Average Error: 0.1 → 0.1
Time: 30.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]
\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]{-c} \cdot \sqrt[3]{-1}\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 r68198 = x;
        double r68199 = y;
        double r68200 = log(r68199);
        double r68201 = r68198 * r68200;
        double r68202 = z;
        double r68203 = r68201 + r68202;
        double r68204 = t;
        double r68205 = r68203 + r68204;
        double r68206 = a;
        double r68207 = r68205 + r68206;
        double r68208 = b;
        double r68209 = 0.5;
        double r68210 = r68208 - r68209;
        double r68211 = c;
        double r68212 = log(r68211);
        double r68213 = r68210 * r68212;
        double r68214 = r68207 + r68213;
        double r68215 = i;
        double r68216 = r68199 * r68215;
        double r68217 = r68214 + r68216;
        return r68217;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68218 = x;
        double r68219 = y;
        double r68220 = log(r68219);
        double r68221 = r68218 * r68220;
        double r68222 = z;
        double r68223 = r68221 + r68222;
        double r68224 = t;
        double r68225 = r68223 + r68224;
        double r68226 = a;
        double r68227 = r68225 + r68226;
        double r68228 = c;
        double r68229 = -r68228;
        double r68230 = cbrt(r68229);
        double r68231 = -1.0;
        double r68232 = cbrt(r68231);
        double r68233 = r68230 * r68232;
        double r68234 = log(r68233);
        double r68235 = 3.0;
        double r68236 = b;
        double r68237 = r68235 * r68236;
        double r68238 = 1.5;
        double r68239 = r68237 - r68238;
        double r68240 = r68234 * r68239;
        double r68241 = r68227 + r68240;
        double r68242 = i;
        double r68243 = r68219 * r68242;
        double r68244 = r68241 + r68243;
        return r68244;
}

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. Simplified0.1

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

  8. Taylor expanded around -inf 64.0

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))