Average Error: 0.1 → 0.1
Time: 5.8s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + z \cdot \left(1 - \log \left(\sqrt{t}\right) \cdot 2\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + y\right) + z \cdot \left(1 - \log \left(\sqrt{t}\right) \cdot 2\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r453123 = x;
        double r453124 = y;
        double r453125 = r453123 + r453124;
        double r453126 = z;
        double r453127 = r453125 + r453126;
        double r453128 = t;
        double r453129 = log(r453128);
        double r453130 = r453126 * r453129;
        double r453131 = r453127 - r453130;
        double r453132 = a;
        double r453133 = 0.5;
        double r453134 = r453132 - r453133;
        double r453135 = b;
        double r453136 = r453134 * r453135;
        double r453137 = r453131 + r453136;
        return r453137;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r453138 = x;
        double r453139 = y;
        double r453140 = r453138 + r453139;
        double r453141 = z;
        double r453142 = 1.0;
        double r453143 = t;
        double r453144 = sqrt(r453143);
        double r453145 = log(r453144);
        double r453146 = 2.0;
        double r453147 = r453145 * r453146;
        double r453148 = r453142 - r453147;
        double r453149 = r453141 * r453148;
        double r453150 = r453140 + r453149;
        double r453151 = a;
        double r453152 = 0.5;
        double r453153 = r453151 - r453152;
        double r453154 = b;
        double r453155 = r453153 * r453154;
        double r453156 = r453150 + r453155;
        return r453156;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  9. Applied associate--l+0.1

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

  11. Applied associate--l+0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(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)))