Average Error: 0.3 → 0.3
Time: 15.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r441622 = x;
        double r441623 = y;
        double r441624 = r441622 + r441623;
        double r441625 = log(r441624);
        double r441626 = z;
        double r441627 = log(r441626);
        double r441628 = r441625 + r441627;
        double r441629 = t;
        double r441630 = r441628 - r441629;
        double r441631 = a;
        double r441632 = 0.5;
        double r441633 = r441631 - r441632;
        double r441634 = log(r441629);
        double r441635 = r441633 * r441634;
        double r441636 = r441630 + r441635;
        return r441636;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r441637 = x;
        double r441638 = y;
        double r441639 = r441637 + r441638;
        double r441640 = log(r441639);
        double r441641 = z;
        double r441642 = log(r441641);
        double r441643 = t;
        double r441644 = r441642 - r441643;
        double r441645 = a;
        double r441646 = 0.5;
        double r441647 = r441645 - r441646;
        double r441648 = log(r441643);
        double r441649 = r441647 * r441648;
        double r441650 = r441644 + r441649;
        double r441651 = r441640 + r441650;
        return r441651;
}

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

Original0.3
Target0.3
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 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  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+0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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))))