Average Error: 0.1 → 0.1
Time: 27.1s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + \left(\left(z - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + y\right) + \left(\left(z - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) - \log \left(\sqrt[3]{t}\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 r345719 = x;
        double r345720 = y;
        double r345721 = r345719 + r345720;
        double r345722 = z;
        double r345723 = r345721 + r345722;
        double r345724 = t;
        double r345725 = log(r345724);
        double r345726 = r345722 * r345725;
        double r345727 = r345723 - r345726;
        double r345728 = a;
        double r345729 = 0.5;
        double r345730 = r345728 - r345729;
        double r345731 = b;
        double r345732 = r345730 * r345731;
        double r345733 = r345727 + r345732;
        return r345733;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r345734 = x;
        double r345735 = y;
        double r345736 = r345734 + r345735;
        double r345737 = z;
        double r345738 = 2.0;
        double r345739 = t;
        double r345740 = cbrt(r345739);
        double r345741 = log(r345740);
        double r345742 = r345738 * r345741;
        double r345743 = r345742 * r345737;
        double r345744 = r345737 - r345743;
        double r345745 = r345741 * r345737;
        double r345746 = r345744 - r345745;
        double r345747 = r345736 + r345746;
        double r345748 = a;
        double r345749 = 0.5;
        double r345750 = r345748 - r345749;
        double r345751 = b;
        double r345752 = r345750 * r345751;
        double r345753 = r345747 + r345752;
        return r345753;
}

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 associate--l+0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-rgt-in0.1

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

  8. Applied associate--r+0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))