Average Error: 0.1 → 0.1
Time: 17.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(x + \left(\left(y + \left(a - \frac{1}{2}\right) \cdot b\right) + z\right)\right) - \left(3 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(x + \left(\left(y + \left(a - \frac{1}{2}\right) \cdot b\right) + z\right)\right) - \left(3 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z
double f(double x, double y, double z, double t, double a, double b) {
        double r298098 = x;
        double r298099 = y;
        double r298100 = r298098 + r298099;
        double r298101 = z;
        double r298102 = r298100 + r298101;
        double r298103 = t;
        double r298104 = log(r298103);
        double r298105 = r298101 * r298104;
        double r298106 = r298102 - r298105;
        double r298107 = a;
        double r298108 = 0.5;
        double r298109 = r298107 - r298108;
        double r298110 = b;
        double r298111 = r298109 * r298110;
        double r298112 = r298106 + r298111;
        return r298112;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r298113 = x;
        double r298114 = y;
        double r298115 = a;
        double r298116 = 1.0;
        double r298117 = 2.0;
        double r298118 = r298116 / r298117;
        double r298119 = r298115 - r298118;
        double r298120 = b;
        double r298121 = r298119 * r298120;
        double r298122 = r298114 + r298121;
        double r298123 = z;
        double r298124 = r298122 + r298123;
        double r298125 = r298113 + r298124;
        double r298126 = 3.0;
        double r298127 = t;
        double r298128 = cbrt(r298127);
        double r298129 = log(r298128);
        double r298130 = r298126 * r298129;
        double r298131 = r298130 * r298123;
        double r298132 = r298125 - r298131;
        return r298132;
}

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. Applied associate-+l+0.1

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

  5. Simplified0.1

    \[\leadsto \left(x + y\right) + \color{blue}{\left(\left(z - z \cdot \log t\right) + \left(a - \frac{1}{2}\right) \cdot b\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.1

    \[\leadsto \left(x + y\right) + \left(\left(z - z \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\]

  8. Applied log-prod0.1

    \[\leadsto \left(x + y\right) + \left(\left(z - z \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\]

  9. Applied distribute-lft-in0.1

    \[\leadsto \left(x + y\right) + \left(\left(z - \color{blue}{\left(z \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)}\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\]

  10. Applied associate--r+0.1

    \[\leadsto \left(x + y\right) + \left(\color{blue}{\left(\left(z - z \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right)\]

  11. Simplified0.1

    \[\leadsto \left(x + y\right) + \left(\left(\color{blue}{\left(z - \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z\right)} - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\]

  12. Final simplification0.1

    \[\leadsto \left(x + \left(\left(y + \left(a - \frac{1}{2}\right) \cdot b\right) + z\right)\right) - \left(3 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\]

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)))