Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.3% → 86.1%

Time: 20.2s

Alternatives: 21

Speedup: 0.7×

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: 56.3% 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: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)\\ t_2 := x + \frac{z - x \cdot a}{y}\\ t_3 := \frac{t}{t\_1}\\ t_4 := \mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, t\_3\right)\right)\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+51}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{t\_1}, y, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot \left(y \cdot y\right)\right)}{t\_1}, t\_3\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+154}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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))
        (t_2 (+ x (/ (- z (* x a)) y)))
        (t_3 (/ t t_1))
        (t_4
         (fma y (/ z (* y y)) (fma x (/ (* y y) (+ b (* y (+ y a)))) t_3))))
   (if (<= y -1.32e+154)
     t_2
     (if (<= y -1.28e+51)
       t_4
       (if (<= y 2.7e+59)
         (fma
          (/ (fma y (fma y z 27464.7644705) 230661.510616) t_1)
          y
          (fma x (/ (* y (* y (* y y))) t_1) t_3))
         (if (<= y 1.25e+154) t_4 t_2))))))

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 t_2 = x + ((z - (x * a)) / y);
	double t_3 = t / t_1;
	double t_4 = fma(y, (z / (y * y)), fma(x, ((y * y) / (b + (y * (y + a)))), t_3));
	double tmp;
	if (y <= -1.32e+154) {
		tmp = t_2;
	} else if (y <= -1.28e+51) {
		tmp = t_4;
	} else if (y <= 2.7e+59) {
		tmp = fma((fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_1), y, fma(x, ((y * (y * (y * y))) / t_1), t_3));
	} else if (y <= 1.25e+154) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	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)
	t_2 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	t_3 = Float64(t / t_1)
	t_4 = fma(y, Float64(z / Float64(y * y)), fma(x, Float64(Float64(y * y) / Float64(b + Float64(y * Float64(y + a)))), t_3))
	tmp = 0.0
	if (y <= -1.32e+154)
		tmp = t_2;
	elseif (y <= -1.28e+51)
		tmp = t_4;
	elseif (y <= 2.7e+59)
		tmp = fma(Float64(fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_1), y, fma(x, Float64(Float64(y * Float64(y * Float64(y * y))) / t_1), t_3));
	elseif (y <= 1.25e+154)
		tmp = t_4;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(z / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * y), $MachinePrecision] / N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.32e+154], t$95$2, If[LessEqual[y, -1.28e+51], t$95$4, If[LessEqual[y, 2.7e+59], N[(N[(N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] * y + N[(x * N[(N[(y * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+154], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.31999999999999998e154 or 1.25000000000000001e154 < y

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -1.31999999999999998e154 < y < -1.27999999999999993e51 or 2.7000000000000001e59 < y < 1.25000000000000001e154

   1. Initial program 5.0%

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

   3. Taylor expanded in 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. Applied rewrites 5.0%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 17.7

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

   8. Applied rewrites 17.7%

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

   9. Taylor expanded in c around 0

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

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-+.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. lower-+.f64 57.0

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

   11. Applied rewrites 57.0%

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

   12. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{{y}^{2}}}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(a + y\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   13. Step-by-step derivation

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 77.5

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

   14. Applied rewrites 77.5%

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

   if -1.27999999999999993e51 < y < 2.7000000000000001e59

   1. Initial program 93.1%

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

   3. Taylor expanded in 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. Applied rewrites 93.8%

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

   7. Applied rewrites 93.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, y, \mathsf{fma}\left(x, \frac{y \cdot \left(y \cdot \left(y \cdot y\right)\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{t\_1} \leq \infty:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))))
   (if (<=
        (/
         (+
          t
          (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
         t_1)
        INFINITY)
     (/
      (+
       t
       (/ y (/ 1.0 (fma y (fma y (fma x y z) 27464.7644705) 230661.510616))))
      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 = i + (y * (c + (y * (b + (y * (y + a))))));
	double tmp;
	if (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1) <= ((double) INFINITY)) {
		tmp = (t + (y / (1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / 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(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	tmp = 0.0
	if (Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / t_1) <= Inf)
		tmp = Float64(Float64(t + Float64(y / Float64(1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / 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[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(t + N[(y / N[(1.0 / N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $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 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. flip-+ N/A

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

      10. clear-num N/A

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

      11. un-div-inv N/A

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

   4. Applied rewrites 91.5%

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

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 80.3%

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

Alternative 3: 82.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ y a)))))))))
   (if (<=
        (/
         (+
          t
          (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
         t_1)
        INFINITY)
     (/
      (fma (fma y (fma y x z) 27464.7644705) (* y y) (fma y 230661.510616 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 = i + (y * (c + (y * (b + (y * (y + a))))));
	double tmp;
	if (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / t_1) <= ((double) INFINITY)) {
		tmp = fma(fma(y, fma(y, x, z), 27464.7644705), (y * y), fma(y, 230661.510616, 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 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))
	tmp = 0.0
	if (Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / t_1) <= Inf)
		tmp = Float64(fma(fma(y, fma(y, x, z), 27464.7644705), Float64(y * y), fma(y, 230661.510616, 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[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] * N[(y * y), $MachinePrecision] + N[(y * 230661.510616 + t), $MachinePrecision]), $MachinePrecision] / t$95$1), $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 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. flip-+ N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

   4. Applied rewrites 80.9%

      \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), -53204732479.65508\right) \cdot y}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), -230661.510616\right)}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Applied rewrites 91.5%

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

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

   1. Initial program 0.0%

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

   3. 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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 80.3%

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

Alternative 4: 82.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (*
    (fma (fma y (fma y x z) 27464.7644705) (* y y) (fma y 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = fma(fma(y, fma(y, x, z), 27464.7644705), (y * y), fma(y, 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(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(fma(fma(y, fma(y, x, z), 27464.7644705), Float64(y * y), fma(y, 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[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(y * N[(y * x + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] * N[(y * y), $MachinePrecision] + N[(y * 230661.510616 + t), $MachinePrecision]), $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 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. flip-+ N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

   4. Applied rewrites 80.9%

      \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), -53204732479.65508\right) \cdot y}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), -230661.510616\right)}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Applied rewrites 91.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. distribute-rgt-in N/A

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

      6. *-commutative N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. lift-*.f64 N/A

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

      11. lift-fma.f64 N/A

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

      12. lower-fma.f64 91.3

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

   8. Applied rewrites 91.3%

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

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 80.2%

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

Alternative 5: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)\\ t_2 := b + y \cdot \left(y + a\right)\\ t_3 := \mathsf{fma}\left(x, \frac{y \cdot y}{t\_2}, \frac{t}{t\_1}\right)\\ t_4 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, t\_3\right)\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{i + y \cdot \left(c + y \cdot t\_2\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{t\_1}, t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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))
        (t_2 (+ b (* y (+ y a))))
        (t_3 (fma x (/ (* y y) t_2) (/ t t_1)))
        (t_4 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.32e+154)
     t_4
     (if (<= y -4.2e+27)
       (fma y (/ z (* y y)) t_3)
       (if (<= y 140000000.0)
         (/
          (+
           t
           (/
            y
            (/ 1.0 (fma y (fma y (fma x y z) 27464.7644705) 230661.510616))))
          (+ i (* y (+ c (* y t_2)))))
         (if (<= y 5e+138)
           (fma y (/ (fma y (fma y z 27464.7644705) 230661.510616) t_1) t_3)
           t_4))))))

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 t_2 = b + (y * (y + a));
	double t_3 = fma(x, ((y * y) / t_2), (t / t_1));
	double t_4 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.32e+154) {
		tmp = t_4;
	} else if (y <= -4.2e+27) {
		tmp = fma(y, (z / (y * y)), t_3);
	} else if (y <= 140000000.0) {
		tmp = (t + (y / (1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / (i + (y * (c + (y * t_2))));
	} else if (y <= 5e+138) {
		tmp = fma(y, (fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_1), t_3);
	} else {
		tmp = t_4;
	}
	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)
	t_2 = Float64(b + Float64(y * Float64(y + a)))
	t_3 = fma(x, Float64(Float64(y * y) / t_2), Float64(t / t_1))
	t_4 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.32e+154)
		tmp = t_4;
	elseif (y <= -4.2e+27)
		tmp = fma(y, Float64(z / Float64(y * y)), t_3);
	elseif (y <= 140000000.0)
		tmp = Float64(Float64(t + Float64(y / Float64(1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / Float64(i + Float64(y * Float64(c + Float64(y * t_2)))));
	elseif (y <= 5e+138)
		tmp = fma(y, Float64(fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_1), t_3);
	else
		tmp = t_4;
	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]}, Block[{t$95$2 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.32e+154], t$95$4, If[LessEqual[y, -4.2e+27], N[(y * N[(z / N[(y * y), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[y, 140000000.0], N[(N[(t + N[(y / N[(1.0 / N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+138], N[(y * N[(N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.31999999999999998e154 or 5.00000000000000016e138 < y

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -1.31999999999999998e154 < y < -4.19999999999999989e27

   1. Initial program 0.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   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. Applied rewrites 4.0%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 4.4

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

   8. Applied rewrites 4.4%

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

   9. Taylor expanded in c around 0

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

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-+.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. lower-+.f64 42.2

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

   11. Applied rewrites 42.2%

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

   12. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{{y}^{2}}}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(a + y\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   13. Step-by-step derivation

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 63.1

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

   14. Applied rewrites 63.1%

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

   if -4.19999999999999989e27 < y < 1.4e8

   1. Initial program 98.2%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. flip-+ N/A

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

      10. clear-num N/A

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

      11. un-div-inv N/A

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

   4. Applied rewrites 98.2%

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

   if 1.4e8 < y < 5.00000000000000016e138

   1. Initial program 36.7%

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

   3. Taylor expanded in 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. Applied rewrites 40.6%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 54.5

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

   8. Applied rewrites 54.5%

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

   9. Taylor expanded in c around 0

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

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-+.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. lower-+.f64 78.0

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

   11. Applied rewrites 78.0%

       \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{y \cdot y}{b + y \cdot \left(a + y\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, y + a, b\right)\\ t_2 := \mathsf{fma}\left(y, \mathsf{fma}\left(y, t\_1, c\right), i\right)\\ t_3 := b + y \cdot \left(y + a\right)\\ t_4 := x + \frac{z - x \cdot a}{y}\\ t_5 := \frac{t}{t\_2}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{t\_3}, t\_5\right)\right)\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{i + y \cdot \left(c + y \cdot t\_3\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{t\_2}, y, \mathsf{fma}\left(y, x \cdot \frac{y}{t\_1}, t\_5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y (+ y a) b))
        (t_2 (fma y (fma y t_1 c) i))
        (t_3 (+ b (* y (+ y a))))
        (t_4 (+ x (/ (- z (* x a)) y)))
        (t_5 (/ t t_2)))
   (if (<= y -1.32e+154)
     t_4
     (if (<= y -4.2e+27)
       (fma y (/ z (* y y)) (fma x (/ (* y y) t_3) t_5))
       (if (<= y 140000000.0)
         (/
          (+
           t
           (/
            y
            (/ 1.0 (fma y (fma y (fma x y z) 27464.7644705) 230661.510616))))
          (+ i (* y (+ c (* y t_3)))))
         (if (<= y 5e+138)
           (fma
            (/ (fma y (fma y z 27464.7644705) 230661.510616) t_2)
            y
            (fma y (* x (/ y t_1)) t_5))
           t_4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, (y + a), b);
	double t_2 = fma(y, fma(y, t_1, c), i);
	double t_3 = b + (y * (y + a));
	double t_4 = x + ((z - (x * a)) / y);
	double t_5 = t / t_2;
	double tmp;
	if (y <= -1.32e+154) {
		tmp = t_4;
	} else if (y <= -4.2e+27) {
		tmp = fma(y, (z / (y * y)), fma(x, ((y * y) / t_3), t_5));
	} else if (y <= 140000000.0) {
		tmp = (t + (y / (1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / (i + (y * (c + (y * t_3))));
	} else if (y <= 5e+138) {
		tmp = fma((fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_2), y, fma(y, (x * (y / t_1)), t_5));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, Float64(y + a), b)
	t_2 = fma(y, fma(y, t_1, c), i)
	t_3 = Float64(b + Float64(y * Float64(y + a)))
	t_4 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	t_5 = Float64(t / t_2)
	tmp = 0.0
	if (y <= -1.32e+154)
		tmp = t_4;
	elseif (y <= -4.2e+27)
		tmp = fma(y, Float64(z / Float64(y * y)), fma(x, Float64(Float64(y * y) / t_3), t_5));
	elseif (y <= 140000000.0)
		tmp = Float64(Float64(t + Float64(y / Float64(1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / Float64(i + Float64(y * Float64(c + Float64(y * t_3)))));
	elseif (y <= 5e+138)
		tmp = fma(Float64(fma(y, fma(y, z, 27464.7644705), 230661.510616) / t_2), y, fma(y, Float64(x * Float64(y / t_1)), t_5));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y * t$95$1 + c), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$3 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t / t$95$2), $MachinePrecision]}, If[LessEqual[y, -1.32e+154], t$95$4, If[LessEqual[y, -4.2e+27], N[(y * N[(z / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * y), $MachinePrecision] / t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 140000000.0], N[(N[(t + N[(y / N[(1.0 / N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+138], N[(N[(N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] / t$95$2), $MachinePrecision] * y + N[(y * N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.31999999999999998e154 or 5.00000000000000016e138 < y

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -1.31999999999999998e154 < y < -4.19999999999999989e27

   1. Initial program 0.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{x \cdot {y}^{4}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)} \]
   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. Applied rewrites 4.0%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 4.4

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

   8. Applied rewrites 4.4%

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

   9. Taylor expanded in c around 0

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

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-+.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. lower-+.f64 42.2

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

   11. Applied rewrites 42.2%

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

   12. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{{y}^{2}}}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(a + y\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   13. Step-by-step derivation

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 63.1

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

   14. Applied rewrites 63.1%

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

   if -4.19999999999999989e27 < y < 1.4e8

   1. Initial program 98.2%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. flip-+ N/A

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

      10. clear-num N/A

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

      11. un-div-inv N/A

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

   4. Applied rewrites 98.2%

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

   if 1.4e8 < y < 5.00000000000000016e138

   1. Initial program 36.7%

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

   3. Taylor expanded in 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. Applied rewrites 40.6%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 54.5

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

   8. Applied rewrites 54.5%

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

   9. Taylor expanded in c around 0

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

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-+.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. lower-+.f64 78.0

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

   11. Applied rewrites 78.0%

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

   13. Applied rewrites 77.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, y, \mathsf{fma}\left(y, \frac{y}{\mathsf{fma}\left(y, y + a, b\right)} \cdot x, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, 27464.7644705\right), 230661.510616\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, y, \mathsf{fma}\left(y, x \cdot \frac{y}{\mathsf{fma}\left(y, y + a, b\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (*
    (/ 1.0 (fma y (fma y (fma y (+ y a) b) c) i))
    (fma y (fma y (fma y (fma x y z) 27464.7644705) 230661.510616) t))
   (+ 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = (1.0 / fma(y, fma(y, fma(y, (y + a), b), c), i)) * fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t);
	} 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(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(Float64(1.0 / fma(y, fma(y, fma(y, Float64(y + a), b), c), i)) * fma(y, fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616), t));
	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[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(1.0 / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision] * N[(y * N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $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 91.4%

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

   4. Applied rewrites 91.2%

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

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 80.2%

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

Alternative 8: 78.9% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (/
    (fma y (fma y (fma y z 27464.7644705) 230661.510616) t)
    (fma y (fma y (fma y (+ y a) b) c) i))
   (+ x (/ (- z (* 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, (y + a), b), c), i);
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(fma(y, fma(y, fma(y, z, 27464.7644705), 230661.510616), t) / fma(y, fma(y, fma(y, Float64(y + a), b), c), i));
	else
		tmp = Float64(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[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * N[(y * N[(y * z + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision] + t), $MachinePrecision] / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(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 91.4%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 85.3

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

   5. Applied rewrites 85.3%

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

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

   1. Initial program 0.0%

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

   3. 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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 76.7%

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

Alternative 9: 74.1% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (*
    (/ 1.0 (fma y (fma y (fma y (+ y a) b) c) i))
    (fma y (fma y 27464.7644705 230661.510616) t))
   (+ 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = (1.0 / fma(y, fma(y, fma(y, (y + a), b), c), i)) * fma(y, fma(y, 27464.7644705, 230661.510616), t);
	} 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(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(Float64(1.0 / fma(y, fma(y, fma(y, Float64(y + a), b), c), i)) * fma(y, fma(y, 27464.7644705, 230661.510616), t));
	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[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(1.0 / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision] * N[(y * N[(y * 27464.7644705 + 230661.510616), $MachinePrecision] + t), $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 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. flip-+ N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

   4. Applied rewrites 80.9%

      \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), y \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), -53204732479.65508\right) \cdot y}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), -230661.510616\right)}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Applied rewrites 91.2%

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

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 76.9%

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

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 71.7%

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

Alternative 10: 73.0% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (/ (fma y 230661.510616 t) (fma (fma y (fma y (+ y a) b) c) y 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = fma(y, 230661.510616, t) / fma(fma(y, fma(y, (y + a), b), c), y, 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(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(fma(y, 230661.510616, t) / fma(fma(y, fma(y, Float64(y + a), b), c), y, 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[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * 230661.510616 + t), $MachinePrecision] / N[(N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] * y + i), $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 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 76.3

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

   5. Applied rewrites 76.3%

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

      1. lift-+.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-+.f64 N/A

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

      13. lower-fma.f64 76.3

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

   7. Applied rewrites 76.3%

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

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 71.4%

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

Alternative 11: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := \mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{t\_1}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ t_3 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{i + y \cdot \left(c + y \cdot t\_1\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2
         (fma
          y
          (/ z (* y y))
          (fma x (/ (* y y) t_1) (/ t (fma y (fma y (fma y (+ y a) b) c) i)))))
        (t_3 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.32e+154)
     t_3
     (if (<= y -4.2e+27)
       t_2
       (if (<= y 3e+62)
         (/
          (+
           t
           (/
            y
            (/ 1.0 (fma y (fma y (fma x y z) 27464.7644705) 230661.510616))))
          (+ i (* y (+ c (* y t_1)))))
         (if (<= y 1.25e+154) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = fma(y, (z / (y * y)), fma(x, ((y * y) / t_1), (t / fma(y, fma(y, fma(y, (y + a), b), c), i))));
	double t_3 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.32e+154) {
		tmp = t_3;
	} else if (y <= -4.2e+27) {
		tmp = t_2;
	} else if (y <= 3e+62) {
		tmp = (t + (y / (1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / (i + (y * (c + (y * t_1))));
	} else if (y <= 1.25e+154) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = fma(y, Float64(z / Float64(y * y)), fma(x, Float64(Float64(y * y) / t_1), Float64(t / fma(y, fma(y, fma(y, Float64(y + a), b), c), i))))
	t_3 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.32e+154)
		tmp = t_3;
	elseif (y <= -4.2e+27)
		tmp = t_2;
	elseif (y <= 3e+62)
		tmp = Float64(Float64(t + Float64(y / Float64(1.0 / fma(y, fma(y, fma(x, y, z), 27464.7644705), 230661.510616)))) / Float64(i + Float64(y * Float64(c + Float64(y * t_1)))));
	elseif (y <= 1.25e+154)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / N[(y * N[(y * N[(y * N[(y + a), $MachinePrecision] + b), $MachinePrecision] + c), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.32e+154], t$95$3, If[LessEqual[y, -4.2e+27], t$95$2, If[LessEqual[y, 3e+62], N[(N[(t + N[(y / N[(1.0 / N[(y * N[(y * N[(x * y + z), $MachinePrecision] + 27464.7644705), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+154], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.31999999999999998e154 or 1.25000000000000001e154 < y

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -1.31999999999999998e154 < y < -4.19999999999999989e27 or 3e62 < y < 1.25000000000000001e154

   1. Initial program 2.8%

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

   3. Taylor expanded in 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. Applied rewrites 5.0%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}, \mathsf{fma}\left(x, \color{blue}{\frac{{y}^{3}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-+.f64 14.9

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

   8. Applied rewrites 14.9%

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

   9. Taylor expanded in c around 0

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

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-+.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. lower-+.f64 54.6

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

   11. Applied rewrites 54.6%

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

   12. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{{y}^{2}}}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(a + y\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right) \]
   13. Step-by-step derivation

       1. lower-/.f64 N/A

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

       2. unpow2 N/A

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

       3. lower-*.f64 72.1

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

   14. Applied rewrites 72.1%

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

   if -4.19999999999999989e27 < y < 3e62

   1. Initial program 95.0%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. flip-+ N/A

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

      10. clear-num N/A

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

      11. un-div-inv N/A

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

   4. Applied rewrites 95.0%

      \[\leadsto \frac{\color{blue}{\frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+62}:\\ \;\;\;\;\frac{t + \frac{y}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(x, y, z\right), 27464.7644705\right), 230661.510616\right)}}}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{y \cdot y}, \mathsf{fma}\left(x, \frac{y \cdot y}{b + y \cdot \left(y + a\right)}, \frac{t}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), i\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (/ (fma y 230661.510616 t) (fma (fma y b c) y 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = fma(y, 230661.510616, t) / fma(fma(y, b, c), y, 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(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(fma(y, 230661.510616, t) / fma(fma(y, b, c), y, 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[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * 230661.510616 + t), $MachinePrecision] / N[(N[(y * b + c), $MachinePrecision] * y + i), $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 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 72.7

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

   8. Applied rewrites 72.7%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lower-fma.f64 72.7

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 72.7

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

   10. Applied rewrites 72.7%

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

   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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 69.3%

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

Alternative 13: 66.5% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (/ (fma y 230661.510616 t) (+ i (* y c)))
   (+ 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = fma(y, 230661.510616, t) / (i + (y * c));
	} 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(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(fma(y, 230661.510616, t) / Float64(i + Float64(y * c)));
	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[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * 230661.510616 + t), $MachinePrecision] / N[(i + N[(y * c), $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 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 67.4

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

   8. Applied rewrites 67.4%

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

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

   1. Initial program 0.0%

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

   3. 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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 66.1%

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

Alternative 14: 56.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        t
        (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
       (+ i (* y (+ c (* y (+ b (* y (+ y a))))))))
      INFINITY)
   (/ (+ t (* y 230661.510616)) 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 (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= ((double) INFINITY)) {
		tmp = (t + (y * 230661.510616)) / i;
	} 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 tmp;
	if (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= Double.POSITIVE_INFINITY) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= math.inf:
		tmp = (t + (y * 230661.510616)) / 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(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))))) <= Inf)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	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)
	tmp = 0.0;
	if (((t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * (b + (y * (y + a)))))))) <= Inf)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x + ((z - (x * a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $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 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 44.9

         \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{i} \]

   8. Applied rewrites 44.9%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

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

   1. Initial program 0.0%

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

   3. 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. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-+.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. lower-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. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 52.9%

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

Alternative 15: 35.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(y * N[(x / a), $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 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 44.9

         \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{i} \]

   8. Applied rewrites 44.9%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

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

   1. Initial program 0.0%

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

   3. 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. Applied rewrites 0.1%

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

   6. Taylor expanded in a around inf

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

      1. lower-/.f64 10.6

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

   8. Applied rewrites 10.6%

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

   9. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)\right)} \]

       2. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)}\right) \]

       4. associate-+r+ N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \color{blue}{\left(\left(-1 \cdot \frac{x}{a} + -1 \cdot \frac{z}{{y}^{2}}\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right) \]

       5. distribute-lft-out N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \left(\color{blue}{-1 \cdot \left(\frac{x}{a} + \frac{z}{{y}^{2}}\right)} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       6. lower-fma.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{{y}^{2}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right) \]

       7. lower-+.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \color{blue}{\frac{x}{a} + \frac{z}{{y}^{2}}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       8. lower-/.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \color{blue}{\frac{x}{a}} + \frac{z}{{y}^{2}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       9. lower-/.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \color{blue}{\frac{z}{{y}^{2}}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{\color{blue}{y \cdot y}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       11. lower-*.f64 N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{\color{blue}{y \cdot y}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       12. mul-1-neg N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{y \cdot y}, \color{blue}{\mathsf{neg}\left(\frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right)\right) \]

       13. lower-neg.f64 N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{y \cdot y}, \color{blue}{\mathsf{neg}\left(\frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right)\right) \]

   11. Applied rewrites 15.2%

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

   12. Taylor expanded in x around inf

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 N/A

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

       3. lower-/.f64 19.3

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

   14. Applied rewrites 19.3%

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

4. Final simplification 34.4%

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

Alternative 16: 34.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / a), $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 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 44.9

         \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{i} \]

   8. Applied rewrites 44.9%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) + t}}{a \cdot {y}^{3}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right), t\right)}}{a \cdot {y}^{3}} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right) + \frac{28832688827}{125000}}, t\right)}{a \cdot {y}^{3}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right), \frac{28832688827}{125000}\right)}, t\right)}{a \cdot {y}^{3}} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(z + x \cdot y\right) + \frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, z + x \cdot y, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      13. cube-mult N/A

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

      14. unpow2 N/A

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

      15. lower-*.f64 N/A

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

      16. unpow2 N/A

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

      17. lower-*.f64 0.3

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

   5. Applied rewrites 0.3%

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

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]

      2. lower-*.f64 10.1

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \]

   8. Applied rewrites 10.1%

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

4. Final simplification 30.6%

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

Alternative 17: 31.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t / i), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / a), $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 91.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 40.4

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

   5. Applied rewrites 40.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) + t}}{a \cdot {y}^{3}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right), t\right)}}{a \cdot {y}^{3}} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right) + \frac{28832688827}{125000}}, t\right)}{a \cdot {y}^{3}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right), \frac{28832688827}{125000}\right)}, t\right)}{a \cdot {y}^{3}} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(z + x \cdot y\right) + \frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, z + x \cdot y, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      13. cube-mult N/A

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

      14. unpow2 N/A

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

      15. lower-*.f64 N/A

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

      16. unpow2 N/A

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

      17. lower-*.f64 0.3

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

   5. Applied rewrites 0.3%

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

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]

      2. lower-*.f64 10.1

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \]

   8. Applied rewrites 10.1%

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

4. Final simplification 28.0%

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

Alternative 18: 50.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 0.065:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- x (/ (* x a) y))))
   (if (<= y -4.4e+109)
     t_1
     (if (<= y -4e-64)
       (* y (/ x a))
       (if (<= y 0.065) (/ (+ t (* y 230661.510616)) 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 - ((x * a) / y);
	double tmp;
	if (y <= -4.4e+109) {
		tmp = t_1;
	} else if (y <= -4e-64) {
		tmp = y * (x / a);
	} else if (y <= 0.065) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x - ((x * a) / y)
    if (y <= (-4.4d+109)) then
        tmp = t_1
    else if (y <= (-4d-64)) then
        tmp = y * (x / a)
    else if (y <= 0.065d0) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x - ((x * a) / y);
	double tmp;
	if (y <= -4.4e+109) {
		tmp = t_1;
	} else if (y <= -4e-64) {
		tmp = y * (x / a);
	} else if (y <= 0.065) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x - ((x * a) / y)
	tmp = 0
	if y <= -4.4e+109:
		tmp = t_1
	elif y <= -4e-64:
		tmp = y * (x / a)
	elif y <= 0.065:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -4.4e+109)
		tmp = t_1;
	elseif (y <= -4e-64)
		tmp = Float64(y * Float64(x / a));
	elseif (y <= 0.065)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x - ((x * a) / y);
	tmp = 0.0;
	if (y <= -4.4e+109)
		tmp = t_1;
	elseif (y <= -4e-64)
		tmp = y * (x / a);
	elseif (y <= 0.065)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+109], t$95$1, If[LessEqual[y, -4e-64], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.065], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999998e109 or 0.065000000000000002 < y

   1. Initial program 10.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \frac{\left(\color{blue}{x \cdot {y}^{3}} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{x \cdot {y}^{3}} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. cube-mult N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 4.3

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

   5. Applied rewrites 4.3%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-+.f64 N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 53.1

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

   8. Applied rewrites 53.1%

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

   if -4.3999999999999998e109 < y < -3.99999999999999986e-64

   1. Initial program 45.7%

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

   3. Taylor expanded in 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. Applied rewrites 45.8%

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

   6. Taylor expanded in a around inf

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

      1. lower-/.f64 23.9

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

   8. Applied rewrites 23.9%

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

   9. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)\right)} \]

       2. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{y \cdot \left(-1 \cdot \frac{x}{a} + \left(-1 \cdot \frac{z}{{y}^{2}} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right)}\right) \]

       4. associate-+r+ N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \color{blue}{\left(\left(-1 \cdot \frac{x}{a} + -1 \cdot \frac{z}{{y}^{2}}\right) + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right) \]

       5. distribute-lft-out N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \left(\color{blue}{-1 \cdot \left(\frac{x}{a} + \frac{z}{{y}^{2}}\right)} + -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       6. lower-fma.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{{y}^{2}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right) \]

       7. lower-+.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \color{blue}{\frac{x}{a} + \frac{z}{{y}^{2}}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       8. lower-/.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \color{blue}{\frac{x}{a}} + \frac{z}{{y}^{2}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       9. lower-/.f64 N/A

          \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \color{blue}{\frac{z}{{y}^{2}}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{\color{blue}{y \cdot y}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       11. lower-*.f64 N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{\color{blue}{y \cdot y}}, -1 \cdot \frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)\right) \]

       12. mul-1-neg N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{y \cdot y}, \color{blue}{\mathsf{neg}\left(\frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right)\right) \]

       13. lower-neg.f64 N/A

           \[\leadsto \mathsf{neg}\left(y \cdot \mathsf{fma}\left(-1, \frac{x}{a} + \frac{z}{y \cdot y}, \color{blue}{\mathsf{neg}\left(\frac{\frac{54929528941}{2000000} + -1 \cdot \left(a \cdot z\right)}{{y}^{3}}\right)}\right)\right) \]

   11. Applied rewrites 14.8%

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

   12. Taylor expanded in x around inf

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 N/A

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

       3. lower-/.f64 20.0

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

   14. Applied rewrites 20.0%

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

   if -3.99999999999999986e-64 < y < 0.065000000000000002

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 95.6

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in i around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 61.4

         \[\leadsto \frac{t + \color{blue}{230661.510616 \cdot y}}{i} \]

   8. Applied rewrites 61.4%

      \[\leadsto \color{blue}{\frac{t + 230661.510616 \cdot y}{i}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 0.065:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.7e-29) (/ t i) (* z (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.7e-29) {
		tmp = t / i;
	} else {
		tmp = z * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1.7d-29) then
        tmp = t / i
    else
        tmp = z * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.7e-29) {
		tmp = t / i;
	} else {
		tmp = z * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.7e-29:
		tmp = t / i
	else:
		tmp = z * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.7e-29)
		tmp = Float64(t / i);
	else
		tmp = Float64(z * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.7e-29)
		tmp = t / i;
	else
		tmp = z * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.7e-29], N[(t / i), $MachinePrecision], N[(z * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.69999999999999986e-29

   1. Initial program 66.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 33.1

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

   5. Applied rewrites 33.1%

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

   if 1.69999999999999986e-29 < y

   1. Initial program 21.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) + t}}{a \cdot {y}^{3}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right), t\right)}}{a \cdot {y}^{3}} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right) + \frac{28832688827}{125000}}, t\right)}{a \cdot {y}^{3}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right), \frac{28832688827}{125000}\right)}, t\right)}{a \cdot {y}^{3}} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(z + x \cdot y\right) + \frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, z + x \cdot y, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      13. cube-mult N/A

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

      14. unpow2 N/A

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

      15. lower-*.f64 N/A

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

      16. unpow2 N/A

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

      17. lower-*.f64 7.4

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

   5. Applied rewrites 7.4%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 12.3

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

   8. Applied rewrites 12.3%

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

      1. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{z}}} \]

      2. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{a} \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{a} \cdot z} \]

      4. lower-/.f64 12.3

         \[\leadsto \color{blue}{\frac{1}{a}} \cdot z \]

   10. Applied rewrites 12.3%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.5% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.7e-29) (/ t i) (/ z a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.7e-29) {
		tmp = t / i;
	} else {
		tmp = z / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1.7d-29) then
        tmp = t / i
    else
        tmp = z / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.7e-29) {
		tmp = t / i;
	} else {
		tmp = z / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.7e-29:
		tmp = t / i
	else:
		tmp = z / a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.7e-29)
		tmp = Float64(t / i);
	else
		tmp = Float64(z / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.7e-29)
		tmp = t / i;
	else
		tmp = z / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.7e-29], N[(t / i), $MachinePrecision], N[(z / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.69999999999999986e-29

   1. Initial program 66.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 33.1

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

   5. Applied rewrites 33.1%

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

   if 1.69999999999999986e-29 < y

   1. Initial program 21.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{a \cdot {y}^{3}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) + t}}{a \cdot {y}^{3}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right), t\right)}}{a \cdot {y}^{3}} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right) + \frac{28832688827}{125000}}, t\right)}{a \cdot {y}^{3}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right), \frac{28832688827}{125000}\right)}, t\right)}{a \cdot {y}^{3}} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(z + x \cdot y\right) + \frac{54929528941}{2000000}}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, z + x \cdot y, \frac{54929528941}{2000000}\right)}, \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{x \cdot y + z}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot x} + z, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, x, z\right)}, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{a \cdot {y}^{3}} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), t\right)}{\color{blue}{{y}^{3} \cdot a}} \]

      13. cube-mult N/A

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

      14. unpow2 N/A

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

      15. lower-*.f64 N/A

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

      16. unpow2 N/A

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

      17. lower-*.f64 7.4

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

   5. Applied rewrites 7.4%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 12.3

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

   8. Applied rewrites 12.3%

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

Alternative 21: 28.2% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \frac{t}{i} \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.9%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 25.2

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

5. Applied rewrites 25.2%

   \[\leadsto \color{blue}{\frac{t}{i}} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024212 
(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)))