Average Error: 0.1 → 0.1
Time: 37.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{\sqrt{c}} \cdot \sqrt[3]{\sqrt{c}}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]
\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(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{\sqrt{c}} \cdot \sqrt[3]{\sqrt{c}}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70178 = x;
        double r70179 = y;
        double r70180 = log(r70179);
        double r70181 = r70178 * r70180;
        double r70182 = z;
        double r70183 = r70181 + r70182;
        double r70184 = t;
        double r70185 = r70183 + r70184;
        double r70186 = a;
        double r70187 = r70185 + r70186;
        double r70188 = b;
        double r70189 = 0.5;
        double r70190 = r70188 - r70189;
        double r70191 = c;
        double r70192 = log(r70191);
        double r70193 = r70190 * r70192;
        double r70194 = r70187 + r70193;
        double r70195 = i;
        double r70196 = r70179 * r70195;
        double r70197 = r70194 + r70196;
        return r70197;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70198 = x;
        double r70199 = y;
        double r70200 = log(r70199);
        double r70201 = r70198 * r70200;
        double r70202 = z;
        double r70203 = r70201 + r70202;
        double r70204 = t;
        double r70205 = r70203 + r70204;
        double r70206 = a;
        double r70207 = r70205 + r70206;
        double r70208 = c;
        double r70209 = sqrt(r70208);
        double r70210 = cbrt(r70209);
        double r70211 = r70210 * r70210;
        double r70212 = log(r70211);
        double r70213 = 3.0;
        double r70214 = b;
        double r70215 = r70213 * r70214;
        double r70216 = 1.5;
        double r70217 = r70215 - r70216;
        double r70218 = r70212 * r70217;
        double r70219 = r70207 + r70218;
        double r70220 = i;
        double r70221 = r70199 * r70220;
        double r70222 = r70219 + r70221;
        return r70222;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Taylor expanded around inf 0.1

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

  8. Taylor expanded around 0 0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(3 \cdot \left(\log \left({c}^{\frac{1}{3}}\right) \cdot b\right) - 1.5 \cdot \log \left({c}^{\frac{1}{3}}\right)\right)}\right) + y \cdot i\]

  9. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\log \left(\sqrt[3]{c}\right) \cdot \left(3 \cdot b - 1.5\right)}\right) + y \cdot i\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{\color{blue}{\sqrt{c} \cdot \sqrt{c}}}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]

  12. Applied cbrt-prod0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \color{blue}{\left(\sqrt[3]{\sqrt{c}} \cdot \sqrt[3]{\sqrt{c}}\right)} \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]

  13. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{\sqrt{c}} \cdot \sqrt[3]{\sqrt{c}}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019325 
(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)))