Average Error: 0.1 → 0.1
Time: 16.6s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x + \left(\left(y - \log y \cdot \left(0.5 + y\right)\right) - z\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x + \left(\left(y - \log y \cdot \left(0.5 + y\right)\right) - z\right)
double f(double x, double y, double z) {
        double r290572 = x;
        double r290573 = y;
        double r290574 = 0.5;
        double r290575 = r290573 + r290574;
        double r290576 = log(r290573);
        double r290577 = r290575 * r290576;
        double r290578 = r290572 - r290577;
        double r290579 = r290578 + r290573;
        double r290580 = z;
        double r290581 = r290579 - r290580;
        return r290581;
}
↓
double f(double x, double y, double z) {
        double r290582 = x;
        double r290583 = y;
        double r290584 = log(r290583);
        double r290585 = 0.5;
        double r290586 = r290585 + r290583;
        double r290587 = r290584 * r290586;
        double r290588 = r290583 - r290587;
        double r290589 = z;
        double r290590 = r290588 - r290589;
        double r290591 = r290582 + r290590;
        return r290591;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 *-un-lft-identity0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied distribute-lft-out0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(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))