Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.5% → 83.9%

Time: 16.6s

Alternatives: 15

Speedup: 0.8×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 55.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/
    (+ t (/ y (/ 1.0 (fma y (fma y (fma x y z) 27464.7644705) 230661.510616))))
    (fma (fma y (+ y a) b) (* y y) (fma y c i)))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = (t + (y / (1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / fma(fma(y, (y + a), b), (y * y), fma(y, c, i));
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(Float64(t + Float64(y / Float64(1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / fma(fma(y, Float64(y + a), b), Float64(y * y), fma(y, c, i)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t + N[(y / N[(1.0 / N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] * N[(y * y), $MachinePrecision] + N[(y * c + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 94.3%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)} + i} \]

      4. lower-fma.f64 94.3

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\color{blue}{\mathsf{fma}\left(y, \left(\left(y + a\right) \cdot y + b\right) \cdot y + c, i\right)}} \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}, i\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c, i\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + c, i\right)} \]

      8. lower-fma.f64 94.3

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \left(y + a\right) \cdot y + b, c\right)}, i\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(y + a\right) \cdot y} + b, c\right), i\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(y + a\right)} + b, c\right), i\right)} \]

      11. lower-+.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(y + a\right) + b}, c\right), i\right)} \]

      12. lift-fma.f64 94.3

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y + a, b\right)}, c\right), i\right)} \]

      13. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right) + i}} \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{y \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(y, y + a, b\right) + c\right)} + i} \]

      15. distribute-rgt-in N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(y \cdot \mathsf{fma}\left(y, y + a, b\right)\right) \cdot y + c \cdot y\right)} + i} \]

      16. associate-+l+ N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(y \cdot \mathsf{fma}\left(y, y + a, b\right)\right) \cdot y + \left(c \cdot y + i\right)}} \]

   6. Applied rewrites 94.3%

      \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (if (<= t_1 INFINITY) t_1 (- (+ x (/ z y)) (* a (/ x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x + (z / y)) - (a * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x + (z / y)) - (a * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (*
    (fma y (fma y (fma y (fma x y z) 27464.7644705) 230661.510616) t)
    (/ 1.0 (fma y (fma y (fma y (+ y a) b) c) i)))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t) * (1.0 / fma(y, fma(y, fma(y, (y + a), b), c), i));
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t) * Float64(1.0 / fma(y, fma(y, fma(y, Float64(y + a), b), c), i)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] * N[(1.0 / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      2. div-inv N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

   4. Applied rewrites 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/
    (fma y (fma y (fma y (fma y x z) 27464.7644705) 230661.510616) t)
    (fma y (fma y (fma y y b) c) i))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, y, b), c), i);
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, y, b), c), i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * N[(y * N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / N[(y * N[(y * N[(y * y + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) + t}}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right), t\right)}}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right) + \frac{28832688827}{125000}}, t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right), \frac{28832688827}{125000}\right)}, t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(z + x \cdot y\right) + \frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, z + x \cdot y, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)} \]

      11. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right) + i}} \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(b + {y}^{2}\right), i\right)}} \]

      13. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(b + {y}^{2}\right) + c}, i\right)} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b + {y}^{2}, c\right)}, i\right)} \]

      15. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{{y}^{2} + b}, c\right), i\right)} \]

      16. unpow2 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot y} + b, c\right), i\right)} \]

      17. lower-fma.f64 88.0

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y, b\right)}, c\right), i\right)} \]

   5. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y, b\right), c\right), i\right)}} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/
    (fma y (fma y (fma y z 27464.7644705) 230661.510616) t)
    (fma y (fma y (fma y (+ y a) b) c) i))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right) + t}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right), t\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right) + \frac{28832688827}{125000}}, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{54929528941}{2000000} + y \cdot z, \frac{28832688827}{125000}\right)}, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot z + \frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + i}} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(b + y \cdot \left(a + y\right)\right), i\right)}} \]

      10. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right) + c}, i\right)} \]

      11. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b + y \cdot \left(a + y\right), c\right)}, i\right)} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(a + y\right) + b}, c\right), i\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, a + y, b\right)}, c\right), i\right)} \]

      14. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

      15. lower-+.f64 86.8

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

   5. Applied rewrites 86.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, 27464.7644705, 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/
    (fma y (fma y 27464.7644705 230661.510616) t)
    (fma (fma y (+ y a) b) (* y y) (fma y c i)))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(y, fma(y, 27464.7644705, 230661.510616), t) / fma(fma(y, (y + a), b), (y * y), fma(y, c, i));
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(y, fma(y, 27464.7644705, 230661.510616), t) / fma(fma(y, Float64(y + a), b), Float64(y * y), fma(y, c, i)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * N[(y * 27464.7644705 + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] * N[(y * y), $MachinePrecision] + N[(y * c + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 94.3%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)} + i} \]

      4. lower-fma.f64 94.3

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\color{blue}{\mathsf{fma}\left(y, \left(\left(y + a\right) \cdot y + b\right) \cdot y + c, i\right)}} \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}, i\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c, i\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + c, i\right)} \]

      8. lower-fma.f64 94.3

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \left(y + a\right) \cdot y + b, c\right)}, i\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(y + a\right) \cdot y} + b, c\right), i\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(y + a\right)} + b, c\right), i\right)} \]

      11. lower-+.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(y + a\right) + b}, c\right), i\right)} \]

      12. lift-fma.f64 94.3

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y + a, b\right)}, c\right), i\right)} \]

      13. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right) + i}} \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{y \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(y, y + a, b\right) + c\right)} + i} \]

      15. distribute-rgt-in N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(y \cdot \mathsf{fma}\left(y, y + a, b\right)\right) \cdot y + c \cdot y\right)} + i} \]

      16. associate-+l+ N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(y \cdot \mathsf{fma}\left(y, y + a, b\right)\right) \cdot y + \left(c \cdot y + i\right)}} \]

   6. Applied rewrites 94.3%

      \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}} \]

   7. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + y \cdot \left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y\right) + t}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y, t\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\frac{54929528941}{2000000} \cdot y + \frac{28832688827}{125000}}, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \frac{54929528941}{2000000}} + \frac{28832688827}{125000}, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

      5. lower-fma.f64 78.2

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, 27464.7644705, 230661.510616\right)}, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

   9. Applied rewrites 78.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, 27464.7644705, 230661.510616\right), t\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, 27464.7644705, 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i\\ \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{t\_1} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i)))
   (if (<=
        (/
         (+
          (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
          t)
         t_1)
        INFINITY)
     (/ (fma y 230661.510616 t) t_1)
     (- (+ x (/ z y)) (* a (/ x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / t_1) <= ((double) INFINITY)) {
		tmp = fma(y, 230661.510616, t) / t_1;
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / t_1) <= Inf)
		tmp = Float64(fma(y, 230661.510616, t) / t_1);
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(y * 230661.510616 + t), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \frac{28832688827}{125000}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lower-fma.f64 75.2

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, 230661.510616, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Applied rewrites 75.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, 230661.510616, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/ (fma 230661.510616 y t) (fma (fma y (+ y a) b) (* y y) (fma y c i)))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(230661.510616, y, t) / fma(fma(y, (y + a), b), (y * y), fma(y, c, i));
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(230661.510616, y, t) / fma(fma(y, Float64(y + a), b), Float64(y * y), fma(y, c, i)));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] * N[(y * y), $MachinePrecision] + N[(y * c + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 94.3%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i} \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)} + i} \]

      4. lower-fma.f64 94.3

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\color{blue}{\mathsf{fma}\left(y, \left(\left(y + a\right) \cdot y + b\right) \cdot y + c, i\right)}} \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}, i\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c, i\right)} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + c, i\right)} \]

      8. lower-fma.f64 94.3

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \left(y + a\right) \cdot y + b, c\right)}, i\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(y + a\right) \cdot y} + b, c\right), i\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(y + a\right)} + b, c\right), i\right)} \]

      11. lower-+.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(y + a\right) + b}, c\right), i\right)} \]

      12. lift-fma.f64 94.3

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, y + a, b\right)}, c\right), i\right)} \]

      13. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right) + i}} \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{y \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(y, y + a, b\right) + c\right)} + i} \]

      15. distribute-rgt-in N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(\left(y \cdot \mathsf{fma}\left(y, y + a, b\right)\right) \cdot y + c \cdot y\right)} + i} \]

      16. associate-+l+ N/A

          \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}} + t}{\color{blue}{\left(y \cdot \mathsf{fma}\left(y, y + a, b\right)\right) \cdot y + \left(c \cdot y + i\right)}} \]

   6. Applied rewrites 94.3%

      \[\leadsto \frac{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}} + t}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}} \]

   7. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

      2. lower-fma.f64 75.2

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

   9. Applied rewrites 75.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, y + a, b\right), y \cdot y, \mathsf{fma}\left(y, c, i\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, 27464.7644705, 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/ (fma y (fma y 27464.7644705 230661.510616) t) (fma y (fma y b c) i))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(y, fma(y, 27464.7644705, 230661.510616), t) / fma(y, fma(y, b, c), i);
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(y, fma(y, 27464.7644705, 230661.510616), t) / fma(y, fma(y, b, c), i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * N[(y * 27464.7644705 + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / N[(y * N[(y * b + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{3}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{3}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. cube-mult N/A

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

      3. unpow2 N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\left(x \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. unpow2 N/A

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

      6. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, c + b \cdot y, i\right)}} \]

      3. +-commutative N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{b \cdot y + c}, i\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{y \cdot b} + c, i\right)} \]

      5. lower-fma.f64 68.2

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b, c\right)}, i\right)} \]

   8. Applied rewrites 68.2%

      \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}} \]

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + y \cdot \left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y\right)}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y\right) + t}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

       2. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + \frac{54929528941}{2000000} \cdot y, t\right)}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

       3. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\frac{54929528941}{2000000} \cdot y + \frac{28832688827}{125000}}, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

       4. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \frac{54929528941}{2000000}} + \frac{28832688827}{125000}, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

       5. lower-fma.f64 72.3

          \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, 27464.7644705, 230661.510616\right)}, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

   11. Applied rewrites 72.3%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, 27464.7644705, 230661.510616\right), t\right)}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, 27464.7644705, 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/ (fma 230661.510616 y t) (fma y (fma y b c) i))
   (- (+ x (/ z y)) (* a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(230661.510616, y, t) / fma(y, fma(y, b, c), i);
	} else {
		tmp = (x + (z / y)) - (a * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(230661.510616, y, t) / fma(y, fma(y, b, c), i));
	else
		tmp = Float64(Float64(x + Float64(z / y)) - Float64(a * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(y * N[(y * b + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{3}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{3}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. cube-mult N/A

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

      3. unpow2 N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\left(x \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. unpow2 N/A

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

      6. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, c + b \cdot y, i\right)}} \]

      3. +-commutative N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{b \cdot y + c}, i\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{y \cdot b} + c, i\right)} \]

      5. lower-fma.f64 68.2

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b, c\right)}, i\right)} \]

   8. Applied rewrites 68.2%

      \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}} \]

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

       2. lower-fma.f64 71.4

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - a \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/ (fma 230661.510616 y t) (fma y (fma y b c) i))
   (+ x (/ z y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = fma(230661.510616, y, t) / fma(y, fma(y, b, c), i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(fma(230661.510616, y, t) / fma(y, fma(y, b, c), i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(y * N[(y * b + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{3}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{3}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. cube-mult N/A

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

      3. unpow2 N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\left(x \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. unpow2 N/A

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

      6. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, c + b \cdot y, i\right)}} \]

      3. +-commutative N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{b \cdot y + c}, i\right)} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{y \cdot b} + c, i\right)} \]

      5. lower-fma.f64 68.2

         \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b, c\right)}, i\right)} \]

   8. Applied rewrites 68.2%

      \[\leadsto \frac{\left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}} \]

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

       2. lower-fma.f64 71.4

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 74.9%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, b, c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/ t i)
   (+ x (/ z y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = t / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= Double.POSITIVE_INFINITY) {
		tmp = t / i;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= math.inf:
		tmp = t / i
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(t / i);
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= Inf)
		tmp = t / i;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(t / i), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 44.1

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

   5. Applied rewrites 44.1%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. flip-+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. clear-num N/A

         \[\leadsto \frac{y \cdot \color{blue}{\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{y}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. clear-num N/A

         \[\leadsto \frac{\frac{y}{\color{blue}{\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. flip-+ N/A

         \[\leadsto \frac{\frac{y}{\frac{1}{\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 0.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   7. Applied rewrites 75.3%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 74.9%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
        t)
       (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
      INFINITY)
   (/ t i)
   (/ z y)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= ((double) INFINITY)) {
		tmp = t / i;
	} else {
		tmp = z / y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= Double.POSITIVE_INFINITY) {
		tmp = t / i;
	} else {
		tmp = z / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= math.inf:
		tmp = t / i
	else:
		tmp = z / y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i)) <= Inf)
		tmp = Float64(t / i);
	else
		tmp = Float64(z / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)) <= Inf)
		tmp = t / i;
	else
		tmp = z / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(t / i), $MachinePrecision], N[(z / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 94.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 44.1

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

   5. Applied rewrites 44.1%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      4. cube-mult N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot \left(y \cdot y\right)\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      7. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      9. +-commutative N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + i}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(b + y \cdot \left(a + y\right)\right), i\right)}} \]

      11. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right) + c}, i\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b + y \cdot \left(a + y\right), c\right)}, i\right)} \]

      13. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(a + y\right) + b}, c\right), i\right)} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, a + y, b\right)}, c\right), i\right)} \]

      15. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

      16. lower-+.f64 0.1

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

   5. Applied rewrites 0.1%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 17.8%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \leq \infty:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 13.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+143}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+122}:\\ \;\;\;\;\frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -3.3e+143) (/ z a) (if (<= a 2.2e+122) (/ z y) (/ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -3.3e+143) {
		tmp = z / a;
	} else if (a <= 2.2e+122) {
		tmp = z / y;
	} else {
		tmp = z / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-3.3d+143)) then
        tmp = z / a
    else if (a <= 2.2d+122) then
        tmp = z / y
    else
        tmp = z / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -3.3e+143) {
		tmp = z / a;
	} else if (a <= 2.2e+122) {
		tmp = z / y;
	} else {
		tmp = z / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -3.3e+143:
		tmp = z / a
	elif a <= 2.2e+122:
		tmp = z / y
	else:
		tmp = z / a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -3.3e+143)
		tmp = Float64(z / a);
	elseif (a <= 2.2e+122)
		tmp = Float64(z / y);
	else
		tmp = Float64(z / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -3.3e+143)
		tmp = z / a;
	elseif (a <= 2.2e+122)
		tmp = z / y;
	else
		tmp = z / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -3.3e+143], N[(z / a), $MachinePrecision], If[LessEqual[a, 2.2e+122], N[(z / y), $MachinePrecision], N[(z / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3e143 or 2.1999999999999999e122 < a

   1. Initial program 56.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      4. cube-mult N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot \left(y \cdot y\right)\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      7. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      9. +-commutative N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + i}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(b + y \cdot \left(a + y\right)\right), i\right)}} \]

      11. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right) + c}, i\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b + y \cdot \left(a + y\right), c\right)}, i\right)} \]

      13. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(a + y\right) + b}, c\right), i\right)} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, a + y, b\right)}, c\right), i\right)} \]

      15. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

      16. lower-+.f64 6.6

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

   5. Applied rewrites 6.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{z}{\color{blue}{a}} \]
   7. Step-by-step derivation

   8. Applied rewrites 17.4%

      \[\leadsto \frac{z}{\color{blue}{a}} \]

   if -3.3e143 < a < 2.1999999999999999e122

   1. Initial program 59.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      4. cube-mult N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot \left(y \cdot y\right)\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      7. unpow2 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      9. +-commutative N/A

         \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + i}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(b + y \cdot \left(a + y\right)\right), i\right)}} \]

      11. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right) + c}, i\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b + y \cdot \left(a + y\right), c\right)}, i\right)} \]

      13. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(a + y\right) + b}, c\right), i\right)} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, a + y, b\right)}, c\right), i\right)} \]

      15. +-commutative N/A

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

      16. lower-+.f64 10.5

          \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

   5. Applied rewrites 10.5%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 12.8%

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

Alternative 15: 7.5% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \frac{z}{a} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (/ z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return z / a;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = z / a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return z / a;
}

Python

def code(x, y, z, t, a, b, c, i):
	return z / a

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(z / a)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = z / a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(z / a), $MachinePrecision]

Derivation

1. Initial program 58.2%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
4. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{{y}^{3} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

   2. *-commutative N/A

      \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto \frac{\color{blue}{z \cdot {y}^{3}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

   4. cube-mult N/A

      \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot \left(y \cdot y\right)\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

   5. unpow2 N/A

      \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{{y}^{2}}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

   6. lower-*.f64 N/A

      \[\leadsto \frac{z \cdot \color{blue}{\left(y \cdot {y}^{2}\right)}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

   7. unpow2 N/A

      \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{z \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

   9. +-commutative N/A

      \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + i}} \]

   10. lower-fma.f64 N/A

       \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\color{blue}{\mathsf{fma}\left(y, c + y \cdot \left(b + y \cdot \left(a + y\right)\right), i\right)}} \]

   11. +-commutative N/A

       \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(b + y \cdot \left(a + y\right)\right) + c}, i\right)} \]

   12. lower-fma.f64 N/A

       \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, b + y \cdot \left(a + y\right), c\right)}, i\right)} \]

   13. +-commutative N/A

       \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(a + y\right) + b}, c\right), i\right)} \]

   14. lower-fma.f64 N/A

       \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, a + y, b\right)}, c\right), i\right)} \]

   15. +-commutative N/A

       \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

   16. lower-+.f64 9.0

       \[\leadsto \frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y + a}, b\right), c\right), i\right)} \]

5. Applied rewrites 9.0%

   \[\leadsto \color{blue}{\frac{z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]

6. Taylor expanded in a around inf

   \[\leadsto \frac{z}{\color{blue}{a}} \]
7. Step-by-step derivation

8. Applied rewrites 8.3%

   \[\leadsto \frac{z}{\color{blue}{a}} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024238 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))