Average Error: 0.1 → 0.1
Time: 26.3s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + \left(z - \log \left(\sqrt{t}\right) \cdot \left(z + z\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\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) + \left(z - \log \left(\sqrt{t}\right) \cdot \left(z + z\right)\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r372137 = x;
        double r372138 = y;
        double r372139 = r372137 + r372138;
        double r372140 = z;
        double r372141 = r372139 + r372140;
        double r372142 = t;
        double r372143 = log(r372142);
        double r372144 = r372140 * r372143;
        double r372145 = r372141 - r372144;
        double r372146 = a;
        double r372147 = 0.5;
        double r372148 = r372146 - r372147;
        double r372149 = b;
        double r372150 = r372148 * r372149;
        double r372151 = r372145 + r372150;
        return r372151;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r372152 = x;
        double r372153 = y;
        double r372154 = r372152 + r372153;
        double r372155 = z;
        double r372156 = t;
        double r372157 = sqrt(r372156);
        double r372158 = log(r372157);
        double r372159 = r372155 + r372155;
        double r372160 = r372158 * r372159;
        double r372161 = r372155 - r372160;
        double r372162 = r372154 + r372161;
        double r372163 = a;
        double r372164 = 0.5;
        double r372165 = r372163 - r372164;
        double r372166 = b;
        double r372167 = r372165 * r372166;
        double r372168 = r372162 + r372167;
        return r372168;
}

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
Target0.4
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. Applied associate--l+0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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)))