Average Error: 0.3 → 0.3
Time: 38.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \left(\log \left(\sqrt[3]{t}\right) + \log \left({t}^{\frac{1}{3}}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \left(\log \left(\sqrt[3]{t}\right) + \log \left({t}^{\frac{1}{3}}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r1290278 = x;
        double r1290279 = y;
        double r1290280 = r1290278 + r1290279;
        double r1290281 = log(r1290280);
        double r1290282 = z;
        double r1290283 = log(r1290282);
        double r1290284 = r1290281 + r1290283;
        double r1290285 = t;
        double r1290286 = r1290284 - r1290285;
        double r1290287 = a;
        double r1290288 = 0.5;
        double r1290289 = r1290287 - r1290288;
        double r1290290 = log(r1290285);
        double r1290291 = r1290289 * r1290290;
        double r1290292 = r1290286 + r1290291;
        return r1290292;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1290293 = a;
        double r1290294 = 0.5;
        double r1290295 = r1290293 - r1290294;
        double r1290296 = t;
        double r1290297 = cbrt(r1290296);
        double r1290298 = log(r1290297);
        double r1290299 = r1290295 * r1290298;
        double r1290300 = 0.3333333333333333;
        double r1290301 = pow(r1290296, r1290300);
        double r1290302 = log(r1290301);
        double r1290303 = r1290298 + r1290302;
        double r1290304 = r1290303 * r1290295;
        double r1290305 = r1290299 + r1290304;
        double r1290306 = y;
        double r1290307 = x;
        double r1290308 = r1290306 + r1290307;
        double r1290309 = log(r1290308);
        double r1290310 = z;
        double r1290311 = log(r1290310);
        double r1290312 = r1290309 + r1290311;
        double r1290313 = r1290312 - r1290296;
        double r1290314 = r1290305 + r1290313;
        return r1290314;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Simplified0.3

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

  8. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(\log \color{blue}{\left({t}^{\frac{1}{3}}\right)} + \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)\]

  9. Final simplification0.3

    \[\leadsto \left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right) + \left(\log \left(\sqrt[3]{t}\right) + \log \left({t}^{\frac{1}{3}}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

Reproduce

herbie shell --seed 2019138 
(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))))