Average Error: 0.1 → 0.1
Time: 3.3s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\left(y \cdot 1 + y \cdot \left(-z\right)\right) + y \cdot \log z\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

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

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1 - z\right) + y \cdot \log z\right)}\]
  4. Using strategy rm

  5. Applied sub-neg0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Final simplification0.1

    \[\leadsto x \cdot 0.5 + \left(\left(y \cdot 1 + y \cdot \left(-z\right)\right) + y \cdot \log z\right)\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

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

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))