Average Error: 0.1 → 0.1
Time: 6.8s
Precision: binary64
Cost: 7104
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))
↓
(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))
double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(z)));
}
↓
double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Alternatives

Alternative 1
Error0.9
Cost13953
\[\begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -55384.11858380467:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \end{array}\]
Alternative 2
Error10.2
Cost7176
\[\begin{array}{l} \mathbf{if}\;y \leq -1.2954443684393733 \cdot 10^{+116} \lor \neg \left(y \leq 1.5280087989140155 \cdot 10^{+44}\right):\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array}\]
Alternative 3
Error18.4
Cost448
\[x \cdot 0.5 - y \cdot z\]
Alternative 4
Error28.7
Cost840
\[\begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5.056455140050101 \cdot 10^{-117} \lor \neg \left(x \cdot 0.5 \leq 4.362766265246417 \cdot 10^{-116}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array}\]
Alternative 5
Error34.9
Cost192
\[x \cdot 0.5\]
Alternative 6
Error61.9
Cost64
\[-1\]
Alternative 7
Error61.9
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(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)))))