Average Error: 0.1 → 0.1
Time: 21.8s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[x - \left(\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(0.5 - a\right) \cdot b\right)\right) - \left(z + y\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
x - \left(\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(0.5 - a\right) \cdot b\right)\right) - \left(z + y\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r353003 = x;
        double r353004 = y;
        double r353005 = r353003 + r353004;
        double r353006 = z;
        double r353007 = r353005 + r353006;
        double r353008 = t;
        double r353009 = log(r353008);
        double r353010 = r353006 * r353009;
        double r353011 = r353007 - r353010;
        double r353012 = a;
        double r353013 = 0.5;
        double r353014 = r353012 - r353013;
        double r353015 = b;
        double r353016 = r353014 * r353015;
        double r353017 = r353011 + r353016;
        return r353017;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r353018 = x;
        double r353019 = t;
        double r353020 = cbrt(r353019);
        double r353021 = r353020 * r353020;
        double r353022 = log(r353021);
        double r353023 = z;
        double r353024 = r353022 * r353023;
        double r353025 = log(r353020);
        double r353026 = r353023 * r353025;
        double r353027 = 0.5;
        double r353028 = a;
        double r353029 = r353027 - r353028;
        double r353030 = b;
        double r353031 = r353029 * r353030;
        double r353032 = r353026 + r353031;
        double r353033 = r353024 + r353032;
        double r353034 = y;
        double r353035 = r353023 + r353034;
        double r353036 = r353033 - r353035;
        double r353037 = r353018 - r353036;
        return r353037;
}

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. Simplified0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Applied associate-+l+0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))