Average Error: 0.1 → 0.1
Time: 9.9s
Precision: binary64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(y + \left(x - \left(y \cdot \log y + \log \left(\sqrt{y}\right)\right)\right)\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(y + \left(x - \left(y \cdot \log y + \log \left(\sqrt{y}\right)\right)\right)\right) - z
(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))
↓
(FPCore (x y z)
 :precision binary64
 (- (+ y (- x (+ (* y (log y)) (log (sqrt y))))) 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 (y + (x - ((y * log(y)) + log(sqrt(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-cbrt_binary64_106840.1

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

  4. Applied log-prod_binary64_107350.2

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

  5. Applied distribute-rgt-in_binary64_105990.2

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

  6. Simplified0.2

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

  7. Simplified0.2

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

  9. Applied pow1/3_binary64_107310.2

    \[\leadsto \left(\left(x - \left(\left(y + 0.5\right) \cdot \left(\log \color{blue}{\left({y}^{0.3333333333333333}\right)} \cdot 2\right) + \left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right)\right)\right) + y\right) - z\]

  10. Taylor expanded around 0 0.2

    \[\leadsto \left(\left(x - \color{blue}{\left(3 \cdot \left(y \cdot \log \left({y}^{0.3333333333333333}\right)\right) + 1.5 \cdot \log \left({y}^{0.3333333333333333}\right)\right)}\right) + y\right) - z\]

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020342 
(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))