Average Error: 0.1 → 0.1
Time: 31.4s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(z + y\right) + x\right) - z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(z + y\right) + x\right) - z \cdot \left(2 \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
double f(double x, double y, double z, double t, double a, double b) {
        double r177105 = x;
        double r177106 = y;
        double r177107 = r177105 + r177106;
        double r177108 = z;
        double r177109 = r177107 + r177108;
        double r177110 = t;
        double r177111 = log(r177110);
        double r177112 = r177108 * r177111;
        double r177113 = r177109 - r177112;
        double r177114 = a;
        double r177115 = 0.5;
        double r177116 = r177114 - r177115;
        double r177117 = b;
        double r177118 = r177116 * r177117;
        double r177119 = r177113 + r177118;
        return r177119;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r177120 = z;
        double r177121 = y;
        double r177122 = r177120 + r177121;
        double r177123 = x;
        double r177124 = r177122 + r177123;
        double r177125 = 2.0;
        double r177126 = t;
        double r177127 = cbrt(r177126);
        double r177128 = log(r177127);
        double r177129 = r177125 * r177128;
        double r177130 = r177120 * r177129;
        double r177131 = r177124 - r177130;
        double r177132 = r177120 * r177128;
        double r177133 = r177131 - r177132;
        double r177134 = a;
        double r177135 = 0.5;
        double r177136 = r177134 - r177135;
        double r177137 = b;
        double r177138 = r177136 * r177137;
        double r177139 = r177133 + r177138;
        return r177139;
}

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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 +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)))