Average Error: 0.3 → 0.3
Time: 1.1m
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2609075 = x;
        double r2609076 = y;
        double r2609077 = r2609075 + r2609076;
        double r2609078 = log(r2609077);
        double r2609079 = z;
        double r2609080 = log(r2609079);
        double r2609081 = r2609078 + r2609080;
        double r2609082 = t;
        double r2609083 = r2609081 - r2609082;
        double r2609084 = a;
        double r2609085 = 0.5;
        double r2609086 = r2609084 - r2609085;
        double r2609087 = log(r2609082);
        double r2609088 = r2609086 * r2609087;
        double r2609089 = r2609083 + r2609088;
        return r2609089;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2609090 = t;
        double r2609091 = sqrt(r2609090);
        double r2609092 = log(r2609091);
        double r2609093 = a;
        double r2609094 = 0.5;
        double r2609095 = r2609093 - r2609094;
        double r2609096 = r2609092 * r2609095;
        double r2609097 = y;
        double r2609098 = x;
        double r2609099 = r2609097 + r2609098;
        double r2609100 = log(r2609099);
        double r2609101 = z;
        double r2609102 = log(r2609101);
        double r2609103 = r2609100 + r2609102;
        double r2609104 = r2609103 - r2609090;
        double r2609105 = r2609104 + r2609096;
        double r2609106 = r2609096 + r2609105;
        return r2609106;
}

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

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 add-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))