Average Error: 0.1 → 0.1
Time: 12.6s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + \left(z + y\right)\right) - z \cdot \left(\log \left(\sqrt{t}\right) + \log \left(\left|\sqrt[3]{t}\right|\right)\right)\right) - \log \left(\sqrt{\sqrt[3]{{t}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{t}}}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + \left(z + y\right)\right) - z \cdot \left(\log \left(\sqrt{t}\right) + \log \left(\left|\sqrt[3]{t}\right|\right)\right)\right) - \log \left(\sqrt{\sqrt[3]{{t}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{t}}}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r422663 = x;
        double r422664 = y;
        double r422665 = r422663 + r422664;
        double r422666 = z;
        double r422667 = r422665 + r422666;
        double r422668 = t;
        double r422669 = log(r422668);
        double r422670 = r422666 * r422669;
        double r422671 = r422667 - r422670;
        double r422672 = a;
        double r422673 = 0.5;
        double r422674 = r422672 - r422673;
        double r422675 = b;
        double r422676 = r422674 * r422675;
        double r422677 = r422671 + r422676;
        return r422677;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r422678 = x;
        double r422679 = z;
        double r422680 = y;
        double r422681 = r422679 + r422680;
        double r422682 = r422678 + r422681;
        double r422683 = t;
        double r422684 = sqrt(r422683);
        double r422685 = log(r422684);
        double r422686 = cbrt(r422683);
        double r422687 = fabs(r422686);
        double r422688 = log(r422687);
        double r422689 = r422685 + r422688;
        double r422690 = r422679 * r422689;
        double r422691 = r422682 - r422690;
        double r422692 = 0.6666666666666666;
        double r422693 = pow(r422683, r422692);
        double r422694 = cbrt(r422693);
        double r422695 = cbrt(r422686);
        double r422696 = r422694 * r422695;
        double r422697 = sqrt(r422696);
        double r422698 = log(r422697);
        double r422699 = r422698 * r422679;
        double r422700 = r422691 - r422699;
        double r422701 = a;
        double r422702 = 0.5;
        double r422703 = r422701 - r422702;
        double r422704 = b;
        double r422705 = r422703 * r422704;
        double r422706 = r422700 + r422705;
        return r422706;
}

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

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

  10. Applied sqrt-prod0.1

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

  11. Applied log-prod0.1

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

  12. Applied distribute-rgt-in0.1

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

  13. Applied associate--r+0.1

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

  14. Simplified0.1

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

  16. Applied add-cube-cbrt0.1

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

  17. Applied cbrt-prod0.1

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

  18. Simplified0.1

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

  19. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

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