Average Error: 0.1 → 0.1
Time: 22.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right)\right) - \left(z \cdot \frac{1}{3}\right) \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right)\right) - \left(z \cdot \frac{1}{3}\right) \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r249511 = x;
        double r249512 = y;
        double r249513 = r249511 + r249512;
        double r249514 = z;
        double r249515 = r249513 + r249514;
        double r249516 = t;
        double r249517 = log(r249516);
        double r249518 = r249514 * r249517;
        double r249519 = r249515 - r249518;
        double r249520 = a;
        double r249521 = 0.5;
        double r249522 = r249520 - r249521;
        double r249523 = b;
        double r249524 = r249522 * r249523;
        double r249525 = r249519 + r249524;
        return r249525;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r249526 = x;
        double r249527 = y;
        double r249528 = r249526 + r249527;
        double r249529 = z;
        double r249530 = r249528 + r249529;
        double r249531 = t;
        double r249532 = sqrt(r249531);
        double r249533 = log(r249532);
        double r249534 = r249533 * r249529;
        double r249535 = r249530 - r249534;
        double r249536 = 2.0;
        double r249537 = cbrt(r249532);
        double r249538 = log(r249537);
        double r249539 = r249536 * r249538;
        double r249540 = r249529 * r249539;
        double r249541 = r249535 - r249540;
        double r249542 = 0.3333333333333333;
        double r249543 = r249529 * r249542;
        double r249544 = r249543 * r249533;
        double r249545 = r249541 - r249544;
        double r249546 = a;
        double r249547 = 0.5;
        double r249548 = r249546 - r249547;
        double r249549 = b;
        double r249550 = r249548 * r249549;
        double r249551 = r249545 + r249550;
        return r249551;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Applied associate--r+0.1

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

  13. Simplified0.1

    \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right)\right)} - z \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right) + \left(a - 0.5\right) \cdot b\]
  14. Using strategy rm

  15. Applied pow1/30.1

    \[\leadsto \left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right)\right) - z \cdot \log \color{blue}{\left({\left(\sqrt{t}\right)}^{\frac{1}{3}}\right)}\right) + \left(a - 0.5\right) \cdot b\]

  16. Applied log-pow0.1

    \[\leadsto \left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right)\right) - z \cdot \color{blue}{\left(\frac{1}{3} \cdot \log \left(\sqrt{t}\right)\right)}\right) + \left(a - 0.5\right) \cdot b\]

  17. Applied associate-*r*0.1

    \[\leadsto \left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right)\right) - \color{blue}{\left(z \cdot \frac{1}{3}\right) \cdot \log \left(\sqrt{t}\right)}\right) + \left(a - 0.5\right) \cdot b\]

  18. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{t}}\right)\right)\right) - \left(z \cdot \frac{1}{3}\right) \cdot \log \left(\sqrt{t}\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2019198 
(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)))