Average Error: 0.1 → 0.1
Time: 2.8min
Precision: binary64
Cost: 7104
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[y \cdot \left(\left(1 - z\right) + \log z\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
y \cdot \left(\left(1 - z\right) + \log z\right) + x \cdot 0.5
(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))
↓
(FPCore (x y z) :precision binary64 (+ (* y (+ (- 1.0 z) (log z))) (* x 0.5)))
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 (y * ((1.0 - z) + log(z))) + (x * 0.5);
}

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
Error1.5
Cost13953
\[\begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -1.240223839603504 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \log \left(z \cdot e\right)\\ \end{array}\]
Alternative 2
Error1.5
Cost13953
\[\begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -1.240223839603504 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x \cdot 0.5 + y \cdot \log z\right)\\ \end{array}\]
Alternative 3
Error11.4
Cost7432
\[\begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -1.5085720415833188 \cdot 10^{-184} \lor \neg \left(x \cdot 0.5 \leq 3.043565708360598 \cdot 10^{-75}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \end{array}\]
Alternative 4
Error11.4
Cost7432
\[\begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -1.5085720415833188 \cdot 10^{-184} \lor \neg \left(x \cdot 0.5 \leq 3.043565708360598 \cdot 10^{-75}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \left(\log z - z\right)\right)\\ \end{array}\]
Alternative 5
Error11.4
Cost7432
\[\begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -1.5085720415833188 \cdot 10^{-184} \lor \neg \left(x \cdot 0.5 \leq 3.043565708360598 \cdot 10^{-75}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot \left(\log z - z\right)\\ \end{array}\]
Alternative 6
Error17.8
Cost448
\[x \cdot 0.5 - y \cdot z\]
Alternative 7
Error29.1
Cost1361
\[\begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -3.0352062157035826 \cdot 10^{-17} \lor \neg \left(x \cdot 0.5 \leq -3.4403799285636905 \cdot 10^{-92} \lor \neg \left(x \cdot 0.5 \leq -2.640333964194819 \cdot 10^{-186}\right) \land x \cdot 0.5 \leq 3.9099457876822657 \cdot 10^{-137}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array}\]
Alternative 8
Error34.2
Cost192
\[x \cdot 0.5\]
Alternative 9
Error61.9
Cost64
\[-1\]
Alternative 10
Error61.9
Cost64
\[1\]

Error

Time

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 add-sqr-sqrt_binary64_1203531.9

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

  4. Simplified31.9

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

  5. Simplified31.9

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

  7. Applied pow1_binary64_1207431.9

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

  8. Applied pow1_binary64_1207431.9

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

  9. Applied pow-prod-down_binary64_1208431.9

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

  10. Simplified0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2021040 
(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)))))