Average Error: 0.1 → 0.1
Time: 12.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(z + \left(x + y\right)\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(z + \left(x + y\right)\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r550105 = x;
        double r550106 = y;
        double r550107 = r550105 + r550106;
        double r550108 = z;
        double r550109 = r550107 + r550108;
        double r550110 = t;
        double r550111 = log(r550110);
        double r550112 = r550108 * r550111;
        double r550113 = r550109 - r550112;
        double r550114 = a;
        double r550115 = 0.5;
        double r550116 = r550114 - r550115;
        double r550117 = b;
        double r550118 = r550116 * r550117;
        double r550119 = r550113 + r550118;
        return r550119;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r550120 = z;
        double r550121 = x;
        double r550122 = y;
        double r550123 = r550121 + r550122;
        double r550124 = r550120 + r550123;
        double r550125 = 2.0;
        double r550126 = t;
        double r550127 = cbrt(r550126);
        double r550128 = log(r550127);
        double r550129 = r550125 * r550128;
        double r550130 = r550129 * r550120;
        double r550131 = r550124 - r550130;
        double r550132 = r550128 * r550120;
        double r550133 = r550131 - r550132;
        double r550134 = a;
        double r550135 = 0.5;
        double r550136 = r550134 - r550135;
        double r550137 = b;
        double r550138 = r550136 * r550137;
        double r550139 = r550133 + r550138;
        return r550139;
}

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-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. Applied associate--r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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)))