Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(x + \left(\left(y - \log y \cdot 0.5\right) - \log y \cdot y\right)\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(x + \left(\left(y - \log y \cdot 0.5\right) - \log y \cdot y\right)\right) - z
double f(double x, double y, double z) {
        double r313343 = x;
        double r313344 = y;
        double r313345 = 0.5;
        double r313346 = r313344 + r313345;
        double r313347 = log(r313344);
        double r313348 = r313346 * r313347;
        double r313349 = r313343 - r313348;
        double r313350 = r313349 + r313344;
        double r313351 = z;
        double r313352 = r313350 - r313351;
        return r313352;
}
↓
double f(double x, double y, double z) {
        double r313353 = x;
        double r313354 = y;
        double r313355 = log(r313354);
        double r313356 = 0.5;
        double r313357 = r313355 * r313356;
        double r313358 = r313354 - r313357;
        double r313359 = r313355 * r313354;
        double r313360 = r313358 - r313359;
        double r313361 = r313353 + r313360;
        double r313362 = z;
        double r313363 = r313361 - r313362;
        return r313363;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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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 sub-neg0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate--r+0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

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

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