Average Error: 0.1 → 0.1
Time: 7.3s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \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
double f(double x, double y, double z, double t, double a, double b) {
        double r356760 = x;
        double r356761 = y;
        double r356762 = r356760 + r356761;
        double r356763 = z;
        double r356764 = r356762 + r356763;
        double r356765 = t;
        double r356766 = log(r356765);
        double r356767 = r356763 * r356766;
        double r356768 = r356764 - r356767;
        double r356769 = a;
        double r356770 = 0.5;
        double r356771 = r356769 - r356770;
        double r356772 = b;
        double r356773 = r356771 * r356772;
        double r356774 = r356768 + r356773;
        return r356774;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r356775 = x;
        double r356776 = y;
        double r356777 = r356775 + r356776;
        double r356778 = z;
        double r356779 = r356777 + r356778;
        double r356780 = 2.0;
        double r356781 = t;
        double r356782 = cbrt(r356781);
        double r356783 = log(r356782);
        double r356784 = r356780 * r356783;
        double r356785 = r356778 * r356784;
        double r356786 = r356778 * r356783;
        double r356787 = r356785 + r356786;
        double r356788 = r356779 - r356787;
        double r356789 = a;
        double r356790 = 0.5;
        double r356791 = r356789 - r356790;
        double r356792 = b;
        double r356793 = r356791 * r356792;
        double r356794 = r356788 + r356793;
        return r356794;
}

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
Target0.3
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

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(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)))