Average Error: 0.1 → 0.1
Time: 47.5s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(z + \left(y + x\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + b \cdot \left(a - 0.5\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(z + \left(y + x\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + b \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r20585716 = x;
        double r20585717 = y;
        double r20585718 = r20585716 + r20585717;
        double r20585719 = z;
        double r20585720 = r20585718 + r20585719;
        double r20585721 = t;
        double r20585722 = log(r20585721);
        double r20585723 = r20585719 * r20585722;
        double r20585724 = r20585720 - r20585723;
        double r20585725 = a;
        double r20585726 = 0.5;
        double r20585727 = r20585725 - r20585726;
        double r20585728 = b;
        double r20585729 = r20585727 * r20585728;
        double r20585730 = r20585724 + r20585729;
        return r20585730;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r20585731 = z;
        double r20585732 = y;
        double r20585733 = x;
        double r20585734 = r20585732 + r20585733;
        double r20585735 = r20585731 + r20585734;
        double r20585736 = t;
        double r20585737 = cbrt(r20585736);
        double r20585738 = log(r20585737);
        double r20585739 = r20585731 * r20585738;
        double r20585740 = r20585739 + r20585739;
        double r20585741 = r20585735 - r20585740;
        double r20585742 = r20585741 - r20585739;
        double r20585743 = b;
        double r20585744 = a;
        double r20585745 = 0.5;
        double r20585746 = r20585744 - r20585745;
        double r20585747 = r20585743 * r20585746;
        double r20585748 = r20585742 + r20585747;
        return r20585748;
}

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. Applied associate--r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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)))