Average Error: 0.1 → 0.1
Time: 22.6s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(y + x\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\right) + b \cdot \left(a - 0.5\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(y + x\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\right) + b \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r13981754 = x;
        double r13981755 = y;
        double r13981756 = r13981754 + r13981755;
        double r13981757 = z;
        double r13981758 = r13981756 + r13981757;
        double r13981759 = t;
        double r13981760 = log(r13981759);
        double r13981761 = r13981757 * r13981760;
        double r13981762 = r13981758 - r13981761;
        double r13981763 = a;
        double r13981764 = 0.5;
        double r13981765 = r13981763 - r13981764;
        double r13981766 = b;
        double r13981767 = r13981765 * r13981766;
        double r13981768 = r13981762 + r13981767;
        return r13981768;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r13981769 = z;
        double r13981770 = y;
        double r13981771 = x;
        double r13981772 = r13981770 + r13981771;
        double r13981773 = r13981769 + r13981772;
        double r13981774 = t;
        double r13981775 = cbrt(r13981774);
        double r13981776 = log(r13981775);
        double r13981777 = r13981769 * r13981776;
        double r13981778 = r13981777 + r13981777;
        double r13981779 = r13981777 + r13981778;
        double r13981780 = r13981773 - r13981779;
        double r13981781 = b;
        double r13981782 = a;
        double r13981783 = 0.5;
        double r13981784 = r13981782 - r13981783;
        double r13981785 = r13981781 * r13981784;
        double r13981786 = r13981780 + r13981785;
        return r13981786;
}

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
Target0.5
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. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))