Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.6% → 95.3%

Time: 11.3s

Alternatives: 10

Speedup: 0.4×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{-1 - x} \cdot \frac{z}{x - z \cdot t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{x} \cdot \frac{t - y}{x} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -5e+17)
     (* (/ y (- -1.0 x)) (/ z (- x (* z t))))
     (if (<= t_1 5e+267)
       t_1
       (if (<= t_1 INFINITY)
         (+ (* (/ z x) (/ (- t y) x)) 1.0)
         (+
          (/ x (+ x 1.0))
          (/ (- (/ y (+ x 1.0)) (/ x (* z (+ x 1.0)))) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)));
	} else if (t_1 <= 5e+267) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)));
	} else if (t_1 <= 5e+267) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)))
	elif t_1 <= 5e+267:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = ((z / x) * ((t - y) / x)) + 1.0
	else:
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) * Float64(z / Float64(x - Float64(z * t))));
	elseif (t_1 <= 5e+267)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(z / x) * Float64(Float64(t - y) / x)) + 1.0);
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(Float64(y / Float64(x + 1.0)) - Float64(x / Float64(z * Float64(x + 1.0)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)));
	elseif (t_1 <= 5e+267)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	else
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(z / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+267], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(N[(z / x), $MachinePrecision] * N[(N[(t - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e17

   1. Initial program 77.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around inf

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

      1. times-frac N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 89.7%

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

   7. Simplified 89.7%

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

   if -5e17 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999999e267

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 4.9999999999999999e267 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 35.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 35.8%

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

   3. Simplified 35.8%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{z \cdot \left(y - t\right)}{{\color{blue}{x}}^{2}}\right)\right) \]

      5. unpow2 N/A

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

      6. times-frac N/A

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

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

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

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

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

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

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

      10. --lowering--.f64 80.8%

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

   7. Simplified 80.8%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

      6. +-commutative N/A

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

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

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

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

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{x + 1} - \frac{\frac{0 - y}{x + 1} + \frac{x}{z \cdot \left(x + 1\right)}}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{-1 - x} \cdot \frac{z}{x - z \cdot t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{z}{x} \cdot \frac{t - y}{x} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{-1 - x} \cdot \frac{z}{x - z \cdot t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{z}{x} \cdot \frac{t - y}{x} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -5e+17)
     (* (/ y (- -1.0 x)) (/ z (- x (* z t))))
     (if (<= t_1 5e+267)
       t_1
       (if (<= t_1 INFINITY)
         (+ (* (/ z x) (/ (- t y) x)) 1.0)
         (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)));
	} else if (t_1 <= 5e+267) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)));
	} else if (t_1 <= 5e+267) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -5e+17:
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)))
	elif t_1 <= 5e+267:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = ((z / x) * ((t - y) / x)) + 1.0
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) * Float64(z / Float64(x - Float64(z * t))));
	elseif (t_1 <= 5e+267)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(z / x) * Float64(Float64(t - y) / x)) + 1.0);
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = (y / (-1.0 - x)) * (z / (x - (z * t)));
	elseif (t_1 <= 5e+267)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(z / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+267], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(N[(z / x), $MachinePrecision] * N[(N[(t - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e17

   1. Initial program 77.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around inf

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

      1. times-frac N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 89.7%

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

   7. Simplified 89.7%

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

   if -5e17 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999999e267

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 4.9999999999999999e267 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 35.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 35.8%

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

   3. Simplified 35.8%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

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

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \left(\frac{z \cdot \left(y - t\right)}{{\color{blue}{x}}^{2}}\right)\right) \]

      5. unpow2 N/A

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

      6. times-frac N/A

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

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

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

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

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

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

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

      10. --lowering--.f64 80.8%

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

   7. Simplified 80.8%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t}}{1 + x}} \]
   6. Step-by-step derivation

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 99.8%

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

   7. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{y}{t} + x}{x + 1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{-1 - x} \cdot \frac{z}{x - z \cdot t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{z}{x} \cdot \frac{t - y}{x} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{x + y \cdot \left(\frac{x}{y \cdot t\_1} - \frac{z}{t\_1}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0)) INFINITY)
     (/ (+ x (* y (- (/ x (* y t_1)) (/ z t_1)))) (+ x 1.0))
     (+ (/ x (+ x 1.0)) (/ (- (/ y (+ x 1.0)) (/ x (* z (+ x 1.0)))) t)))))

C

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

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= Double.POSITIVE_INFINITY) {
		tmp = (x + (y * ((x / (y * t_1)) - (z / t_1)))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if ((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= math.inf:
		tmp = (x + (y * ((x / (y * t_1)) - (z / t_1)))) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 92.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

      12. *-lowering-*.f64 96.7%

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

   7. Simplified 96.7%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

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

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

      6. +-commutative N/A

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

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

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

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

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{x + 1} - \frac{\frac{0 - y}{x + 1} + \frac{x}{z \cdot \left(x + 1\right)}}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

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

Alternative 4: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;x \leq -7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-107}:\\ \;\;\;\;\frac{y}{-1 - x} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{x}{t\_1}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{\frac{x}{z} - y}{t} - x}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= x -7e-12)
     (/ x (+ x 1.0))
     (if (<= x -1.55e-107)
       (* (/ y (- -1.0 x)) (/ z t_1))
       (if (<= x -6e-127)
         (+ x (/ x t_1))
         (if (<= x 2e+15) (/ (- (/ (- (/ x z) y) t) x) (- -1.0 x)) 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (x <= -7e-12) {
		tmp = x / (x + 1.0);
	} else if (x <= -1.55e-107) {
		tmp = (y / (-1.0 - x)) * (z / t_1);
	} else if (x <= -6e-127) {
		tmp = x + (x / t_1);
	} else if (x <= 2e+15) {
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (z * t)
    if (x <= (-7d-12)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-1.55d-107)) then
        tmp = (y / ((-1.0d0) - x)) * (z / t_1)
    else if (x <= (-6d-127)) then
        tmp = x + (x / t_1)
    else if (x <= 2d+15) then
        tmp = ((((x / z) - y) / t) - x) / ((-1.0d0) - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (x <= -7e-12) {
		tmp = x / (x + 1.0);
	} else if (x <= -1.55e-107) {
		tmp = (y / (-1.0 - x)) * (z / t_1);
	} else if (x <= -6e-127) {
		tmp = x + (x / t_1);
	} else if (x <= 2e+15) {
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if x <= -7e-12:
		tmp = x / (x + 1.0)
	elif x <= -1.55e-107:
		tmp = (y / (-1.0 - x)) * (z / t_1)
	elif x <= -6e-127:
		tmp = x + (x / t_1)
	elif x <= 2e+15:
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (x <= -7e-12)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -1.55e-107)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) * Float64(z / t_1));
	elseif (x <= -6e-127)
		tmp = Float64(x + Float64(x / t_1));
	elseif (x <= 2e+15)
		tmp = Float64(Float64(Float64(Float64(Float64(x / z) - y) / t) - x) / Float64(-1.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	tmp = 0.0;
	if (x <= -7e-12)
		tmp = x / (x + 1.0);
	elseif (x <= -1.55e-107)
		tmp = (y / (-1.0 - x)) * (z / t_1);
	elseif (x <= -6e-127)
		tmp = x + (x / t_1);
	elseif (x <= 2e+15)
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-12], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e-107], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-127], N[(x + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+15], N[(N[(N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.0000000000000001e-12

   1. Initial program 87.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 86.1%

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

   7. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -7.0000000000000001e-12 < x < -1.55000000000000011e-107

   1. Initial program 88.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around inf

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

      1. times-frac N/A

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

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

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

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

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 65.5%

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

   7. Simplified 65.5%

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

   if -1.55000000000000011e-107 < x < -6.00000000000000017e-127

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 90.6%

      \[\leadsto \frac{x - \frac{\color{blue}{x}}{z \cdot t - x}}{x + 1} \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \color{blue}{1}\right) \]
   9. Step-by-step derivation

   10. Simplified 90.6%

       \[\leadsto \frac{x - \frac{x}{z \cdot t - x}}{\color{blue}{1}} \]
   11. Step-by-step derivation

       1. /-rgt-identity N/A

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

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

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

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

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

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

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

       5. *-lowering-*.f64 90.6%

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

   12. Applied egg-rr 90.6%

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

   if -6.00000000000000017e-127 < x < 2e15

   1. Initial program 92.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around -inf

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

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

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

      2. associate-*r/ N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. distribute-lft-in N/A

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

      7. neg-mul-1 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

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

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

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

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

      14. /-lowering-/.f64 77.1%

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

   7. Simplified 77.1%

      \[\leadsto \frac{\color{blue}{x + \frac{y - \frac{x}{z}}{t}}}{x + 1} \]

   if 2e15 < x

   1. Initial program 86.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 92.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-107}:\\ \;\;\;\;\frac{y}{-1 - x} \cdot \frac{z}{x - z \cdot t}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{x}{x - z \cdot t}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{\frac{x}{z} - y}{t} - x}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-127}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{\frac{x}{z} - y}{t} - x}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e-127)
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))
   (if (<= x 1.55e+15) (/ (- (/ (- (/ x z) y) t) x) (- -1.0 x)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-127) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else if (x <= 1.55e+15) {
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.35d-127)) then
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    else if (x <= 1.55d+15) then
        tmp = ((((x / z) - y) / t) - x) / ((-1.0d0) - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-127) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else if (x <= 1.55e+15) {
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e-127:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	elif x <= 1.55e+15:
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e-127)
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	elseif (x <= 1.55e+15)
		tmp = Float64(Float64(Float64(Float64(Float64(x / z) - y) / t) - x) / Float64(-1.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.35e-127)
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	elseif (x <= 1.55e+15)
		tmp = ((((x / z) - y) / t) - x) / (-1.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e-127], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+15], N[(N[(N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e-127

   1. Initial program 88.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.8%

      \[\leadsto \frac{x - \frac{\color{blue}{x}}{z \cdot t - x}}{x + 1} \]

   if -1.35e-127 < x < 1.55e15

   1. Initial program 92.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around -inf

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

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

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

      2. associate-*r/ N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. distribute-lft-in N/A

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

      7. neg-mul-1 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

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

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

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

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

      14. /-lowering-/.f64 77.1%

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

   7. Simplified 77.1%

      \[\leadsto \frac{\color{blue}{x + \frac{y - \frac{x}{z}}{t}}}{x + 1} \]

   if 1.55e15 < x

   1. Initial program 86.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 92.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-127}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{\frac{x}{z} - y}{t} - x}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.45e+72) 1.0 (if (<= x 1.3e+16) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+72) {
		tmp = 1.0;
	} else if (x <= 1.3e+16) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.45d+72)) then
        tmp = 1.0d0
    else if (x <= 1.3d+16) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+72) {
		tmp = 1.0;
	} else if (x <= 1.3e+16) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.45e+72:
		tmp = 1.0
	elif x <= 1.3e+16:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.45e+72)
		tmp = 1.0;
	elseif (x <= 1.3e+16)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.45e+72)
		tmp = 1.0;
	elseif (x <= 1.3e+16)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.45e+72], 1.0, If[LessEqual[x, 1.3e+16], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45000000000000009e72 or 1.3e16 < x

   1. Initial program 88.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 93.7%

      \[\leadsto \color{blue}{1} \]

   if -1.45000000000000009e72 < x < 1.3e16

   1. Initial program 89.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t}}{1 + x}} \]
   6. Step-by-step derivation

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 65.7%

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

   7. Simplified 65.7%

      \[\leadsto \color{blue}{\frac{\frac{y}{t} + x}{x + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.0054:\\ \;\;\;\;x + \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.1e-43) 1.0 (if (<= x 0.0054) (+ x (/ y t)) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.1e-43) {
		tmp = 1.0;
	} else if (x <= 0.0054) {
		tmp = x + (y / t);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.1d-43)) then
        tmp = 1.0d0
    else if (x <= 0.0054d0) then
        tmp = x + (y / t)
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.1e-43) {
		tmp = 1.0;
	} else if (x <= 0.0054) {
		tmp = x + (y / t);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.1e-43:
		tmp = 1.0
	elif x <= 0.0054:
		tmp = x + (y / t)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.1e-43)
		tmp = 1.0;
	elseif (x <= 0.0054)
		tmp = Float64(x + Float64(y / t));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.1e-43)
		tmp = 1.0;
	elseif (x <= 0.0054)
		tmp = x + (y / t);
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.1e-43], 1.0, If[LessEqual[x, 0.0054], N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.0999999999999998e-43

   1. Initial program 88.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 81.9%

      \[\leadsto \color{blue}{1} \]

   if -4.0999999999999998e-43 < x < 0.0054000000000000003

   1. Initial program 91.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t}}{1 + x}} \]
   6. Step-by-step derivation

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. +-commutative N/A

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

      6. +-lowering-+.f64 67.5%

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

   7. Simplified 67.5%

      \[\leadsto \color{blue}{\frac{\frac{y}{t} + x}{x + 1}} \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \color{blue}{1}\right) \]
   9. Step-by-step derivation

   10. Simplified 66.9%

       \[\leadsto \frac{\frac{y}{t} + x}{\color{blue}{1}} \]

   if 0.0054000000000000003 < x

   1. Initial program 86.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 92.7%

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

   7. Simplified 92.7%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.0054:\\ \;\;\;\;x + \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-127}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.8e-127) 1.0 (if (<= x 5.5e-76) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.8e-127) {
		tmp = 1.0;
	} else if (x <= 5.5e-76) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9.8d-127)) then
        tmp = 1.0d0
    else if (x <= 5.5d-76) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.8e-127) {
		tmp = 1.0;
	} else if (x <= 5.5e-76) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.8e-127:
		tmp = 1.0
	elif x <= 5.5e-76:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.8e-127)
		tmp = 1.0;
	elseif (x <= 5.5e-76)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.8e-127)
		tmp = 1.0;
	elseif (x <= 5.5e-76)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.8e-127], 1.0, If[LessEqual[x, 5.5e-76], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.8000000000000002e-127

   1. Initial program 88.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 72.7%

      \[\leadsto \color{blue}{1} \]

   if -9.8000000000000002e-127 < x < 5.50000000000000014e-76

   1. Initial program 91.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 58.4%

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

   7. Simplified 58.4%

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

   if 5.50000000000000014e-76 < x

   1. Initial program 88.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 86.9%

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

   7. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 67.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-127}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.0048:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-127) 1.0 (if (<= x 0.0048) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-127) {
		tmp = 1.0;
	} else if (x <= 0.0048) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.2d-127)) then
        tmp = 1.0d0
    else if (x <= 0.0048d0) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-127) {
		tmp = 1.0;
	} else if (x <= 0.0048) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-127:
		tmp = 1.0
	elif x <= 0.0048:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-127)
		tmp = 1.0;
	elseif (x <= 0.0048)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.2e-127)
		tmp = 1.0;
	elseif (x <= 0.0048)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-127], 1.0, If[LessEqual[x, 0.0048], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000001e-127 or 0.00479999999999999958 < x

   1. Initial program 88.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 80.3%

      \[\leadsto \color{blue}{1} \]

   if -2.2000000000000001e-127 < x < 0.00479999999999999958

   1. Initial program 92.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

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

      7. distribute-frac-neg N/A

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

      8. sub-neg N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

      14. *-commutative N/A

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

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

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

      16. +-lowering-+.f64 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 53.0%

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

   7. Simplified 53.0%

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

Alternative 10: 53.9% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 89.3%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Step-by-step derivation

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

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

   6. sub0-neg N/A

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

   7. distribute-frac-neg N/A

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

   8. sub-neg N/A

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

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

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

   10. /-lowering-/.f64 N/A

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

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

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

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

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

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

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

   14. *-commutative N/A

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

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

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

   16. +-lowering-+.f64 89.3%

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

3. Simplified 89.3%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
6. Step-by-step derivation

7. Simplified 57.2%

   \[\leadsto \color{blue}{1} \]
8. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(y / Float64(t - Float64(x / z))) - Float64(x / Float64(Float64(t * z) - x)))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))