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

Percentage Accurate: 76.3% → 91.1%

Time: 12.2s

Alternatives: 12

Speedup: 0.8×

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: 76.3% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-196}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(\frac{t}{a - t} + 1\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_1 -4e-196)
     (+ x (* y (+ (/ (- z t) (- t a)) 1.0)))
     (if (<= t_1 0.0)
       (+ x (/ y (/ t (- z a))))
       (+ x (* z (+ (/ y (- t a)) (/ (* y (+ (/ t (- a t)) 1.0)) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_1 <= -4e-196) {
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	} else if (t_1 <= 0.0) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) + ((y * (z - t)) / (t - a))
    if (t_1 <= (-4d-196)) then
        tmp = x + (y * (((z - t) / (t - a)) + 1.0d0))
    else if (t_1 <= 0.0d0) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0d0)) / z)))
    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 - t)) / (t - a));
	double tmp;
	if (t_1 <= -4e-196) {
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	} else if (t_1 <= 0.0) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if t_1 <= -4e-196:
		tmp = x + (y * (((z - t) / (t - a)) + 1.0))
	elif t_1 <= 0.0:
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_1 <= -4e-196)
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0)));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y / Float64(t - a)) + Float64(Float64(y * Float64(Float64(t / Float64(a - t)) + 1.0)) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if (t_1 <= -4e-196)
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	elseif (t_1 <= 0.0)
		tmp = x + (y / (t / (z - a)));
	else
		tmp = x + (z * ((y / (t - a)) + ((y * ((t / (a - t)) + 1.0)) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-196], N[(x + N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.0000000000000002e-196

   1. Initial program 87.1%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 97.0%

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

   3. Simplified 97.0%

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

   if -4.0000000000000002e-196 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 11.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

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

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

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

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

      7. --lowering--.f64 99.6%

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

   7. Simplified 99.6%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. --lowering--.f64 99.9%

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

   9. Applied egg-rr 99.9%

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

   if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 85.4%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. 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 93.4%

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

   7. Simplified 93.4%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-196}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 0:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(\frac{t}{a - t} + 1\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (+ (/ (- z t) (- t a)) 1.0))))
        (t_2 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_2 -4e-196) t_1 (if (<= t_2 0.0) (+ x (/ y (/ t (- z 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 t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -4e-196) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x + (y / (t / (z - 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) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (((z - t) / (t - a)) + 1.0d0))
    t_2 = (x + y) + ((y * (z - t)) / (t - a))
    if (t_2 <= (-4d-196)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = x + (y / (t / (z - 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 t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -4e-196) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x + (y / (t / (z - 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))
	t_2 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if t_2 <= -4e-196:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = x + (y / (t / (z - 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)))
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= -4e-196)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - 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));
	t_2 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if (t_2 <= -4e-196)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = x + (y / (t / (z - 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]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-196], t$95$1, If[LessEqual[t$95$2, 0.0], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.0000000000000002e-196 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 86.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 94.9%

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

   3. Simplified 94.9%

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

   if -4.0000000000000002e-196 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 11.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

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

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

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

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

      7. --lowering--.f64 99.6%

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

   7. Simplified 99.6%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. --lowering--.f64 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-196}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 0:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - a}{t}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{-24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z a) t))))
   (if (<= a -8.8e-24)
     (+ x y)
     (if (<= a -4.7e-197)
       t_1
       (if (<= a 2e-181) x (if (<= a 1.02e-122) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - a) / t);
	double tmp;
	if (a <= -8.8e-24) {
		tmp = x + y;
	} else if (a <= -4.7e-197) {
		tmp = t_1;
	} else if (a <= 2e-181) {
		tmp = x;
	} else if (a <= 1.02e-122) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - a) / t)
    if (a <= (-8.8d-24)) then
        tmp = x + y
    else if (a <= (-4.7d-197)) then
        tmp = t_1
    else if (a <= 2d-181) then
        tmp = x
    else if (a <= 1.02d-122) then
        tmp = t_1
    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 t_1 = y * ((z - a) / t);
	double tmp;
	if (a <= -8.8e-24) {
		tmp = x + y;
	} else if (a <= -4.7e-197) {
		tmp = t_1;
	} else if (a <= 2e-181) {
		tmp = x;
	} else if (a <= 1.02e-122) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - a) / t)
	tmp = 0
	if a <= -8.8e-24:
		tmp = x + y
	elif a <= -4.7e-197:
		tmp = t_1
	elif a <= 2e-181:
		tmp = x
	elif a <= 1.02e-122:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (a <= -8.8e-24)
		tmp = Float64(x + y);
	elseif (a <= -4.7e-197)
		tmp = t_1;
	elseif (a <= 2e-181)
		tmp = x;
	elseif (a <= 1.02e-122)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - a) / t);
	tmp = 0.0;
	if (a <= -8.8e-24)
		tmp = x + y;
	elseif (a <= -4.7e-197)
		tmp = t_1;
	elseif (a <= 2e-181)
		tmp = x;
	elseif (a <= 1.02e-122)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e-24], N[(x + y), $MachinePrecision], If[LessEqual[a, -4.7e-197], t$95$1, If[LessEqual[a, 2e-181], x, If[LessEqual[a, 1.02e-122], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.80000000000000006e-24 or 1.02000000000000002e-122 < a

   1. Initial program 83.1%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 94.1%

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

   3. Simplified 94.1%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 66.1%

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

   7. Simplified 66.1%

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

   if -8.80000000000000006e-24 < a < -4.7000000000000001e-197 or 2.00000000000000009e-181 < a < 1.02000000000000002e-122

   1. Initial program 68.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

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

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

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

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

      7. --lowering--.f64 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 61.4%

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

   10. Simplified 61.4%

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

   if -4.7000000000000001e-197 < a < 2.00000000000000009e-181

   1. Initial program 77.7%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 66.4%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+110}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+110)
   (+ x (* y (+ (/ t (- a t)) 1.0)))
   (if (<= a 2e+53) (+ x (* z (/ y (- t a)))) (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+110) {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	} else if (a <= 2e+53) {
		tmp = x + (z * (y / (t - a)));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	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 <= (-1d+110)) then
        tmp = x + (y * ((t / (a - t)) + 1.0d0))
    else if (a <= 2d+53) then
        tmp = x + (z * (y / (t - a)))
    else
        tmp = (x + y) - (y * (z / a))
    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 <= -1e+110) {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	} else if (a <= 2e+53) {
		tmp = x + (z * (y / (t - a)));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+110:
		tmp = x + (y * ((t / (a - t)) + 1.0))
	elif a <= 2e+53:
		tmp = x + (z * (y / (t - a)))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+110)
		tmp = Float64(x + Float64(y * Float64(Float64(t / Float64(a - t)) + 1.0)));
	elseif (a <= 2e+53)
		tmp = Float64(x + Float64(z * Float64(y / Float64(t - a))));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+110)
		tmp = x + (y * ((t / (a - t)) + 1.0));
	elseif (a <= 2e+53)
		tmp = x + (z * (y / (t - a)));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+110], N[(x + N[(y * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+53], N[(x + N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e110

   1. Initial program 79.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 86.9%

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

   7. Simplified 86.9%

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

   if -1e110 < a < 2e53

   1. Initial program 80.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 89.3%

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

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 90.7%

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

   10. Simplified 90.7%

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

   if 2e53 < a

   1. Initial program 78.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 86.5%

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

   5. Simplified 86.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+110}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+55}:\\ \;\;\;\;x + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z a)))))
   (if (<= a -3.1e+106)
     t_1
     (if (<= a 1.6e+55) (+ x (* z (/ y (- 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 <= -3.1e+106) {
		tmp = t_1;
	} else if (a <= 1.6e+55) {
		tmp = x + (z * (y / (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 <= (-3.1d+106)) then
        tmp = t_1
    else if (a <= 1.6d+55) then
        tmp = x + (z * (y / (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 <= -3.1e+106) {
		tmp = t_1;
	} else if (a <= 1.6e+55) {
		tmp = x + (z * (y / (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 <= -3.1e+106:
		tmp = t_1
	elif a <= 1.6e+55:
		tmp = x + (z * (y / (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 <= -3.1e+106)
		tmp = t_1;
	elseif (a <= 1.6e+55)
		tmp = Float64(x + Float64(z * Float64(y / 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 <= -3.1e+106)
		tmp = t_1;
	elseif (a <= 1.6e+55)
		tmp = x + (z * (y / (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, -3.1e+106], t$95$1, If[LessEqual[a, 1.6e+55], N[(x + N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0999999999999999e106 or 1.6000000000000001e55 < a

   1. Initial program 78.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 85.9%

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

   5. Simplified 85.9%

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

   if -3.0999999999999999e106 < a < 1.6000000000000001e55

   1. Initial program 80.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 89.3%

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

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 90.7%

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

   10. Simplified 90.7%

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

Alternative 6: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+188}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+126}:\\ \;\;\;\;x + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.9e+188)
   (+ x y)
   (if (<= a 2.8e+126) (+ x (* z (/ y (- t a)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.9e+188) {
		tmp = x + y;
	} else if (a <= 2.8e+126) {
		tmp = x + (z * (y / (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 <= (-4.9d+188)) then
        tmp = x + y
    else if (a <= 2.8d+126) then
        tmp = x + (z * (y / (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 <= -4.9e+188) {
		tmp = x + y;
	} else if (a <= 2.8e+126) {
		tmp = x + (z * (y / (t - a)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.9e+188:
		tmp = x + y
	elif a <= 2.8e+126:
		tmp = x + (z * (y / (t - a)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.9e+188)
		tmp = Float64(x + y);
	elseif (a <= 2.8e+126)
		tmp = Float64(x + Float64(z * Float64(y / 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 <= -4.9e+188)
		tmp = x + y;
	elseif (a <= 2.8e+126)
		tmp = x + (z * (y / (t - a)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.9e+188], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.8e+126], N[(x + N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.9e188 or 2.80000000000000009e126 < a

   1. Initial program 79.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 94.2%

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

   3. Simplified 94.2%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 87.8%

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

   7. Simplified 87.8%

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

   if -4.9e188 < a < 2.80000000000000009e126

   1. Initial program 79.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(z \cdot \left(\frac{y}{t - a} + \frac{y \cdot \left(1 - \frac{t}{t - a}\right)}{z}\right)\right)}\right) \]
   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 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 87.1%

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

   10. Simplified 87.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+188}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+126}:\\ \;\;\;\;x + z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+25}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+25)
   (+ x y)
   (if (<= a 3.8e+52) (+ x (* y (/ (- z a) t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+25) {
		tmp = x + y;
	} else if (a <= 3.8e+52) {
		tmp = x + (y * ((z - a) / 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 <= (-5.5d+25)) then
        tmp = x + y
    else if (a <= 3.8d+52) then
        tmp = x + (y * ((z - a) / 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 <= -5.5e+25) {
		tmp = x + y;
	} else if (a <= 3.8e+52) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+25:
		tmp = x + y
	elif a <= 3.8e+52:
		tmp = x + (y * ((z - a) / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+25)
		tmp = Float64(x + y);
	elseif (a <= 3.8e+52)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / 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 <= -5.5e+25)
		tmp = x + y;
	elseif (a <= 3.8e+52)
		tmp = x + (y * ((z - a) / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+25], N[(x + y), $MachinePrecision], If[LessEqual[a, 3.8e+52], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.50000000000000018e25 or 3.8e52 < a

   1. Initial program 80.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 94.0%

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

   3. Simplified 94.0%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 76.4%

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

   7. Simplified 76.4%

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

   if -5.50000000000000018e25 < a < 3.8e52

   1. Initial program 78.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

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

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

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

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

      7. --lowering--.f64 83.1%

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

   7. Simplified 83.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+25}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -520000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -520000.0) (+ x y) (if (<= a 2e+53) (+ x (* y (/ z t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -520000.0) {
		tmp = x + y;
	} else if (a <= 2e+53) {
		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 <= (-520000.0d0)) then
        tmp = x + y
    else if (a <= 2d+53) 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 <= -520000.0) {
		tmp = x + y;
	} else if (a <= 2e+53) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -520000.0:
		tmp = x + y
	elif a <= 2e+53:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -520000.0)
		tmp = Float64(x + y);
	elseif (a <= 2e+53)
		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 <= -520000.0)
		tmp = x + y;
	elseif (a <= 2e+53)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -520000.0], N[(x + y), $MachinePrecision], If[LessEqual[a, 2e+53], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.2e5 or 2e53 < a

   1. Initial program 80.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 74.4%

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

   7. Simplified 74.4%

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

   if -5.2e5 < a < 2e53

   1. Initial program 79.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 88.7%

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

   3. Simplified 88.7%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -520000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+100) (+ x y) (if (<= a 9.6e+49) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+100) {
		tmp = x + y;
	} else if (a <= 9.6e+49) {
		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 <= (-1.7d+100)) then
        tmp = x + y
    else if (a <= 9.6d+49) 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 <= -1.7e+100) {
		tmp = x + y;
	} else if (a <= 9.6e+49) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+100:
		tmp = x + y
	elif a <= 9.6e+49:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+100)
		tmp = Float64(x + y);
	elseif (a <= 9.6e+49)
		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 <= -1.7e+100)
		tmp = x + y;
	elseif (a <= 9.6e+49)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+100], N[(x + y), $MachinePrecision], If[LessEqual[a, 9.6e+49], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999997e100 or 9.5999999999999999e49 < a

   1. Initial program 78.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 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. 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 76.5%

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

   7. Simplified 76.5%

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

   if -1.69999999999999997e100 < a < 9.5999999999999999e49

   1. Initial program 80.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 51.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.8 \cdot 10^{+245}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 5.8e+245) (+ x y) (/ (* y z) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 5.8e+245) {
		tmp = x + y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 5.8d+245) then
        tmp = x + y
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 5.8e+245) {
		tmp = x + y;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 5.8e+245:
		tmp = x + y
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 5.8e+245)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 5.8e+245)
		tmp = x + y;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 5.8e+245], N[(x + y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.8000000000000003e245

   1. Initial program 80.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 90.1%

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

   3. Simplified 90.1%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 58.6%

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

   7. Simplified 58.6%

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

   if 5.8000000000000003e245 < z

   1. Initial program 68.4%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

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

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

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

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

      7. --lowering--.f64 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 55.5%

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

   10. Simplified 55.5%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.8 \cdot 10^{+245}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.55 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 1.55e+150) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.55e+150) {
		tmp = x;
	} else {
		tmp = 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 <= 1.55d+150) then
        tmp = x
    else
        tmp = 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 <= 1.55e+150) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.55e+150:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1.55e+150)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 1.55e+150)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 1.55e+150], x, y]

Derivation

1. Split input into 2 regimes

2. if a < 1.55000000000000007e150

   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 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 50.1%

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

   if 1.55000000000000007e150 < a

   1. Initial program 79.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 91.8%

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

   3. Simplified 91.8%

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{z - t}{t - a} + 1\right)} \]
   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 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in y around inf

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

   10. Simplified 67.9%

       \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 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 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 90.5%

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

3. Simplified 90.5%

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

5. Taylor expanded in x around inf

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

7. Simplified 46.9%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 88.0% 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 2024160 
(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))))