Average Error: 0.0 → 0.7
Time: 16.6s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\left(z \cdot t + x \cdot y\right) + \left(\sqrt[3]{c \cdot i + a \cdot b} \cdot \sqrt[3]{c \cdot i + a \cdot b}\right) \cdot \sqrt[3]{c \cdot i + a \cdot b}\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\left(z \cdot t + x \cdot y\right) + \left(\sqrt[3]{c \cdot i + a \cdot b} \cdot \sqrt[3]{c \cdot i + a \cdot b}\right) \cdot \sqrt[3]{c \cdot i + a \cdot b}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5617254 = x;
        double r5617255 = y;
        double r5617256 = r5617254 * r5617255;
        double r5617257 = z;
        double r5617258 = t;
        double r5617259 = r5617257 * r5617258;
        double r5617260 = r5617256 + r5617259;
        double r5617261 = a;
        double r5617262 = b;
        double r5617263 = r5617261 * r5617262;
        double r5617264 = r5617260 + r5617263;
        double r5617265 = c;
        double r5617266 = i;
        double r5617267 = r5617265 * r5617266;
        double r5617268 = r5617264 + r5617267;
        return r5617268;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5617269 = z;
        double r5617270 = t;
        double r5617271 = r5617269 * r5617270;
        double r5617272 = x;
        double r5617273 = y;
        double r5617274 = r5617272 * r5617273;
        double r5617275 = r5617271 + r5617274;
        double r5617276 = c;
        double r5617277 = i;
        double r5617278 = r5617276 * r5617277;
        double r5617279 = a;
        double r5617280 = b;
        double r5617281 = r5617279 * r5617280;
        double r5617282 = r5617278 + r5617281;
        double r5617283 = cbrt(r5617282);
        double r5617284 = r5617283 * r5617283;
        double r5617285 = r5617284 * r5617283;
        double r5617286 = r5617275 + r5617285;
        return r5617286;
}

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 0.0

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

  3. Applied associate-+l+0.0

    \[\leadsto \color{blue}{\left(x \cdot y + z \cdot t\right) + \left(a \cdot b + c \cdot i\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))