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

Percentage Accurate: 89.2% → 97.1%

Time: 9.5s

Alternatives: 17

Speedup: 0.3×

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: 89.2% 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: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x - \frac{x - z \cdot y}{t\_1}}{x - -1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{\frac{-1}{\frac{\frac{t\_1}{y}}{z}} - x}{-1 - x}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\mathsf{fma}\left(t, x, t\right)} - \frac{x}{-1 - x}\right) - \frac{x}{\mathsf{fma}\left(t, x, t\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ (- x (/ (- x (* z y)) t_1)) (- x -1.0))))
   (if (<= t_2 (- INFINITY))
     (/ (- (/ -1.0 (/ (/ t_1 y) z)) x) (- -1.0 x))
     (if (<= t_2 5e+259)
       t_2
       (- (- (/ y (fma t x t)) (/ x (- -1.0 x))) (/ x (* (fma t x t) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x - ((x - (z * y)) / t_1)) / (x - -1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((-1.0 / ((t_1 / y) / z)) - x) / (-1.0 - x);
	} else if (t_2 <= 5e+259) {
		tmp = t_2;
	} else {
		tmp = ((y / fma(t, x, t)) - (x / (-1.0 - x))) - (x / (fma(t, x, t) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_1)) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-1.0 / Float64(Float64(t_1 / y) / z)) - x) / Float64(-1.0 - x));
	elseif (t_2 <= 5e+259)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / fma(t, x, t)) - Float64(x / Float64(-1.0 - x))) - Float64(x / Float64(fma(t, x, t) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(-1.0 / N[(N[(t$95$1 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+259], t$95$2, N[(N[(N[(y / N[(t * x + t), $MachinePrecision]), $MachinePrecision] - N[(x / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * x + t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 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 59.6%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 59.6

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 59.6

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

   4. Applied rewrites 59.6%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 94.9

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

   7. Applied rewrites 94.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.0%

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

   if 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.1%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-rgt-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. lower-*.f64 N/A

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

      15. +-commutative N/A

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

      16. distribute-lft-in N/A

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

      17. *-rgt-identity N/A

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

      18. lower-fma.f64 94.1

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

   5. Applied rewrites 94.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{\frac{-1}{\frac{\frac{t \cdot z - x}{y}}{z}} - x}{-1 - x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\mathsf{fma}\left(t, x, t\right)} - \frac{x}{-1 - x}\right) - \frac{x}{\mathsf{fma}\left(t, x, t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ t_2 := \mathsf{fma}\left(t, z, -x\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{t\_2} \cdot y}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x - \frac{z \cdot y}{x - t \cdot z}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{\frac{y}{t} + x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)))
        (t_2 (fma t z (- x))))
   (if (<= t_1 -2e+29)
     (/ (* (/ z t_2) y) (- x -1.0))
     (if (<= t_1 2e-21)
       (/ (- x (/ (- (/ x z) y) t)) (- x -1.0))
       (if (<= t_1 1.0)
         (/ (- x (/ x t_2)) (- x -1.0))
         (if (<= t_1 5e+259)
           (/ (- x (/ (* z y) (- x (* t z)))) (- x -1.0))
           (/ 1.0 (/ (- x -1.0) (+ (/ y t) x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double t_2 = fma(t, z, -x);
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = ((z / t_2) * y) / (x - -1.0);
	} else if (t_1 <= 2e-21) {
		tmp = (x - (((x / z) - y) / t)) / (x - -1.0);
	} else if (t_1 <= 1.0) {
		tmp = (x - (x / t_2)) / (x - -1.0);
	} else if (t_1 <= 5e+259) {
		tmp = (x - ((z * y) / (x - (t * z)))) / (x - -1.0);
	} else {
		tmp = 1.0 / ((x - -1.0) / ((y / t) + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	t_2 = fma(t, z, Float64(-x))
	tmp = 0.0
	if (t_1 <= -2e+29)
		tmp = Float64(Float64(Float64(z / t_2) * y) / Float64(x - -1.0));
	elseif (t_1 <= 2e-21)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x - -1.0));
	elseif (t_1 <= 1.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x - -1.0));
	elseif (t_1 <= 5e+259)
		tmp = Float64(Float64(x - Float64(Float64(z * y) / Float64(x - Float64(t * z)))) / Float64(x - -1.0));
	else
		tmp = Float64(1.0 / Float64(Float64(x - -1.0) / Float64(Float64(y / t) + x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * z + (-x)), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+29], N[(N[(N[(z / t$95$2), $MachinePrecision] * y), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], N[(N[(x - N[(N[(z * y), $MachinePrecision] / N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(x - -1.0), $MachinePrecision] / N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1.99999999999999983e29

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 94.3

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

   5. Applied rewrites 94.3%

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

   if -1.99999999999999983e29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999982e-21

   1. Initial program 95.7%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if 1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{\mathsf{neg}\left(x\right)}\right)}}{x + 1} \]

      7. lower-neg.f64 99.1

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{-x}\right)}}{x + 1} \]

   5. Applied rewrites 99.1%

      \[\leadsto \frac{\color{blue}{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}}{x + 1} \]

   if 1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.6

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

   5. Applied rewrites 98.6%

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

   if 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 33.1

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 33.1

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

   4. Applied rewrites 33.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 93.8

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

   7. Applied rewrites 93.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 93.9

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-+.f64 93.9

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 93.9

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

   9. Applied rewrites 93.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{1 + x}{\frac{y}{t} + x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{\mathsf{fma}\left(t, z, -x\right)} \cdot y}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 1:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x - \frac{z \cdot y}{x - t \cdot z}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{\frac{y}{t} + x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ t_2 := \mathsf{fma}\left(t, z, -x\right)\\ t_3 := \frac{y}{t} + x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{t\_2} \cdot y}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{t\_3}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x - \frac{z \cdot y}{x - t \cdot z}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{t\_3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)))
        (t_2 (fma t z (- x)))
        (t_3 (+ (/ y t) x)))
   (if (<= t_1 -2e+29)
     (/ (* (/ z t_2) y) (- x -1.0))
     (if (<= t_1 2e-21)
       (/ t_3 (- x -1.0))
       (if (<= t_1 1.0)
         (/ (- x (/ x t_2)) (- x -1.0))
         (if (<= t_1 5e+259)
           (/ (- x (/ (* z y) (- x (* t z)))) (- x -1.0))
           (/ 1.0 (/ (- x -1.0) t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double t_2 = fma(t, z, -x);
	double t_3 = (y / t) + x;
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = ((z / t_2) * y) / (x - -1.0);
	} else if (t_1 <= 2e-21) {
		tmp = t_3 / (x - -1.0);
	} else if (t_1 <= 1.0) {
		tmp = (x - (x / t_2)) / (x - -1.0);
	} else if (t_1 <= 5e+259) {
		tmp = (x - ((z * y) / (x - (t * z)))) / (x - -1.0);
	} else {
		tmp = 1.0 / ((x - -1.0) / t_3);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	t_2 = fma(t, z, Float64(-x))
	t_3 = Float64(Float64(y / t) + x)
	tmp = 0.0
	if (t_1 <= -2e+29)
		tmp = Float64(Float64(Float64(z / t_2) * y) / Float64(x - -1.0));
	elseif (t_1 <= 2e-21)
		tmp = Float64(t_3 / Float64(x - -1.0));
	elseif (t_1 <= 1.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x - -1.0));
	elseif (t_1 <= 5e+259)
		tmp = Float64(Float64(x - Float64(Float64(z * y) / Float64(x - Float64(t * z)))) / Float64(x - -1.0));
	else
		tmp = Float64(1.0 / Float64(Float64(x - -1.0) / t_3));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+29], N[(N[(N[(z / t$95$2), $MachinePrecision] * y), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], N[(t$95$3 / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], N[(N[(x - N[(N[(z * y), $MachinePrecision] / N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(x - -1.0), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1.99999999999999983e29

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 94.3

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

   5. Applied rewrites 94.3%

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

   if -1.99999999999999983e29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999982e-21

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 84.5

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

   5. Applied rewrites 84.5%

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

   if 1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{\mathsf{neg}\left(x\right)}\right)}}{x + 1} \]

      7. lower-neg.f64 99.1

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{-x}\right)}}{x + 1} \]

   5. Applied rewrites 99.1%

      \[\leadsto \frac{\color{blue}{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}}{x + 1} \]

   if 1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.6

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

   5. Applied rewrites 98.6%

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

   if 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 33.1

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 33.1

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

   4. Applied rewrites 33.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 93.8

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

   7. Applied rewrites 93.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 93.9

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-+.f64 93.9

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 93.9

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

   9. Applied rewrites 93.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{1 + x}{\frac{y}{t} + x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{\mathsf{fma}\left(t, z, -x\right)} \cdot y}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 1:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x - \frac{z \cdot y}{x - t \cdot z}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{\frac{y}{t} + x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ t_2 := \mathsf{fma}\left(t, z, -x\right)\\ t_3 := \frac{y}{t} + x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{t\_2} \cdot y}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{t\_3}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{t\_3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)))
        (t_2 (fma t z (- x)))
        (t_3 (+ (/ y t) x)))
   (if (<= t_1 -2e+29)
     (/ (* (/ z t_2) y) (- x -1.0))
     (if (<= t_1 2e-21)
       (/ t_3 (- x -1.0))
       (if (<= t_1 2.0)
         (/ (- x (/ x t_2)) (- x -1.0))
         (if (<= t_1 5e+259)
           (/ (* z y) (* (- -1.0 x) (- x (* t z))))
           (/ 1.0 (/ (- x -1.0) t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double t_2 = fma(t, z, -x);
	double t_3 = (y / t) + x;
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = ((z / t_2) * y) / (x - -1.0);
	} else if (t_1 <= 2e-21) {
		tmp = t_3 / (x - -1.0);
	} else if (t_1 <= 2.0) {
		tmp = (x - (x / t_2)) / (x - -1.0);
	} else if (t_1 <= 5e+259) {
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)));
	} else {
		tmp = 1.0 / ((x - -1.0) / t_3);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	t_2 = fma(t, z, Float64(-x))
	t_3 = Float64(Float64(y / t) + x)
	tmp = 0.0
	if (t_1 <= -2e+29)
		tmp = Float64(Float64(Float64(z / t_2) * y) / Float64(x - -1.0));
	elseif (t_1 <= 2e-21)
		tmp = Float64(t_3 / Float64(x - -1.0));
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x - -1.0));
	elseif (t_1 <= 5e+259)
		tmp = Float64(Float64(z * y) / Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z))));
	else
		tmp = Float64(1.0 / Float64(Float64(x - -1.0) / t_3));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+29], N[(N[(N[(z / t$95$2), $MachinePrecision] * y), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], N[(t$95$3 / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], N[(N[(z * y), $MachinePrecision] / N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(x - -1.0), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1.99999999999999983e29

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 94.3

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

   5. Applied rewrites 94.3%

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

   if -1.99999999999999983e29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999982e-21

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 84.5

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

   5. Applied rewrites 84.5%

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

   if 1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{\mathsf{neg}\left(x\right)}\right)}}{x + 1} \]

      7. lower-neg.f64 99.1

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{-x}\right)}}{x + 1} \]

   5. Applied rewrites 99.1%

      \[\leadsto \frac{\color{blue}{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}}{x + 1} \]

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.2

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 98.4

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

   7. Applied rewrites 98.4%

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

   9. Applied rewrites 98.4%

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

   if 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 33.1

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 33.1

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

   4. Applied rewrites 33.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 93.8

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

   7. Applied rewrites 93.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 93.9

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-+.f64 93.9

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 93.9

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

   9. Applied rewrites 93.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{1 + x}{\frac{y}{t} + x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{\mathsf{fma}\left(t, z, -x\right)} \cdot y}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{\frac{y}{t} + x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ t_2 := \mathsf{fma}\left(t, z, -x\right)\\ t_3 := \frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{t\_2} \cdot y}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)))
        (t_2 (fma t z (- x)))
        (t_3 (/ (+ (/ y t) x) (- x -1.0))))
   (if (<= t_1 -2e+29)
     (/ (* (/ z t_2) y) (- x -1.0))
     (if (<= t_1 2e-21)
       t_3
       (if (<= t_1 2.0)
         (/ (- x (/ x t_2)) (- x -1.0))
         (if (<= t_1 5e+259) (/ (* z y) (* (- -1.0 x) (- x (* t z)))) t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double t_2 = fma(t, z, -x);
	double t_3 = ((y / t) + x) / (x - -1.0);
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = ((z / t_2) * y) / (x - -1.0);
	} else if (t_1 <= 2e-21) {
		tmp = t_3;
	} else if (t_1 <= 2.0) {
		tmp = (x - (x / t_2)) / (x - -1.0);
	} else if (t_1 <= 5e+259) {
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	t_2 = fma(t, z, Float64(-x))
	t_3 = Float64(Float64(Float64(y / t) + x) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= -2e+29)
		tmp = Float64(Float64(Float64(z / t_2) * y) / Float64(x - -1.0));
	elseif (t_1 <= 2e-21)
		tmp = t_3;
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x - -1.0));
	elseif (t_1 <= 5e+259)
		tmp = Float64(Float64(z * y) / Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z))));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+29], N[(N[(N[(z / t$95$2), $MachinePrecision] * y), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], t$95$3, If[LessEqual[t$95$1, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], N[(N[(z * y), $MachinePrecision] / N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

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))) < -1.99999999999999983e29

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 94.3

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

   5. Applied rewrites 94.3%

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

   if -1.99999999999999983e29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999982e-21 or 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if 1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{\mathsf{neg}\left(x\right)}\right)}}{x + 1} \]

      7. lower-neg.f64 99.1

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{-x}\right)}}{x + 1} \]

   5. Applied rewrites 99.1%

      \[\leadsto \frac{\color{blue}{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}}{x + 1} \]

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.2

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 98.4

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

   7. Applied rewrites 98.4%

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

   9. Applied rewrites 98.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{z}{\mathsf{fma}\left(t, z, -x\right)} \cdot y}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ t_2 := \mathsf{fma}\left(t, z, -x\right)\\ t_3 := \frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{z}{x - -1} \cdot \frac{y}{t\_2}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)))
        (t_2 (fma t z (- x)))
        (t_3 (/ (+ (/ y t) x) (- x -1.0))))
   (if (<= t_1 -2e+29)
     (* (/ z (- x -1.0)) (/ y t_2))
     (if (<= t_1 2e-21)
       t_3
       (if (<= t_1 2.0)
         (/ (- x (/ x t_2)) (- x -1.0))
         (if (<= t_1 5e+259) (/ (* z y) (* (- -1.0 x) (- x (* t z)))) t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double t_2 = fma(t, z, -x);
	double t_3 = ((y / t) + x) / (x - -1.0);
	double tmp;
	if (t_1 <= -2e+29) {
		tmp = (z / (x - -1.0)) * (y / t_2);
	} else if (t_1 <= 2e-21) {
		tmp = t_3;
	} else if (t_1 <= 2.0) {
		tmp = (x - (x / t_2)) / (x - -1.0);
	} else if (t_1 <= 5e+259) {
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	t_2 = fma(t, z, Float64(-x))
	t_3 = Float64(Float64(Float64(y / t) + x) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= -2e+29)
		tmp = Float64(Float64(z / Float64(x - -1.0)) * Float64(y / t_2));
	elseif (t_1 <= 2e-21)
		tmp = t_3;
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x - -1.0));
	elseif (t_1 <= 5e+259)
		tmp = Float64(Float64(z * y) / Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z))));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+29], N[(N[(z / N[(x - -1.0), $MachinePrecision]), $MachinePrecision] * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], t$95$3, If[LessEqual[t$95$1, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], N[(N[(z * y), $MachinePrecision] / N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

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))) < -1.99999999999999983e29

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if -1.99999999999999983e29 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999982e-21 or 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if 1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{\mathsf{neg}\left(x\right)}\right)}}{x + 1} \]

      7. lower-neg.f64 99.1

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{-x}\right)}}{x + 1} \]

   5. Applied rewrites 99.1%

      \[\leadsto \frac{\color{blue}{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}}{x + 1} \]

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.2

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 98.4

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

   7. Applied rewrites 98.4%

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

   9. Applied rewrites 98.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{z}{x - -1} \cdot \frac{y}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_2 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x - -1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_2 2e-21)
     t_1
     (if (<= t_2 2.0)
       (/ (- x (/ x (fma t z (- x)))) (- x -1.0))
       (if (<= t_2 5e+259) (/ (* z y) (* (- -1.0 x) (- x (* t z)))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x - -1.0);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 2e-21) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / fma(t, z, -x))) / (x - -1.0);
	} else if (t_2 <= 5e+259) {
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x - -1.0))
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= 2e-21)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / fma(t, z, Float64(-x)))) / Float64(x - -1.0));
	elseif (t_2 <= 5e+259)
		tmp = Float64(Float64(z * y) / Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 2e-21], t$95$1, If[LessEqual[t$95$2, 2.0], N[(N[(x - N[(x / N[(t * z + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+259], N[(N[(z * y), $MachinePrecision] / N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999982e-21 or 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 82.6

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

   5. Applied rewrites 82.6%

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

   if 1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{\mathsf{neg}\left(x\right)}\right)}}{x + 1} \]

      7. lower-neg.f64 99.1

         \[\leadsto \frac{x - \frac{x}{\mathsf{fma}\left(t, z, \color{blue}{-x}\right)}}{x + 1} \]

   5. Applied rewrites 99.1%

      \[\leadsto \frac{\color{blue}{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}}{x + 1} \]

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.2

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 98.4

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

   7. Applied rewrites 98.4%

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

   9. Applied rewrites 98.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_2 \leq 0.99999996:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_2 0.99999996)
     t_1
     (if (<= t_2 2.0)
       1.0
       (if (<= t_2 5e+259) (/ (* z y) (* (- -1.0 x) (- x (* t z)))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x - -1.0);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.99999996) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+259) {
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)));
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = ((y / t) + x) / (x - (-1.0d0))
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_2 <= 0.99999996d0) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_2 <= 5d+259) then
        tmp = (z * y) / (((-1.0d0) - x) * (x - (t * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x - -1.0);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.99999996) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+259) {
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x - -1.0)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_2 <= 0.99999996:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	elif t_2 <= 5e+259:
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x - -1.0))
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= 0.99999996)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+259)
		tmp = Float64(Float64(z * y) / Float64(Float64(-1.0 - x) * Float64(x - Float64(t * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (x - -1.0);
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_2 <= 0.99999996)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+259)
		tmp = (z * y) / ((-1.0 - x) * (x - (t * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.99999996], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, If[LessEqual[t$95$2, 5e+259], N[(N[(z * y), $MachinePrecision] / N[(N[(-1.0 - x), $MachinePrecision] * N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999996000000002 or 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if 0.99999996000000002 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.9%

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

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.2

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 98.4

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

   7. Applied rewrites 98.4%

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

   9. Applied rewrites 98.4%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.99999996:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{\left(-1 - x\right) \cdot \left(x - t \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x - \frac{x - z \cdot y}{t\_2}}{x - -1}\\ \mathbf{if}\;t\_3 \leq 0.99999996:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{1 \cdot t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (- x (/ (- x (* z y)) t_2)) (- x -1.0))))
   (if (<= t_3 0.99999996)
     t_1
     (if (<= t_3 2.0) 1.0 (if (<= t_3 5e+259) (/ (* z y) (* 1.0 t_2)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x - -1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x - ((x - (z * y)) / t_2)) / (x - -1.0);
	double tmp;
	if (t_3 <= 0.99999996) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+259) {
		tmp = (z * y) / (1.0 * t_2);
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((y / t) + x) / (x - (-1.0d0))
    t_2 = (t * z) - x
    t_3 = (x - ((x - (z * y)) / t_2)) / (x - (-1.0d0))
    if (t_3 <= 0.99999996d0) then
        tmp = t_1
    else if (t_3 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_3 <= 5d+259) then
        tmp = (z * y) / (1.0d0 * t_2)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x - -1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x - ((x - (z * y)) / t_2)) / (x - -1.0);
	double tmp;
	if (t_3 <= 0.99999996) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+259) {
		tmp = (z * y) / (1.0 * t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x - -1.0)
	t_2 = (t * z) - x
	t_3 = (x - ((x - (z * y)) / t_2)) / (x - -1.0)
	tmp = 0
	if t_3 <= 0.99999996:
		tmp = t_1
	elif t_3 <= 2.0:
		tmp = 1.0
	elif t_3 <= 5e+259:
		tmp = (z * y) / (1.0 * t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x - -1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_2)) / Float64(x - -1.0))
	tmp = 0.0
	if (t_3 <= 0.99999996)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+259)
		tmp = Float64(Float64(z * y) / Float64(1.0 * t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (x - -1.0);
	t_2 = (t * z) - x;
	t_3 = (x - ((x - (z * y)) / t_2)) / (x - -1.0);
	tmp = 0.0;
	if (t_3 <= 0.99999996)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+259)
		tmp = (z * y) / (1.0 * t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 0.99999996], t$95$1, If[LessEqual[t$95$3, 2.0], 1.0, If[LessEqual[t$95$3, 5e+259], N[(N[(z * y), $MachinePrecision] / N[(1.0 * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999996000000002 or 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if 0.99999996000000002 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.9%

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

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.2

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 98.4

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

   7. Applied rewrites 98.4%

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

   9. Applied rewrites 98.4%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 83.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.99999996:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot y}{1 \cdot \left(t \cdot z - x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\left(x - -1\right) \cdot t}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_2 \leq -200000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.99999996:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* (- x -1.0) t)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_2 -200000.0)
     t_1
     (if (<= t_2 0.99999996) (/ x (- x -1.0)) (if (<= t_2 2.0) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / ((x - -1.0) * t);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= -200000.0) {
		tmp = t_1;
	} else if (t_2 <= 0.99999996) {
		tmp = x / (x - -1.0);
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = y / ((x - (-1.0d0)) * t)
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_2 <= (-200000.0d0)) then
        tmp = t_1
    else if (t_2 <= 0.99999996d0) then
        tmp = x / (x - (-1.0d0))
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / ((x - -1.0) * t);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= -200000.0) {
		tmp = t_1;
	} else if (t_2 <= 0.99999996) {
		tmp = x / (x - -1.0);
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / ((x - -1.0) * t)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_2 <= -200000.0:
		tmp = t_1
	elif t_2 <= 0.99999996:
		tmp = x / (x - -1.0)
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(Float64(x - -1.0) * t))
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= -200000.0)
		tmp = t_1;
	elseif (t_2 <= 0.99999996)
		tmp = Float64(x / Float64(x - -1.0));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / ((x - -1.0) * t);
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_2 <= -200000.0)
		tmp = t_1;
	elseif (t_2 <= 0.99999996)
		tmp = x / (x - -1.0);
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(N[(x - -1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -200000.0], t$95$1, If[LessEqual[t$95$2, 0.99999996], N[(x / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2e5 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 75.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 75.8

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 75.2

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

   7. Applied rewrites 75.2%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 66.5%

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

   if -2e5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999996000000002

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 53.1

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

   5. Applied rewrites 53.1%

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

   if 0.99999996000000002 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -200000:\\ \;\;\;\;\frac{y}{\left(x - -1\right) \cdot t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.99999996:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(x - -1\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -200000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.99999996:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 -200000.0)
     (/ y t)
     (if (<= t_1 0.99999996) (/ x (- x -1.0)) (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = y / t;
	} else if (t_1 <= 0.99999996) {
		tmp = x / (x - -1.0);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_1 <= (-200000.0d0)) then
        tmp = y / t
    else if (t_1 <= 0.99999996d0) then
        tmp = x / (x - (-1.0d0))
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = y / t;
	} else if (t_1 <= 0.99999996) {
		tmp = x / (x - -1.0);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= -200000.0:
		tmp = y / t
	elif t_1 <= 0.99999996:
		tmp = x / (x - -1.0)
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= -200000.0)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.99999996)
		tmp = Float64(x / Float64(x - -1.0));
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= -200000.0)
		tmp = y / t;
	elseif (t_1 <= 0.99999996)
		tmp = x / (x - -1.0);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200000.0], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.99999996], N[(x / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2e5 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 61.1

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

   5. Applied rewrites 61.1%

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

   if -2e5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999996000000002

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 53.1

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

   5. Applied rewrites 53.1%

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

   if 0.99999996000000002 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.9%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -200000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.99999996:\\ \;\;\;\;\frac{x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -200000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-20}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 -200000.0)
     (/ y t)
     (if (<= t_1 4e-20) (* (- 1.0 x) x) (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = y / t;
	} else if (t_1 <= 4e-20) {
		tmp = (1.0 - x) * x;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_1 <= (-200000.0d0)) then
        tmp = y / t
    else if (t_1 <= 4d-20) then
        tmp = (1.0d0 - x) * x
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = y / t;
	} else if (t_1 <= 4e-20) {
		tmp = (1.0 - x) * x;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_1 <= -200000.0:
		tmp = y / t
	elif t_1 <= 4e-20:
		tmp = (1.0 - x) * x
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= -200000.0)
		tmp = Float64(y / t);
	elseif (t_1 <= 4e-20)
		tmp = Float64(Float64(1.0 - x) * x);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_1 <= -200000.0)
		tmp = y / t;
	elseif (t_1 <= 4e-20)
		tmp = (1.0 - x) * x;
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200000.0], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 4e-20], N[(N[(1.0 - x), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2e5 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 61.1

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

   5. Applied rewrites 61.1%

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

   if -2e5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.99999999999999978e-20

   1. Initial program 95.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 53.2

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

   5. Applied rewrites 53.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot x\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.2%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{x} \]

   if 3.99999999999999978e-20 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -200000:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 4 \cdot 10^{-20}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{x - -1} \cdot \frac{y}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\mathsf{fma}\left(t, x, t\right)} - \frac{x}{-1 - x}\right) - \frac{x}{\mathsf{fma}\left(t, x, t\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 (- INFINITY))
     (* (/ z (- x -1.0)) (/ y (fma t z (- x))))
     (if (<= t_1 5e+259)
       t_1
       (- (- (/ y (fma t x t)) (/ x (- -1.0 x))) (/ x (* (fma t x t) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (z / (x - -1.0)) * (y / fma(t, z, -x));
	} else if (t_1 <= 5e+259) {
		tmp = t_1;
	} else {
		tmp = ((y / fma(t, x, t)) - (x / (-1.0 - x))) - (x / (fma(t, x, t) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(z / Float64(x - -1.0)) * Float64(y / fma(t, z, Float64(-x))));
	elseif (t_1 <= 5e+259)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y / fma(t, x, t)) - Float64(x / Float64(-1.0 - x))) - Float64(x / Float64(fma(t, x, t) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z / N[(x - -1.0), $MachinePrecision]), $MachinePrecision] * N[(y / N[(t * z + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], t$95$1, N[(N[(N[(y / N[(t * x + t), $MachinePrecision]), $MachinePrecision] - N[(x / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * x + t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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 59.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.0%

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

   if 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.1%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-rgt-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. lower-*.f64 N/A

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

      15. +-commutative N/A

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

      16. distribute-lft-in N/A

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

      17. *-rgt-identity N/A

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

      18. lower-fma.f64 94.1

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

   5. Applied rewrites 94.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{z}{x - -1} \cdot \frac{y}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\mathsf{fma}\left(t, x, t\right)} - \frac{x}{-1 - x}\right) - \frac{x}{\mathsf{fma}\left(t, x, t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{x - -1} \cdot \frac{y}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{\frac{y}{t} + x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_1 (- INFINITY))
     (* (/ z (- x -1.0)) (/ y (fma t z (- x))))
     (if (<= t_1 5e+259) t_1 (/ 1.0 (/ (- x -1.0) (+ (/ y t) x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (z / (x - -1.0)) * (y / fma(t, z, -x));
	} else if (t_1 <= 5e+259) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((x - -1.0) / ((y / t) + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(z / Float64(x - -1.0)) * Float64(y / fma(t, z, Float64(-x))));
	elseif (t_1 <= 5e+259)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(Float64(x - -1.0) / Float64(Float64(y / t) + x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z / N[(x - -1.0), $MachinePrecision]), $MachinePrecision] * N[(y / N[(t * z + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+259], t$95$1, N[(1.0 / N[(N[(x - -1.0), $MachinePrecision] / N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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 59.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000033e259

   1. Initial program 99.0%

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

   if 5.00000000000000033e259 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. neg-sub0 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{0 - \left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      7. lift--.f64 N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z - x\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      8. sub-neg N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      9. +-commutative N/A

         \[\leadsto \frac{x + \frac{1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t \cdot z\right)}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      10. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t \cdot z}}{\mathsf{neg}\left(\left(y \cdot z - x\right)\right)}}}{x + 1} \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 N/A

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

      14. neg-sub0 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{0 - \left(y \cdot z - x\right)}}}}{x + 1} \]

      15. lift--.f64 N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z - x\right)}}}}{x + 1} \]

      16. sub-neg N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(x\right)\right)\right)}}}}{x + 1} \]

      17. +-commutative N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y \cdot z\right)}}}}{x + 1} \]

      18. associate--r+ N/A

          \[\leadsto \frac{x + \frac{1}{\frac{x - t \cdot z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - y \cdot z}}}}{x + 1} \]

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 33.1

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 33.1

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

   4. Applied rewrites 33.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 93.8

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

   7. Applied rewrites 93.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 93.9

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-+.f64 93.9

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 93.9

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

   9. Applied rewrites 93.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq -\infty:\\ \;\;\;\;\frac{z}{x - -1} \cdot \frac{y}{\mathsf{fma}\left(t, z, -x\right)}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x - -1}{\frac{y}{t} + x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x - -1}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1}\\ \mathbf{if}\;t\_2 \leq 0.99999996:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (- x -1.0)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0))))
   (if (<= t_2 0.99999996) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x - -1.0);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.99999996) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = ((y / t) + x) / (x - (-1.0d0))
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))
    if (t_2 <= 0.99999996d0) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x - -1.0);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	double tmp;
	if (t_2 <= 0.99999996) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x - -1.0)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)
	tmp = 0
	if t_2 <= 0.99999996:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x - -1.0))
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0))
	tmp = 0.0
	if (t_2 <= 0.99999996)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (x - -1.0);
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0);
	tmp = 0.0;
	if (t_2 <= 0.99999996)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.99999996], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

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))) < 0.99999996000000002 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 83.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if 0.99999996000000002 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 0.99999996:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 4 \cdot 10^{-20}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- x (/ (- x (* z y)) (- (* t z) x))) (- x -1.0)) 4e-20)
   (* (- 1.0 x) x)
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 4e-20) {
		tmp = (1.0 - x) * 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 - ((x - (z * y)) / ((t * z) - x))) / (x - (-1.0d0))) <= 4d-20) then
        tmp = (1.0d0 - x) * 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 - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 4e-20) {
		tmp = (1.0 - x) * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 4e-20:
		tmp = (1.0 - x) * x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(x - -1.0)) <= 4e-20)
		tmp = Float64(Float64(1.0 - x) * x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (x - -1.0)) <= 4e-20)
		tmp = (1.0 - x) * x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - -1.0), $MachinePrecision]), $MachinePrecision], 4e-20], N[(N[(1.0 - x), $MachinePrecision] * x), $MachinePrecision], 1.0]

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))) < 3.99999999999999978e-20

   1. Initial program 88.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 31.9

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

   5. Applied rewrites 31.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot x\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 31.0%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{x} \]

   if 3.99999999999999978e-20 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{x - -1} \leq 4 \cdot 10^{-20}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.3% accurate, 45.0× 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 91.9%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 54.2%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.7× 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 2024297 
(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)))