Average Error: 0.1 → 0.1
Time: 26.5s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(y + x\right)\right) - \left(\left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot z + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(y + x\right)\right) - \left(\left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot z + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r18245506 = x;
        double r18245507 = y;
        double r18245508 = r18245506 + r18245507;
        double r18245509 = z;
        double r18245510 = r18245508 + r18245509;
        double r18245511 = t;
        double r18245512 = log(r18245511);
        double r18245513 = r18245509 * r18245512;
        double r18245514 = r18245510 - r18245513;
        double r18245515 = a;
        double r18245516 = 0.5;
        double r18245517 = r18245515 - r18245516;
        double r18245518 = b;
        double r18245519 = r18245517 * r18245518;
        double r18245520 = r18245514 + r18245519;
        return r18245520;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r18245521 = z;
        double r18245522 = y;
        double r18245523 = x;
        double r18245524 = r18245522 + r18245523;
        double r18245525 = r18245521 + r18245524;
        double r18245526 = t;
        double r18245527 = cbrt(r18245526);
        double r18245528 = log(r18245527);
        double r18245529 = r18245528 + r18245528;
        double r18245530 = r18245529 * r18245521;
        double r18245531 = 1.0;
        double r18245532 = r18245531 / r18245526;
        double r18245533 = -0.3333333333333333;
        double r18245534 = pow(r18245532, r18245533);
        double r18245535 = log(r18245534);
        double r18245536 = r18245535 * r18245521;
        double r18245537 = r18245530 + r18245536;
        double r18245538 = r18245525 - r18245537;
        double r18245539 = a;
        double r18245540 = 0.5;
        double r18245541 = r18245539 - r18245540;
        double r18245542 = b;
        double r18245543 = r18245541 * r18245542;
        double r18245544 = r18245538 + r18245543;
        return r18245544;
}

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. Simplified0.1

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

  7. Taylor expanded around inf 0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(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)))