Average Error: 0.3 → 0.3
Time: 11.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r53191 = x;
        double r53192 = y;
        double r53193 = r53191 + r53192;
        double r53194 = log(r53193);
        double r53195 = z;
        double r53196 = log(r53195);
        double r53197 = r53194 + r53196;
        double r53198 = t;
        double r53199 = r53197 - r53198;
        double r53200 = a;
        double r53201 = 0.5;
        double r53202 = r53200 - r53201;
        double r53203 = log(r53198);
        double r53204 = r53202 * r53203;
        double r53205 = r53199 + r53204;
        return r53205;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r53206 = x;
        double r53207 = y;
        double r53208 = r53206 + r53207;
        double r53209 = cbrt(r53208);
        double r53210 = r53209 * r53209;
        double r53211 = log(r53210);
        double r53212 = log(r53209);
        double r53213 = z;
        double r53214 = log(r53213);
        double r53215 = r53212 + r53214;
        double r53216 = r53211 + r53215;
        double r53217 = t;
        double r53218 = r53216 - r53217;
        double r53219 = a;
        double r53220 = 0.5;
        double r53221 = r53219 - r53220;
        double r53222 = log(r53217);
        double r53223 = r53221 * r53222;
        double r53224 = r53218 + r53223;
        return r53224;
}

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-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019352 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))