Average Error: 0.1 → 0.1
Time: 28.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(y + z\right) + x\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + b \cdot \left(a - 0.5\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(y + z\right) + x\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + b \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r12978814 = x;
        double r12978815 = y;
        double r12978816 = r12978814 + r12978815;
        double r12978817 = z;
        double r12978818 = r12978816 + r12978817;
        double r12978819 = t;
        double r12978820 = log(r12978819);
        double r12978821 = r12978817 * r12978820;
        double r12978822 = r12978818 - r12978821;
        double r12978823 = a;
        double r12978824 = 0.5;
        double r12978825 = r12978823 - r12978824;
        double r12978826 = b;
        double r12978827 = r12978825 * r12978826;
        double r12978828 = r12978822 + r12978827;
        return r12978828;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r12978829 = y;
        double r12978830 = z;
        double r12978831 = r12978829 + r12978830;
        double r12978832 = x;
        double r12978833 = r12978831 + r12978832;
        double r12978834 = t;
        double r12978835 = cbrt(r12978834);
        double r12978836 = log(r12978835);
        double r12978837 = r12978836 * r12978830;
        double r12978838 = r12978837 + r12978837;
        double r12978839 = r12978833 - r12978838;
        double r12978840 = r12978839 - r12978837;
        double r12978841 = b;
        double r12978842 = a;
        double r12978843 = 0.5;
        double r12978844 = r12978842 - r12978843;
        double r12978845 = r12978841 * r12978844;
        double r12978846 = r12978840 + r12978845;
        return r12978846;
}

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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +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)))