Average Error: 0.1 → 0.1
Time: 14.4s
Precision: binary64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + 0.3333333333333333 \cdot \left(x \cdot \log y\right)\right) - y\right) + \left(\log t - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + 0.3333333333333333 \cdot \left(x \cdot \log y\right)\right) - y\right) + \left(\log t - z\right)
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
↓
(FPCore (x y z t)
 :precision binary64
 (+
  (- (+ (* x (* 2.0 (log (cbrt y)))) (* 0.3333333333333333 (* x (log y)))) y)
  (- (log t) z)))
double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(t);
}
↓
double code(double x, double y, double z, double t) {
	return (((x * (2.0 * log(cbrt(y)))) + (0.3333333333333333 * (x * log(y)))) - y) + (log(t) - z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(x \cdot \log y - y\right) - \left(z - \log t\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt_binary64_31820.1

    \[\leadsto \left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - y\right) - \left(z - \log t\right)\]

  5. Applied log-prod_binary64_32330.1

    \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - y\right) - \left(z - \log t\right)\]

  6. Applied distribute-rgt-in_binary64_30970.1

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)} - y\right) - \left(z - \log t\right)\]

  7. Simplified0.1

    \[\leadsto \left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + \log \left(\sqrt[3]{y}\right) \cdot x\right) - y\right) - \left(z - \log t\right)\]
  8. Using strategy rm

  9. Applied pow1/3_binary64_32290.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \color{blue}{\left({y}^{0.3333333333333333}\right)} \cdot x\right) - y\right) - \left(z - \log t\right)\]

  10. Applied log-pow_binary64_32360.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \color{blue}{\left(0.3333333333333333 \cdot \log y\right)} \cdot x\right) - y\right) - \left(z - \log t\right)\]

  11. Applied associate-*l*_binary64_30880.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \color{blue}{0.3333333333333333 \cdot \left(\log y \cdot x\right)}\right) - y\right) - \left(z - \log t\right)\]

  12. Final simplification0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + 0.3333333333333333 \cdot \left(x \cdot \log y\right)\right) - y\right) + \left(\log t - z\right)\]

Reproduce

herbie shell --seed 2021176 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))