Average Error: 0.1 → 0.1
Time: 11.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(e^{\log \left({y}^{\frac{1}{3}}\right)}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(e^{\log \left({y}^{\frac{1}{3}}\right)}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68231 = x;
        double r68232 = y;
        double r68233 = log(r68232);
        double r68234 = r68231 * r68233;
        double r68235 = z;
        double r68236 = r68234 + r68235;
        double r68237 = t;
        double r68238 = r68236 + r68237;
        double r68239 = a;
        double r68240 = r68238 + r68239;
        double r68241 = b;
        double r68242 = 0.5;
        double r68243 = r68241 - r68242;
        double r68244 = c;
        double r68245 = log(r68244);
        double r68246 = r68243 * r68245;
        double r68247 = r68240 + r68246;
        double r68248 = i;
        double r68249 = r68232 * r68248;
        double r68250 = r68247 + r68249;
        return r68250;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68251 = x;
        double r68252 = 2.0;
        double r68253 = y;
        double r68254 = 0.3333333333333333;
        double r68255 = pow(r68253, r68254);
        double r68256 = log(r68255);
        double r68257 = exp(r68256);
        double r68258 = log(r68257);
        double r68259 = r68252 * r68258;
        double r68260 = r68251 * r68259;
        double r68261 = cbrt(r68253);
        double r68262 = log(r68261);
        double r68263 = r68251 * r68262;
        double r68264 = r68260 + r68263;
        double r68265 = z;
        double r68266 = r68264 + r68265;
        double r68267 = t;
        double r68268 = r68266 + r68267;
        double r68269 = a;
        double r68270 = r68268 + r68269;
        double r68271 = b;
        double r68272 = 0.5;
        double r68273 = r68271 - r68272;
        double r68274 = c;
        double r68275 = log(r68274);
        double r68276 = r68273 * r68275;
        double r68277 = r68270 + r68276;
        double r68278 = i;
        double r68279 = r68253 * r68278;
        double r68280 = r68277 + r68279;
        return r68280;
}

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

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied add-exp-log0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020020 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))