Average Error: 0.1 → 0.1
Time: 6.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + z\right) + \left(\left(a - 0.5\right) \cdot b - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + y\right) + z\right) + \left(\left(a - 0.5\right) \cdot b - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r368116 = x;
        double r368117 = y;
        double r368118 = r368116 + r368117;
        double r368119 = z;
        double r368120 = r368118 + r368119;
        double r368121 = t;
        double r368122 = log(r368121);
        double r368123 = r368119 * r368122;
        double r368124 = r368120 - r368123;
        double r368125 = a;
        double r368126 = 0.5;
        double r368127 = r368125 - r368126;
        double r368128 = b;
        double r368129 = r368127 * r368128;
        double r368130 = r368124 + r368129;
        return r368130;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r368131 = x;
        double r368132 = y;
        double r368133 = r368131 + r368132;
        double r368134 = z;
        double r368135 = r368133 + r368134;
        double r368136 = a;
        double r368137 = 0.5;
        double r368138 = r368136 - r368137;
        double r368139 = b;
        double r368140 = r368138 * r368139;
        double r368141 = 2.0;
        double r368142 = t;
        double r368143 = cbrt(r368142);
        double r368144 = log(r368143);
        double r368145 = r368141 * r368144;
        double r368146 = r368134 * r368145;
        double r368147 = r368134 * r368144;
        double r368148 = r368146 + r368147;
        double r368149 = r368140 - r368148;
        double r368150 = r368135 + r368149;
        return r368150;
}

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 sub-neg0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  7. Applied add-cube-cbrt0.1

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

  8. Applied log-prod0.1

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

  9. Applied distribute-lft-in0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(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)))