Average Error: 0.1 → 0.1
Time: 22.8s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + y\right) + z\right) - \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]
\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(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r21871050 = x;
        double r21871051 = y;
        double r21871052 = r21871050 + r21871051;
        double r21871053 = z;
        double r21871054 = r21871052 + r21871053;
        double r21871055 = t;
        double r21871056 = log(r21871055);
        double r21871057 = r21871053 * r21871056;
        double r21871058 = r21871054 - r21871057;
        double r21871059 = a;
        double r21871060 = 0.5;
        double r21871061 = r21871059 - r21871060;
        double r21871062 = b;
        double r21871063 = r21871061 * r21871062;
        double r21871064 = r21871058 + r21871063;
        return r21871064;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r21871065 = x;
        double r21871066 = y;
        double r21871067 = r21871065 + r21871066;
        double r21871068 = z;
        double r21871069 = r21871067 + r21871068;
        double r21871070 = t;
        double r21871071 = cbrt(r21871070);
        double r21871072 = r21871071 * r21871071;
        double r21871073 = log(r21871072);
        double r21871074 = r21871073 * r21871068;
        double r21871075 = log(r21871071);
        double r21871076 = r21871075 * r21871068;
        double r21871077 = r21871074 + r21871076;
        double r21871078 = r21871069 - r21871077;
        double r21871079 = a;
        double r21871080 = 0.5;
        double r21871081 = r21871079 - r21871080;
        double r21871082 = b;
        double r21871083 = r21871081 * r21871082;
        double r21871084 = r21871078 + r21871083;
        return r21871084;
}

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-rgt-in0.1

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

  6. Final simplification0.1

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

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)))