Average Error: 0.1 → 0.1
Time: 29.1s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(z + \left(x + y\right)\right) - \left(\log \left(\left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) - z \cdot \log \left({t}^{\frac{1}{3}}\right)\right) + b \cdot \left(a - 0.5\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(z + \left(x + y\right)\right) - \left(\log \left(\left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) - z \cdot \log \left({t}^{\frac{1}{3}}\right)\right) + b \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r14113366 = x;
        double r14113367 = y;
        double r14113368 = r14113366 + r14113367;
        double r14113369 = z;
        double r14113370 = r14113368 + r14113369;
        double r14113371 = t;
        double r14113372 = log(r14113371);
        double r14113373 = r14113369 * r14113372;
        double r14113374 = r14113370 - r14113373;
        double r14113375 = a;
        double r14113376 = 0.5;
        double r14113377 = r14113375 - r14113376;
        double r14113378 = b;
        double r14113379 = r14113377 * r14113378;
        double r14113380 = r14113374 + r14113379;
        return r14113380;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r14113381 = z;
        double r14113382 = x;
        double r14113383 = y;
        double r14113384 = r14113382 + r14113383;
        double r14113385 = r14113381 + r14113384;
        double r14113386 = t;
        double r14113387 = cbrt(r14113386);
        double r14113388 = cbrt(r14113387);
        double r14113389 = r14113388 * r14113388;
        double r14113390 = r14113389 * r14113388;
        double r14113391 = log(r14113390);
        double r14113392 = log(r14113387);
        double r14113393 = r14113391 + r14113392;
        double r14113394 = r14113393 * r14113381;
        double r14113395 = r14113385 - r14113394;
        double r14113396 = 0.3333333333333333;
        double r14113397 = pow(r14113386, r14113396);
        double r14113398 = log(r14113397);
        double r14113399 = r14113381 * r14113398;
        double r14113400 = r14113395 - r14113399;
        double r14113401 = b;
        double r14113402 = a;
        double r14113403 = 0.5;
        double r14113404 = r14113402 - r14113403;
        double r14113405 = r14113401 * r14113404;
        double r14113406 = r14113400 + r14113405;
        return r14113406;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.4
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  11. Applied add-cube-cbrt0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

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