Average Error: 0.1 → 0.1
Time: 9.8s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \mathsf{fma}\left(\log \left({y}^{\frac{1}{3}}\right), x, t + \left(z + a\right)\right)\right)\right)\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \mathsf{fma}\left(\log \left({y}^{\frac{1}{3}}\right), x, t + \left(z + a\right)\right)\right)\right)
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return fma(i, y, fma(log(c), (b - 0.5), ((log((cbrt(y) * cbrt(y))) * x) + fma(log(pow(y, 0.3333333333333333)), x, (t + (z + a))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{\left(x \cdot \log y + z\right)} + \left(t + a\right)\right)\right)\]

  5. Applied associate-+l+0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{x \cdot \log y + \left(z + \left(t + a\right)\right)}\right)\right)\]

  6. Simplified0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y + \color{blue}{\left(t + \left(z + a\right)\right)}\right)\right)\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + \left(t + \left(z + a\right)\right)\right)\right)\]

  9. Applied log-prod0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} + \left(t + \left(z + a\right)\right)\right)\right)\]

  10. Applied distribute-rgt-in0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)} + \left(t + \left(z + a\right)\right)\right)\right)\]

  11. Applied associate-+l+0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x + \left(t + \left(z + a\right)\right)\right)}\right)\right)\]

  12. Simplified0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \color{blue}{\mathsf{fma}\left(\log \left(\sqrt[3]{y}\right), x, t + \left(z + a\right)\right)}\right)\right)\]
  13. Using strategy rm

  14. Applied pow1/30.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \mathsf{fma}\left(\log \color{blue}{\left({y}^{\frac{1}{3}}\right)}, x, t + \left(z + a\right)\right)\right)\right)\]

  15. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \mathsf{fma}\left(\log \left({y}^{\frac{1}{3}}\right), x, t + \left(z + a\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))