Average Error: 0.1 → 0.1
Time: 28.9s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
double f(double x, double y, double z) {
        double r264336 = x;
        double r264337 = y;
        double r264338 = 0.5;
        double r264339 = r264337 + r264338;
        double r264340 = log(r264337);
        double r264341 = r264339 * r264340;
        double r264342 = r264336 - r264341;
        double r264343 = r264342 + r264337;
        double r264344 = z;
        double r264345 = r264343 - r264344;
        return r264345;
}
↓
double f(double x, double y, double z) {
        double r264346 = x;
        double r264347 = y;
        double r264348 = 0.5;
        double r264349 = r264347 + r264348;
        double r264350 = log(r264347);
        double r264351 = r264349 * r264350;
        double r264352 = r264346 - r264351;
        double r264353 = r264352 + r264347;
        double r264354 = z;
        double r264355 = r264353 - r264354;
        return r264355;
}

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-cbrt0.1

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

  4. Applied log-prod0.2

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

  5. Applied distribute-lft-in0.2

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

  6. Simplified0.2

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

  7. Simplified0.2

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

  9. Applied distribute-rgt-out0.2

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(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))