Average Error: 0.1 → 0.2
Time: 6.3s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(\left(x - \left(\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right)\right) + y\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(\left(x - \left(\left(y + 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left(\sqrt[3]{y}\right) \cdot \left(y + 0.5\right)\right)\right) + y\right) - z
double f(double x, double y, double z) {
        double r359462 = x;
        double r359463 = y;
        double r359464 = 0.5;
        double r359465 = r359463 + r359464;
        double r359466 = log(r359463);
        double r359467 = r359465 * r359466;
        double r359468 = r359462 - r359467;
        double r359469 = r359468 + r359463;
        double r359470 = z;
        double r359471 = r359469 - r359470;
        return r359471;
}
↓
double f(double x, double y, double z) {
        double r359472 = x;
        double r359473 = y;
        double r359474 = 0.5;
        double r359475 = r359473 + r359474;
        double r359476 = 2.0;
        double r359477 = cbrt(r359473);
        double r359478 = log(r359477);
        double r359479 = r359476 * r359478;
        double r359480 = r359475 * r359479;
        double r359481 = r359478 * r359475;
        double r359482 = r359480 + r359481;
        double r359483 = r359472 - r359482;
        double r359484 = r359483 + r359473;
        double r359485 = z;
        double r359486 = r359484 - r359485;
        return r359486;
}

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
Herbie0.2
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

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

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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