Average Error: 0.3 → 0.3
Time: 29.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\left(\log \left(\sqrt[3]{x + y}\right) - t\right) + \left(\log t \cdot \left(a - 0.5\right) + \log z\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\left(\log \left(\sqrt[3]{x + y}\right) - t\right) + \left(\log t \cdot \left(a - 0.5\right) + \log z\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r270083 = x;
        double r270084 = y;
        double r270085 = r270083 + r270084;
        double r270086 = log(r270085);
        double r270087 = z;
        double r270088 = log(r270087);
        double r270089 = r270086 + r270088;
        double r270090 = t;
        double r270091 = r270089 - r270090;
        double r270092 = a;
        double r270093 = 0.5;
        double r270094 = r270092 - r270093;
        double r270095 = log(r270090);
        double r270096 = r270094 * r270095;
        double r270097 = r270091 + r270096;
        return r270097;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r270098 = x;
        double r270099 = y;
        double r270100 = r270098 + r270099;
        double r270101 = cbrt(r270100);
        double r270102 = r270101 * r270101;
        double r270103 = log(r270102);
        double r270104 = log(r270101);
        double r270105 = t;
        double r270106 = r270104 - r270105;
        double r270107 = log(r270105);
        double r270108 = a;
        double r270109 = 0.5;
        double r270110 = r270108 - r270109;
        double r270111 = r270107 * r270110;
        double r270112 = z;
        double r270113 = log(r270112);
        double r270114 = r270111 + r270113;
        double r270115 = r270106 + r270114;
        double r270116 = r270103 + r270115;
        return r270116;
}

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. Simplified0.3

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

  4. Applied add-cube-cbrt0.3

    \[\leadsto \log \color{blue}{\left(\left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) \cdot \sqrt[3]{y + x}\right)} - \left(\left(t - \log z\right) - \left(a - 0.5\right) \cdot \log t\right)\]

  5. Applied log-prod0.3

    \[\leadsto \color{blue}{\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \log \left(\sqrt[3]{y + x}\right)\right)} - \left(\left(t - \log z\right) - \left(a - 0.5\right) \cdot \log t\right)\]

  6. Applied associate--l+0.3

    \[\leadsto \color{blue}{\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) - \left(\left(t - \log z\right) - \left(a - 0.5\right) \cdot \log t\right)\right)}\]

  7. Simplified0.3

    \[\leadsto \log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \color{blue}{\left(\left(\log \left(\sqrt[3]{y + x}\right) - t\right) + \left(\log z + \left(a - 0.5\right) \cdot \log t\right)\right)}\]

  8. Final simplification0.3

    \[\leadsto \log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\left(\log \left(\sqrt[3]{x + y}\right) - t\right) + \left(\log t \cdot \left(a - 0.5\right) + \log z\right)\right)\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

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

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