Average Error: 0.1 → 0.1
Time: 4.1s
Precision: binary64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left({y}^{0.3333333333333333}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot 2\right) + x \cdot \log \left({y}^{0.3333333333333333}\right)\right) - y\right) - z\right) + \log t
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
↓
(FPCore (x y z t)
 :precision binary64
 (+
  (-
   (-
    (+ (* x (* (log (cbrt y)) 2.0)) (* x (log (pow y 0.3333333333333333))))
    y)
   z)
  (log t)))
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (x * ((double) log(y)))) - y)) - z)) + ((double) log(t))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (((double) (x * ((double) (((double) log(((double) cbrt(y)))) * 2.0)))) + ((double) (x * ((double) log(((double) pow(y, 0.3333333333333333)))))))) - y)) - z)) + ((double) log(t))));
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020198 
(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)))