Average Error: 0.1 → 0.2
Time: 9.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\mathsf{fma}\left(i, y, \sqrt[3]{{\left(\log c\right)}^{2}} \cdot \left(\sqrt[3]{\log c} \cdot \left(b - 0.5\right)\right) + \left(\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)\]
\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, \sqrt[3]{{\left(\log c\right)}^{2}} \cdot \left(\sqrt[3]{\log c} \cdot \left(b - 0.5\right)\right) + \left(\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\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, ((cbrt(pow(log(c), 2.0)) * (cbrt(log(c)) * (b - 0.5))) + (fma(x, log(y), z) + (t + 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

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

  6. Applied add-cube-cbrt0.3

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

  7. Applied associate-*l*0.3

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

  9. Applied cbrt-unprod0.2

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

  10. Simplified0.2

    \[\leadsto \mathsf{fma}\left(i, y, \sqrt[3]{\color{blue}{{\left(\log c\right)}^{2}}} \cdot \left(\sqrt[3]{\log c} \cdot \left(b - 0.5\right)\right) + \left(\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)\]

  11. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(i, y, \sqrt[3]{{\left(\log c\right)}^{2}} \cdot \left(\sqrt[3]{\log c} \cdot \left(b - 0.5\right)\right) + \left(\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right)\right)\]

Reproduce

herbie shell --seed 2020091 +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)))