Average Error: 0.2 → 0.3
Time: 13.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r342032 = x;
        double r342033 = y;
        double r342034 = r342032 + r342033;
        double r342035 = log(r342034);
        double r342036 = z;
        double r342037 = log(r342036);
        double r342038 = r342035 + r342037;
        double r342039 = t;
        double r342040 = r342038 - r342039;
        double r342041 = a;
        double r342042 = 0.5;
        double r342043 = r342041 - r342042;
        double r342044 = log(r342039);
        double r342045 = r342043 * r342044;
        double r342046 = r342040 + r342045;
        return r342046;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r342047 = x;
        double r342048 = y;
        double r342049 = r342047 + r342048;
        double r342050 = sqrt(r342049);
        double r342051 = log(r342050);
        double r342052 = z;
        double r342053 = log(r342052);
        double r342054 = t;
        double r342055 = r342053 - r342054;
        double r342056 = a;
        double r342057 = 0.5;
        double r342058 = r342056 - r342057;
        double r342059 = log(r342054);
        double r342060 = r342058 * r342059;
        double r342061 = r342055 + r342060;
        double r342062 = r342051 + r342061;
        double r342063 = r342051 + r342062;
        return r342063;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied associate--l+0.3

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

  4. Applied associate-+l+0.2

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

  6. Applied add-sqr-sqrt0.2

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

  7. Applied log-prod0.2

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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