Average Error: 0.1 → 0.1
Time: 37.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-1} \cdot \sqrt[3]{-c}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]
\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]{-1} \cdot \sqrt[3]{-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 r76266 = x;
        double r76267 = y;
        double r76268 = log(r76267);
        double r76269 = r76266 * r76268;
        double r76270 = z;
        double r76271 = r76269 + r76270;
        double r76272 = t;
        double r76273 = r76271 + r76272;
        double r76274 = a;
        double r76275 = r76273 + r76274;
        double r76276 = b;
        double r76277 = 0.5;
        double r76278 = r76276 - r76277;
        double r76279 = c;
        double r76280 = log(r76279);
        double r76281 = r76278 * r76280;
        double r76282 = r76275 + r76281;
        double r76283 = i;
        double r76284 = r76267 * r76283;
        double r76285 = r76282 + r76284;
        return r76285;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r76286 = x;
        double r76287 = y;
        double r76288 = log(r76287);
        double r76289 = r76286 * r76288;
        double r76290 = z;
        double r76291 = r76289 + r76290;
        double r76292 = t;
        double r76293 = r76291 + r76292;
        double r76294 = a;
        double r76295 = r76293 + r76294;
        double r76296 = -1.0;
        double r76297 = cbrt(r76296);
        double r76298 = c;
        double r76299 = -r76298;
        double r76300 = cbrt(r76299);
        double r76301 = r76297 * r76300;
        double r76302 = log(r76301);
        double r76303 = 3.0;
        double r76304 = b;
        double r76305 = r76303 * r76304;
        double r76306 = 1.5;
        double r76307 = r76305 - r76306;
        double r76308 = r76302 * r76307;
        double r76309 = r76295 + r76308;
        double r76310 = i;
        double r76311 = r76287 * r76310;
        double r76312 = r76309 + r76311;
        return r76312;
}

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

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

  7. Taylor expanded around -inf 64.0

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(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)))