Average Error: 0.1 → 0.1
Time: 11.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \left({t}^{\frac{1}{3}}\right)\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \left({t}^{\frac{1}{3}}\right)\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{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 r323191 = x;
        double r323192 = y;
        double r323193 = r323191 + r323192;
        double r323194 = z;
        double r323195 = r323193 + r323194;
        double r323196 = t;
        double r323197 = log(r323196);
        double r323198 = r323194 * r323197;
        double r323199 = r323195 - r323198;
        double r323200 = a;
        double r323201 = 0.5;
        double r323202 = r323200 - r323201;
        double r323203 = b;
        double r323204 = r323202 * r323203;
        double r323205 = r323199 + r323204;
        return r323205;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r323206 = x;
        double r323207 = z;
        double r323208 = y;
        double r323209 = r323207 + r323208;
        double r323210 = r323206 + r323209;
        double r323211 = 2.0;
        double r323212 = t;
        double r323213 = 0.3333333333333333;
        double r323214 = pow(r323212, r323213);
        double r323215 = log(r323214);
        double r323216 = r323211 * r323215;
        double r323217 = r323216 * r323207;
        double r323218 = r323210 - r323217;
        double r323219 = cbrt(r323212);
        double r323220 = log(r323219);
        double r323221 = r323207 * r323220;
        double r323222 = r323218 - r323221;
        double r323223 = a;
        double r323224 = 0.5;
        double r323225 = r323223 - r323224;
        double r323226 = b;
        double r323227 = r323225 * r323226;
        double r323228 = r323222 + r323227;
        return r323228;
}

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-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \color{blue}{\left({t}^{\frac{1}{3}}\right)}\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(x + \left(z + y\right)\right) - \left(2 \cdot \log \left({t}^{\frac{1}{3}}\right)\right) \cdot z\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2020045 
(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)))