Average Error: 0.3 → 0.3
Time: 37.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2462194 = x;
        double r2462195 = y;
        double r2462196 = r2462194 + r2462195;
        double r2462197 = log(r2462196);
        double r2462198 = z;
        double r2462199 = log(r2462198);
        double r2462200 = r2462197 + r2462199;
        double r2462201 = t;
        double r2462202 = r2462200 - r2462201;
        double r2462203 = a;
        double r2462204 = 0.5;
        double r2462205 = r2462203 - r2462204;
        double r2462206 = log(r2462201);
        double r2462207 = r2462205 * r2462206;
        double r2462208 = r2462202 + r2462207;
        return r2462208;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2462209 = y;
        double r2462210 = x;
        double r2462211 = r2462209 + r2462210;
        double r2462212 = cbrt(r2462211);
        double r2462213 = r2462212 * r2462212;
        double r2462214 = log(r2462213);
        double r2462215 = log(r2462212);
        double r2462216 = t;
        double r2462217 = log(r2462216);
        double r2462218 = a;
        double r2462219 = 0.5;
        double r2462220 = r2462218 - r2462219;
        double r2462221 = r2462217 * r2462220;
        double r2462222 = z;
        double r2462223 = log(r2462222);
        double r2462224 = r2462223 - r2462216;
        double r2462225 = r2462221 + r2462224;
        double r2462226 = r2462215 + r2462225;
        double r2462227 = r2462214 + r2462226;
        return r2462227;
}

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 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. Using strategy rm

  6. Applied add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 
(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))))