Average Error: 0.1 → 0.1
Time: 19.5s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \left(\left(\left(\log \left(\sqrt{y}\right) \cdot \left(y + 0.5\right) - y\right) + \log \left(\sqrt{y}\right) \cdot \left(y + 0.5\right)\right) + z\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \left(\left(\left(\log \left(\sqrt{y}\right) \cdot \left(y + 0.5\right) - y\right) + \log \left(\sqrt{y}\right) \cdot \left(y + 0.5\right)\right) + z\right)
double f(double x, double y, double z) {
        double r15456097 = x;
        double r15456098 = y;
        double r15456099 = 0.5;
        double r15456100 = r15456098 + r15456099;
        double r15456101 = log(r15456098);
        double r15456102 = r15456100 * r15456101;
        double r15456103 = r15456097 - r15456102;
        double r15456104 = r15456103 + r15456098;
        double r15456105 = z;
        double r15456106 = r15456104 - r15456105;
        return r15456106;
}
↓
double f(double x, double y, double z) {
        double r15456107 = x;
        double r15456108 = y;
        double r15456109 = sqrt(r15456108);
        double r15456110 = log(r15456109);
        double r15456111 = 0.5;
        double r15456112 = r15456108 + r15456111;
        double r15456113 = r15456110 * r15456112;
        double r15456114 = r15456113 - r15456108;
        double r15456115 = r15456114 + r15456113;
        double r15456116 = z;
        double r15456117 = r15456115 + r15456116;
        double r15456118 = r15456107 - r15456117;
        return r15456118;
}

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 associate-+l-0.1

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

  4. Applied associate--l-0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied log-prod0.1

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

  8. Applied distribute-rgt-in0.1

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

  9. Applied associate--l+0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(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))