Average Error: 0.1 → 0.1
Time: 8.1s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \left(\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot \left(y + 0.5\right)\right)\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \left(\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot \left(y + 0.5\right)\right)\right) + y\right) - z
double code(double x, double y, double z) {
	return (((x - ((y + 0.5) * log(y))) + y) - z);
}
↓
double code(double x, double y, double z) {
	return (((x - (((y + 0.5) * (2.0 * log(cbrt(y)))) + (log(pow((1.0 / y), -0.3333333333333333)) * (y + 0.5)))) + y) - z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)}\right) + y\right) - z\]

  4. Applied log-prod0.2

    \[\leadsto \left(\left(x - \left(y + 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)}\right) + y\right) - z\]

  5. Applied distribute-lft-in0.2

    \[\leadsto \left(\left(x - \color{blue}{\left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right)}\right) + y\right) - z\]

  6. Simplified0.2

    \[\leadsto \left(\left(x - \left(\color{blue}{\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right)\right) + y\right) - z\]

  7. Simplified0.2

    \[\leadsto \left(\left(x - \left(\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \color{blue}{\log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)}\right)\right) + y\right) - z\]

  8. Taylor expanded around inf 0.1

    \[\leadsto \left(\left(x - \left(\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \color{blue}{\left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)} \cdot \left(y + 0.5\right)\right)\right) + y\right) - z\]

  9. Final simplification0.1

    \[\leadsto \left(\left(x - \left(\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot \left(y + 0.5\right)\right)\right) + y\right) - z\]

Reproduce

herbie shell --seed 2020053 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))