if (<= a -2.3e+20) t_1 (if (<= a 4.6e+57) (+ x (* y (/ z (- t a)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y / (a / z));
	double tmp;
	if (a <= -2.3e+20) {
		tmp = t_1;
	} else if (a <= 4.6e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (y / (a / z))
    if (a <= (-2.3d+20)) then
        tmp = t_1
    else if (a <= 4.6d+57) then
        tmp = x + (y * (z / (t - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y / (a / z));
	double tmp;
	if (a <= -2.3e+20) {
		tmp = t_1;
	} else if (a <= 4.6e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y / (a / z))
	tmp = 0
	if a <= -2.3e+20:
		tmp = t_1
	elif a <= 4.6e+57:
		tmp = x + (y * (z / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -2.3e+20)
		tmp = t_1;
	elseif (a <= 4.6e+57)
		tmp = Float64(x + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y / (a / z));
	tmp = 0.0;
	if (a <= -2.3e+20)
		tmp = t_1;
	elseif (a <= 4.6e+57)
		tmp = x + (y * (z / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+20], t$95$1, If[LessEqual[a, 4.6e+57], N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3e20 or 4.5999999999999998e57 < a

   1. Initial program 78.4%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 88.4%

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

   5. Simplified 88.4%

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

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

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

      6. /-lowering-/.f64 88.4%

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

   7. Applied egg-rr 88.4%

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

   if -2.3e20 < a < 4.5999999999999998e57

   1. Initial program 74.0%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 93.1%

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

   7. Simplified 93.1%

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

Alternative 7: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z a)))))
   (if (<= a -6.6e+20) t_1 (if (<= a 9e+57) (+ x (* y (/ z (- t a)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -6.6e+20) {
		tmp = t_1;
	} else if (a <= 9e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (y * (z / a))
    if (a <= (-6.6d+20)) then
        tmp = t_1
    else if (a <= 9d+57) then
        tmp = x + (y * (z / (t - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -6.6e+20) {
		tmp = t_1;
	} else if (a <= 9e+57) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / a))
	tmp = 0
	if a <= -6.6e+20:
		tmp = t_1
	elif a <= 9e+57:
		tmp = x + (y * (z / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -6.6e+20)
		tmp = t_1;
	elseif (a <= 9e+57)
		tmp = Float64(x + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / a));
	tmp = 0.0;
	if (a <= -6.6e+20)
		tmp = t_1;
	elseif (a <= 9e+57)
		tmp = x + (y * (z / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.6e+20], t$95$1, If[LessEqual[a, 9e+57], N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.6e20 or 8.99999999999999991e57 < a

   1. Initial program 78.4%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 88.4%

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

   5. Simplified 88.4%

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

   if -6.6e20 < a < 8.99999999999999991e57

   1. Initial program 74.0%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 93.1%

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

   7. Simplified 93.1%

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

Alternative 8: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e+76)
   (+ x y)
   (if (<= a 6e+58) (+ x (* y (/ z (- t a)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+76) {
		tmp = x + y;
	} else if (a <= 6e+58) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d+76)) then
        tmp = x + y
    else if (a <= 6d+58) then
        tmp = x + (y * (z / (t - a)))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+76) {
		tmp = x + y;
	} else if (a <= 6e+58) {
		tmp = x + (y * (z / (t - a)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e+76:
		tmp = x + y
	elif a <= 6e+58:
		tmp = x + (y * (z / (t - a)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e+76)
		tmp = Float64(x + y);
	elseif (a <= 6e+58)
		tmp = Float64(x + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e+76)
		tmp = x + y;
	elseif (a <= 6e+58)
		tmp = x + (y * (z / (t - a)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e+76], N[(x + y), $MachinePrecision], If[LessEqual[a, 6e+58], N[(x + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7999999999999999e76 or 6.0000000000000005e58 < a

   1. Initial program 78.9%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 94.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 83.7%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 83.7%

      \[\leadsto \color{blue}{y + x} \]

   if -2.7999999999999999e76 < a < 6.0000000000000005e58

   1. Initial program 74.0%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+20) (+ x y) (if (<= a 3.8e+57) (+ x (* z (/ y t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+20) {
		tmp = x + y;
	} else if (a <= 3.8e+57) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	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 <= (-1.3d+20)) then
        tmp = x + y
    else if (a <= 3.8d+57) then
        tmp = x + (z * (y / t))
    else
        tmp = x + y
    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 <= -1.3e+20) {
		tmp = x + y;
	} else if (a <= 3.8e+57) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e+20:
		tmp = x + y
	elif a <= 3.8e+57:
		tmp = x + (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+20)
		tmp = Float64(x + y);
	elseif (a <= 3.8e+57)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e+20)
		tmp = x + y;
	elseif (a <= 3.8e+57)
		tmp = x + (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+20], N[(x + y), $MachinePrecision], If[LessEqual[a, 3.8e+57], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e20 or 3.7999999999999999e57 < a

   1. Initial program 78.4%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 93.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 80.5%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 80.5%

      \[\leadsto \color{blue}{y + x} \]

   if -1.3e20 < a < 3.7999999999999999e57

   1. Initial program 74.0%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(1 - \frac{t}{t - a}\right)}{z}\right)\right)}\right) \]
   6. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(t, a\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \left(t - a\right)\right)\right)\right), z\right)\right)\right)\right) \]

      9. --lowering--.f64 94.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(t, a\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(t, a\right)\right)\right)\right), z\right)\right)\right)\right) \]

   7. Simplified 94.8%

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

   8. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 84.9%

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

   10. Simplified 84.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e+19) (+ x y) (if (<= a 2.9e+57) (+ x (* y (/ z t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+19) {
		tmp = x + y;
	} else if (a <= 2.9e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d+19)) then
        tmp = x + y
    else if (a <= 2.9d+57) then
        tmp = x + (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+19) {
		tmp = x + y;
	} else if (a <= 2.9e+57) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e+19:
		tmp = x + y
	elif a <= 2.9e+57:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e+19)
		tmp = Float64(x + y);
	elseif (a <= 2.9e+57)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e+19)
		tmp = x + y;
	elseif (a <= 2.9e+57)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e+19], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.9e+57], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8e19 or 2.9000000000000002e57 < a

   1. Initial program 78.4%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 93.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 80.5%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 80.5%

      \[\leadsto \color{blue}{y + x} \]

   if -2.8e19 < a < 2.9000000000000002e57

   1. Initial program 74.0%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0

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

      1. /-lowering-/.f64 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t - a}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+78}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- t a)))))
   (if (<= z -2.05e+18) t_1 (if (<= z 2.1e+78) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (t - a));
	double tmp;
	if (z <= -2.05e+18) {
		tmp = t_1;
	} else if (z <= 2.1e+78) {
		tmp = x + y;
	} 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 = z * (y / (t - a))
    if (z <= (-2.05d+18)) then
        tmp = t_1
    else if (z <= 2.1d+78) then
        tmp = x + y
    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 = z * (y / (t - a));
	double tmp;
	if (z <= -2.05e+18) {
		tmp = t_1;
	} else if (z <= 2.1e+78) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (t - a))
	tmp = 0
	if z <= -2.05e+18:
		tmp = t_1
	elif z <= 2.1e+78:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (z <= -2.05e+18)
		tmp = t_1;
	elseif (z <= 2.1e+78)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (t - a));
	tmp = 0.0;
	if (z <= -2.05e+18)
		tmp = t_1;
	elseif (z <= 2.1e+78)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+18], t$95$1, If[LessEqual[z, 2.1e+78], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e18 or 2.1000000000000001e78 < z

   1. Initial program 79.5%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 87.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 48.1%

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

   7. Simplified 48.1%

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

      1. associate-*l/ N/A

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

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

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

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

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

      4. --lowering--.f64 58.1%

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

   9. Applied egg-rr 58.1%

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

   if -2.05e18 < z < 2.1000000000000001e78

   1. Initial program 72.6%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 88.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 76.3%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 76.3%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+78}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-225}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e-225) (+ x y) (if (<= a 1.05e-36) (/ z (/ t y)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e-225) {
		tmp = x + y;
	} else if (a <= 1.05e-36) {
		tmp = z / (t / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d-225)) then
        tmp = x + y
    else if (a <= 1.05d-36) then
        tmp = z / (t / y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e-225) {
		tmp = x + y;
	} else if (a <= 1.05e-36) {
		tmp = z / (t / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e-225:
		tmp = x + y
	elif a <= 1.05e-36:
		tmp = z / (t / y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e-225)
		tmp = Float64(x + y);
	elseif (a <= 1.05e-36)
		tmp = Float64(z / Float64(t / y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e-225)
		tmp = x + y;
	elseif (a <= 1.05e-36)
		tmp = z / (t / y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e-225], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.05e-36], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.19999999999999993e-225 or 1.04999999999999995e-36 < a

   1. Initial program 77.1%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 91.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{y + x} \]

   if -6.19999999999999993e-225 < a < 1.04999999999999995e-36

   1. Initial program 72.9%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 80.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 56.1%

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

   7. Simplified 56.1%

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. --lowering--.f64 62.2%

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

   9. Applied egg-rr 62.2%

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

   10. Taylor expanded in t around inf

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

       1. /-lowering-/.f64 55.5%

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

   12. Simplified 55.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-225}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-225}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.2e-225) (+ x y) (if (<= a 1.05e-36) (* y (/ z t)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.2e-225) {
		tmp = x + y;
	} else if (a <= 1.05e-36) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	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 <= (-8.2d-225)) then
        tmp = x + y
    else if (a <= 1.05d-36) then
        tmp = y * (z / t)
    else
        tmp = x + y
    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 <= -8.2e-225) {
		tmp = x + y;
	} else if (a <= 1.05e-36) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.2e-225:
		tmp = x + y
	elif a <= 1.05e-36:
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.2e-225)
		tmp = Float64(x + y);
	elseif (a <= 1.05e-36)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.2e-225)
		tmp = x + y;
	elseif (a <= 1.05e-36)
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.2e-225], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.05e-36], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.20000000000000044e-225 or 1.04999999999999995e-36 < a

   1. Initial program 77.1%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 91.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{y + x} \]

   if -8.20000000000000044e-225 < a < 1.04999999999999995e-36

   1. Initial program 72.9%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 80.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 56.1%

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

   7. Simplified 56.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 59.9%

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

   9. Applied egg-rr 59.9%

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

   10. Taylor expanded in t around inf

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

       1. /-lowering-/.f64 53.2%

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

   12. Simplified 53.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-225}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.1e-38) (+ x y) (if (<= a 2.2e+57) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.1e-38) {
		tmp = x + y;
	} else if (a <= 2.2e+57) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.1d-38)) then
        tmp = x + y
    else if (a <= 2.2d+57) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.1e-38) {
		tmp = x + y;
	} else if (a <= 2.2e+57) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.1e-38:
		tmp = x + y
	elif a <= 2.2e+57:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.1e-38)
		tmp = Float64(x + y);
	elseif (a <= 2.2e+57)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.1e-38)
		tmp = x + y;
	elseif (a <= 2.2e+57)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.1e-38], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.2e+57], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.09999999999999972e-38 or 2.2000000000000001e57 < a

   1. Initial program 78.2%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 92.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 76.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{y + x} \]

   if -6.09999999999999972e-38 < a < 2.2000000000000001e57

   1. Initial program 73.9%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 84.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 49.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-210}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.8e-61) x (if (<= x 1.35e-210) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.8e-61) {
		tmp = x;
	} else if (x <= 1.35e-210) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.8d-61)) then
        tmp = x
    else if (x <= 1.35d-210) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.8e-61) {
		tmp = x;
	} else if (x <= 1.35e-210) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.8e-61:
		tmp = x
	elif x <= 1.35e-210:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.8e-61)
		tmp = x;
	elseif (x <= 1.35e-210)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.8e-61)
		tmp = x;
	elseif (x <= 1.35e-210)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.8e-61], x, If[LessEqual[x, 1.35e-210], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e-61 or 1.34999999999999996e-210 < x

   1. Initial program 78.7%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 92.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 59.8%

      \[\leadsto \color{blue}{x} \]

   if -2.8000000000000001e-61 < x < 1.34999999999999996e-210

   1. Initial program 67.3%

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

      1. associate--l+ N/A

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

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

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

      3. associate-*l/ N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. distribute-rgt1-in N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

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

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

      10. distribute-frac-neg2 N/A

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

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

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

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 74.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto y + \color{blue}{x} \]

      2. +-lowering-+.f64 34.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 34.8%

      \[\leadsto \color{blue}{y + x} \]

   8. Taylor expanded in y around inf

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

   10. Simplified 30.0%

       \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 51.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

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 = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 75.8%

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

   1. associate--l+ N/A

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

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

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

   3. associate-*l/ N/A

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

   4. cancel-sign-sub-inv N/A

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

   5. distribute-rgt1-in N/A

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

   6. *-commutative N/A

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

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

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

   8. metadata-eval N/A

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

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

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

   10. distribute-frac-neg2 N/A

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

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

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

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

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   13. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   15. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   16. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   17. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   19. metadata-eval 87.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

3. Simplified 87.8%

   \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 47.1%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))