Average Error: 0.1 → 0.1
Time: 12.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \left({t}^{\frac{1}{3}}\right)\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \left({t}^{\frac{1}{3}}\right)\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r362046 = x;
        double r362047 = y;
        double r362048 = r362046 + r362047;
        double r362049 = z;
        double r362050 = r362048 + r362049;
        double r362051 = t;
        double r362052 = log(r362051);
        double r362053 = r362049 * r362052;
        double r362054 = r362050 - r362053;
        double r362055 = a;
        double r362056 = 0.5;
        double r362057 = r362055 - r362056;
        double r362058 = b;
        double r362059 = r362057 * r362058;
        double r362060 = r362054 + r362059;
        return r362060;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r362061 = x;
        double r362062 = z;
        double r362063 = y;
        double r362064 = r362062 + r362063;
        double r362065 = r362061 + r362064;
        double r362066 = 2.0;
        double r362067 = t;
        double r362068 = 0.3333333333333333;
        double r362069 = pow(r362067, r362068);
        double r362070 = log(r362069);
        double r362071 = r362066 * r362070;
        double r362072 = r362071 * r362062;
        double r362073 = r362065 - r362072;
        double r362074 = cbrt(r362067);
        double r362075 = log(r362074);
        double r362076 = r362062 * r362075;
        double r362077 = r362073 - r362076;
        double r362078 = a;
        double r362079 = 0.5;
        double r362080 = r362078 - r362079;
        double r362081 = b;
        double r362082 = r362080 * r362081;
        double r362083 = r362077 + r362082;
        return r362083;
}

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. 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

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

  9. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \color{blue}{\left({t}^{\frac{1}{3}}\right)}\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \left({t}^{\frac{1}{3}}\right)\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2020045 
(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)))