Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.2% → 83.0%

Time: 18.3s

Alternatives: 16

Speedup: 2.0×

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: 56.2% 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: 83.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $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] / 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 * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision] + N[(x * N[(N[(y * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / 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 87.4%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]

   5. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{{y}^{4}}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(y \cdot \left(y \cdot z + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right)}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}} + \left(x \cdot \frac{{y}^{4}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\right) \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y \cdot \left(y \cdot z + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right) \cdot y}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \left(x \cdot \frac{{y}^{4}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\right) \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(y \cdot z + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right) \cdot \frac{y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}} + \left(x \cdot \frac{{y}^{4}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\right) \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot \left(y \cdot z + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}, \frac{y}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}, x \cdot \frac{{y}^{4}}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} + \frac{t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\right)} \]

   7. Applied egg-rr 90.6%

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

   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. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 64.7

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

   5. Simplified 64.7%

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

4. Final simplification 81.9%

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

Alternative 2: 82.9% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y (fma y (fma y (+ y a) b) c) i)))
   (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_1)
      (/ t t_1))
     (+ x (/ (- z (* x a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, fma(y, fma(y, (y + a), b), c), 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_1), (t / t_1));
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $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] / 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[(y * N[(N[(y * N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / 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 87.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

   5. Simplified 89.7%

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

   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. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 64.7

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

   5. Simplified 64.7%

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

4. Final simplification 81.3%

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

Alternative 3: 82.2% accurate, 0.5× speedup

Math

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

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 (* x a)) 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 - (x * a)) / 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 - (x * a)) / 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 - (x * a)) / 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(x + Float64(Float64(z - Float64(x * a)) / 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 - (x * a)) / 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[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / 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 87.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 64.7

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

   5. Simplified 64.7%

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

4. Final simplification 79.8%

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

Alternative 4: 82.1% accurate, 0.5× speedup

Math

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

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 (* x a)) 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 - (x * a)) / 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(x + Float64(Float64(z - Float64(x * a)) / 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[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / 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 87.4%

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

      1. div-inv N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

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

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

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

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

   4. Applied egg-rr 87.3%

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

   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. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 64.7

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

   5. Simplified 64.7%

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

4. Final simplification 79.7%

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

Alternative 5: 78.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.95e+37)
     t_1
     (if (<= y 1.8e+23)
       (/
        (fma y (fma y (fma y z 27464.7644705) 230661.510616) t)
        (fma y (fma y (fma y (+ y a) b) c) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.95e+37) {
		tmp = t_1;
	} else if (y <= 1.8e+23) {
		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 = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.95e+37)
		tmp = t_1;
	elseif (y <= 1.8e+23)
		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 = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+37], t$95$1, If[LessEqual[y, 1.8e+23], 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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9499999999999999e37 or 1.7999999999999999e23 < y

   1. Initial program 8.0%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 59.1

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

   5. Simplified 59.1%

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

   if -1.9499999999999999e37 < y < 1.7999999999999999e23

   1. Initial program 96.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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. /-lowering-/.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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. +-lowering-+.f64 92.1

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

   5. Simplified 92.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.25e+34)
     t_1
     (if (<= y 1.6e+23)
       (/
        (fma y (fma y (fma y z 27464.7644705) 230661.510616) t)
        (+ i (* y (+ c (* y b)))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.25e+34) {
		tmp = t_1;
	} else if (y <= 1.6e+23) {
		tmp = fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.25e+34)
		tmp = t_1;
	elseif (y <= 1.6e+23)
		tmp = Float64(fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+34], t$95$1, If[LessEqual[y, 1.6e+23], N[(N[(y * N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e34 or 1.6e23 < y

   1. Initial program 8.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 58.6

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

   5. Simplified 58.6%

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

   if -1.25e34 < y < 1.6e23

   1. Initial program 96.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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. /-lowering-/.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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. +-lowering-+.f64 92.1

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

   5. Simplified 92.1%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 85.3

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

   8. Simplified 85.3%

      \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\color{blue}{i + y \cdot \left(c + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{i}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -5.4e+32)
     t_1
     (if (<= y -1.5e-203)
       (/ (fma y (fma y (fma y (fma y x z) 27464.7644705) 230661.510616) t) i)
       (if (<= y 1.55e+22) (/ t (fma y (fma y (fma y (+ y a) b) c) i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -5.4e+32) {
		tmp = t_1;
	} else if (y <= -1.5e-203) {
		tmp = fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t) / i;
	} else if (y <= 1.55e+22) {
		tmp = t / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -5.4e+32)
		tmp = t_1;
	elseif (y <= -1.5e-203)
		tmp = Float64(fma(y, fma(y, fma(y, fma(y, x, z), 27464.7644705), 230661.510616), t) / i);
	elseif (y <= 1.55e+22)
		tmp = Float64(t / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+32], t$95$1, If[LessEqual[y, -1.5e-203], N[(N[(y * N[(y * N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.55e+22], N[(t / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.40000000000000025e32 or 1.5500000000000001e22 < y

   1. Initial program 8.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 58.6

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

   5. Simplified 58.6%

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

   if -5.40000000000000025e32 < y < -1.5000000000000001e-203

   1. Initial program 95.1%

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

   3. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 60.0

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

   5. Simplified 60.0%

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

   if -1.5000000000000001e-203 < y < 1.5500000000000001e22

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf

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

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

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

      2. +-commutative N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 75.4

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

   5. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{i}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{i}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -8e+18)
     t_1
     (if (<= y -6.2e-204)
       (/ (fma y (fma y (fma y z 27464.7644705) 230661.510616) t) i)
       (if (<= y 1.8e+23) (/ t (fma y (fma y (fma y (+ y a) b) c) i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -8e+18) {
		tmp = t_1;
	} else if (y <= -6.2e-204) {
		tmp = fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / i;
	} else if (y <= 1.8e+23) {
		tmp = t / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -8e+18)
		tmp = t_1;
	elseif (y <= -6.2e-204)
		tmp = Float64(fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / i);
	elseif (y <= 1.8e+23)
		tmp = Float64(t / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+18], t$95$1, If[LessEqual[y, -6.2e-204], N[(N[(y * N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[y, 1.8e+23], N[(t / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e18 or 1.7999999999999999e23 < y

   1. Initial program 9.5%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 57.2

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

   5. Simplified 57.2%

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

   if -8e18 < y < -6.1999999999999998e-204

   1. Initial program 99.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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. /-lowering-/.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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. +-lowering-+.f64 91.6

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

   5. Simplified 91.6%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 58.9%

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

   if -6.1999999999999998e-204 < y < 1.7999999999999999e23

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf

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

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

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

      2. +-commutative N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 75.4

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

   5. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{i}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+22}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.85e+34)
     t_1
     (if (<= y 9e+22)
       (/ (fma y 230661.510616 t) (fma y (fma y (fma y (+ y a) b) c) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.85e+34) {
		tmp = t_1;
	} else if (y <= 9e+22) {
		tmp = fma(y, 230661.510616, t) / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.85e+34)
		tmp = t_1;
	elseif (y <= 9e+22)
		tmp = Float64(fma(y, 230661.510616, t) / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+34], t$95$1, If[LessEqual[y, 9e+22], N[(N[(y * 230661.510616 + t), $MachinePrecision] / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000004e34 or 8.9999999999999996e22 < y

   1. Initial program 8.0%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 59.1

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

   5. Simplified 59.1%

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

   if -1.85000000000000004e34 < y < 8.9999999999999996e22

   1. Initial program 96.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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. /-lowering-/.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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. +-lowering-+.f64 92.1

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

   5. Simplified 92.1%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 82.0%

      \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{230661.510616}, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+22}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -9e+14)
     t_1
     (if (<= y 1.4e-9)
       (/ (fma y (fma y (fma y z 27464.7644705) 230661.510616) t) i)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -9e+14) {
		tmp = t_1;
	} else if (y <= 1.4e-9) {
		tmp = fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -9e+14)
		tmp = t_1;
	elseif (y <= 1.4e-9)
		tmp = Float64(fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / i);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+14], t$95$1, If[LessEqual[y, 1.4e-9], N[(N[(y * N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9e14 or 1.39999999999999992e-9 < y

   1. Initial program 15.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 52.5

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

   5. Simplified 52.5%

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

   if -9e14 < y < 1.39999999999999992e-9

   1. Initial program 99.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   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. /-lowering-/.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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. accelerator-lowering-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. +-lowering-+.f64 96.4

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

   5. Simplified 96.4%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 67.8%

      \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{\color{blue}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right), t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -470000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10600000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -470000.0)
     t_1
     (if (<= y 10600000000.0) (fma y (/ 230661.510616 i) (/ t i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -470000.0) {
		tmp = t_1;
	} else if (y <= 10600000000.0) {
		tmp = fma(y, (230661.510616 / i), (t / i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -470000.0)
		tmp = t_1;
	elseif (y <= 10600000000.0)
		tmp = fma(y, Float64(230661.510616 / i), Float64(t / i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -470000.0], t$95$1, If[LessEqual[y, 10600000000.0], N[(y * N[(230661.510616 / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e5 or 1.06e10 < y

   1. Initial program 14.6%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 54.1

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

   5. Simplified 54.1%

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

   if -4.7e5 < y < 1.06e10

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000} \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\frac{28832688827}{125000}}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \color{blue}{\frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

      9. unpow2 N/A

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

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

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

      11. /-lowering-/.f64 47.8

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

   5. Simplified 47.8%

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

   6. Taylor expanded in i around inf

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

      1. /-lowering-/.f64 62.2

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

   8. Simplified 62.2%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616}{i}}, \frac{t}{i}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -470000:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 10600000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -290000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 23500000000:\\ \;\;\;\;\mathsf{fma}\left(230661.510616, \frac{y}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -290000.0)
     t_1
     (if (<= y 23500000000.0) (fma 230661.510616 (/ y i) (/ t i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -290000.0) {
		tmp = t_1;
	} else if (y <= 23500000000.0) {
		tmp = fma(230661.510616, (y / i), (t / i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -290000.0)
		tmp = t_1;
	elseif (y <= 23500000000.0)
		tmp = fma(230661.510616, Float64(y / i), Float64(t / i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -290000.0], t$95$1, If[LessEqual[y, 23500000000.0], N[(230661.510616 * N[(y / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e5 or 2.35e10 < y

   1. Initial program 14.6%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 54.1

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

   5. Simplified 54.1%

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

   if -2.9e5 < y < 2.35e10

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000} \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\frac{28832688827}{125000}}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \color{blue}{\frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

      9. unpow2 N/A

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

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

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

      11. /-lowering-/.f64 47.8

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

   5. Simplified 47.8%

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

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{28832688827}{125000} \cdot \frac{y}{i} + \frac{t}{i}} \]
   7. Step-by-step derivation

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

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

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

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

      3. /-lowering-/.f64 62.2

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

   8. Simplified 62.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(230661.510616, \frac{y}{i}, \frac{t}{i}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -290000:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 23500000000:\\ \;\;\;\;\mathsf{fma}\left(230661.510616, \frac{y}{i}, \frac{t}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -57000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 430000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -57000.0)
     t_1
     (if (<= y 430000000000.0) (/ (fma 230661.510616 y t) i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -57000.0) {
		tmp = t_1;
	} else if (y <= 430000000000.0) {
		tmp = fma(230661.510616, y, t) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -57000.0)
		tmp = t_1;
	elseif (y <= 430000000000.0)
		tmp = Float64(fma(230661.510616, y, t) / i);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -57000.0], t$95$1, If[LessEqual[y, 430000000000.0], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -57000 or 4.3e11 < y

   1. Initial program 14.6%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. cancel-sign-sub N/A

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

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

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

      9. mul-1-neg N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 54.1

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

   5. Simplified 54.1%

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

   if -57000 < y < 4.3e11

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000} \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\frac{28832688827}{125000}}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \color{blue}{\frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

      9. unpow2 N/A

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

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

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

      11. /-lowering-/.f64 47.8

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

   5. Simplified 47.8%

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

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]
   7. Step-by-step derivation

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

         \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{i} \]

      3. accelerator-lowering-fma.f64 62.2

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

   8. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -57000:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 430000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2050000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.25e-16)
   x
   (if (<= y 2050000000.0) (/ (fma 230661.510616 y t) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.25e-16) {
		tmp = x;
	} else if (y <= 2050000000.0) {
		tmp = fma(230661.510616, y, t) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.25e-16)
		tmp = x;
	elseif (y <= 2050000000.0)
		tmp = Float64(fma(230661.510616, y, t) / i);
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.25e-16], x, If[LessEqual[y, 2050000000.0], N[(N[(230661.510616 * y + t), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2500000000000001e-16 or 2.05e9 < y

   1. Initial program 19.7%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 40.3%

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

   if -1.2500000000000001e-16 < y < 2.05e9

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right)} \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000} \cdot 1}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\frac{28832688827}{125000}}}{i} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}} - \frac{c \cdot t}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \color{blue}{\frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{t \cdot c}}{{i}^{2}}, \frac{t}{i}\right) \]

      9. unpow2 N/A

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

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

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

      11. /-lowering-/.f64 50.2

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

   5. Simplified 50.2%

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

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]
   7. Step-by-step derivation

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

         \[\leadsto \color{blue}{\frac{t + \frac{28832688827}{125000} \cdot y}{i}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000} \cdot y + t}}{i} \]

      3. accelerator-lowering-fma.f64 65.7

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

   8. Simplified 65.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{i}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 50.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.25e+39) x (if (<= y 3.2e+23) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.25e+39) {
		tmp = x;
	} else if (y <= 3.2e+23) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	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 (y <= (-1.25d+39)) then
        tmp = x
    else if (y <= 3.2d+23) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.25e+39) {
		tmp = x;
	} else if (y <= 3.2e+23) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.25e+39:
		tmp = x
	elif y <= 3.2e+23:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.25e+39)
		tmp = x;
	elseif (y <= 3.2e+23)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.25e+39)
		tmp = x;
	elseif (y <= 3.2e+23)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.25e+39], x, If[LessEqual[y, 3.2e+23], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000004e39 or 3.2e23 < y

   1. Initial program 8.1%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 46.8%

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

   if -1.25000000000000004e39 < y < 3.2e23

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 49.2

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

   5. Simplified 49.2%

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

Alternative 16: 25.7% accurate, 71.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
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;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := x

Derivation

1. Initial program 58.0%

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

3. Taylor expanded in y around inf

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

5. Simplified 22.6%

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

Reproduce

herbie shell --seed 2024198 
(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)))