Average Error: 0.1 → 0.1
Time: 29.0s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + \left(z - \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\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(z - \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r325674 = x;
        double r325675 = y;
        double r325676 = r325674 + r325675;
        double r325677 = z;
        double r325678 = r325676 + r325677;
        double r325679 = t;
        double r325680 = log(r325679);
        double r325681 = r325677 * r325680;
        double r325682 = r325678 - r325681;
        double r325683 = a;
        double r325684 = 0.5;
        double r325685 = r325683 - r325684;
        double r325686 = b;
        double r325687 = r325685 * r325686;
        double r325688 = r325682 + r325687;
        return r325688;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r325689 = x;
        double r325690 = y;
        double r325691 = r325689 + r325690;
        double r325692 = z;
        double r325693 = 2.0;
        double r325694 = t;
        double r325695 = cbrt(r325694);
        double r325696 = log(r325695);
        double r325697 = r325693 * r325696;
        double r325698 = r325697 * r325692;
        double r325699 = r325696 * r325692;
        double r325700 = r325698 + r325699;
        double r325701 = r325692 - r325700;
        double r325702 = r325691 + r325701;
        double r325703 = a;
        double r325704 = 0.5;
        double r325705 = r325703 - r325704;
        double r325706 = b;
        double r325707 = r325705 * r325706;
        double r325708 = r325702 + r325707;
        return r325708;
}

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-lft-in0.1

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

  8. Simplified0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

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)))