Average Error: 0.0 → 0.0
Time: 1.6m
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\left(z \cdot t + x \cdot y\right) + \left(c \cdot i + a \cdot b\right)\]
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r17931331 = x;
        double r17931332 = y;
        double r17931333 = r17931331 * r17931332;
        double r17931334 = z;
        double r17931335 = t;
        double r17931336 = r17931334 * r17931335;
        double r17931337 = r17931333 + r17931336;
        double r17931338 = a;
        double r17931339 = b;
        double r17931340 = r17931338 * r17931339;
        double r17931341 = r17931337 + r17931340;
        double r17931342 = c;
        double r17931343 = i;
        double r17931344 = r17931342 * r17931343;
        double r17931345 = r17931341 + r17931344;
        return r17931345;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r17931346 = z;
        double r17931347 = t;
        double r17931348 = r17931346 * r17931347;
        double r17931349 = x;
        double r17931350 = y;
        double r17931351 = r17931349 * r17931350;
        double r17931352 = r17931348 + r17931351;
        double r17931353 = c;
        double r17931354 = i;
        double r17931355 = r17931353 * r17931354;
        double r17931356 = a;
        double r17931357 = b;
        double r17931358 = r17931356 * r17931357;
        double r17931359 = r17931355 + r17931358;
        double r17931360 = r17931352 + r17931359;
        return r17931360;
}


\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(c \cdot i + a \cdot b\right)

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

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))