Average Error: 0.1 → 0.1
Time: 19.8s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \log \left(\sqrt{\sqrt{t}}\right)\right) - z \cdot \log \left(\sqrt{\sqrt{t}}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt{t}\right) \cdot z\right) - z \cdot \log \left(\sqrt{\sqrt{t}}\right)\right) - z \cdot \log \left(\sqrt{\sqrt{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 r300084 = x;
        double r300085 = y;
        double r300086 = r300084 + r300085;
        double r300087 = z;
        double r300088 = r300086 + r300087;
        double r300089 = t;
        double r300090 = log(r300089);
        double r300091 = r300087 * r300090;
        double r300092 = r300088 - r300091;
        double r300093 = a;
        double r300094 = 0.5;
        double r300095 = r300093 - r300094;
        double r300096 = b;
        double r300097 = r300095 * r300096;
        double r300098 = r300092 + r300097;
        return r300098;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r300099 = x;
        double r300100 = y;
        double r300101 = r300099 + r300100;
        double r300102 = z;
        double r300103 = r300101 + r300102;
        double r300104 = t;
        double r300105 = sqrt(r300104);
        double r300106 = log(r300105);
        double r300107 = r300106 * r300102;
        double r300108 = r300103 - r300107;
        double r300109 = sqrt(r300105);
        double r300110 = log(r300109);
        double r300111 = r300102 * r300110;
        double r300112 = r300108 - r300111;
        double r300113 = r300112 - r300111;
        double r300114 = a;
        double r300115 = 0.5;
        double r300116 = r300114 - r300115;
        double r300117 = b;
        double r300118 = r300116 * r300117;
        double r300119 = r300113 + r300118;
        return r300119;
}

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 add-sqr-sqrt0.1

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

  10. Applied sqrt-prod0.1

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

  11. Applied log-prod0.1

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

  12. Applied distribute-lft-in0.1

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

  13. Applied associate--r+0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(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)))