Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Average Error: 6.4 → 1.9

Time: 32.4s

Precision: 64

Math

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]

↓

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r481333 = 2.0;
        double r481334 = x;
        double r481335 = y;
        double r481336 = r481334 * r481335;
        double r481337 = z;
        double r481338 = t;
        double r481339 = r481337 * r481338;
        double r481340 = r481336 + r481339;
        double r481341 = a;
        double r481342 = b;
        double r481343 = c;
        double r481344 = r481342 * r481343;
        double r481345 = r481341 + r481344;
        double r481346 = r481345 * r481343;
        double r481347 = i;
        double r481348 = r481346 * r481347;
        double r481349 = r481340 - r481348;
        double r481350 = r481333 * r481349;
        return r481350;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r481351 = 2.0;
        double r481352 = x;
        double r481353 = y;
        double r481354 = r481352 * r481353;
        double r481355 = z;
        double r481356 = t;
        double r481357 = r481355 * r481356;
        double r481358 = r481354 + r481357;
        double r481359 = a;
        double r481360 = b;
        double r481361 = c;
        double r481362 = r481360 * r481361;
        double r481363 = r481359 + r481362;
        double r481364 = i;
        double r481365 = r481364 * r481361;
        double r481366 = r481363 * r481365;
        double r481367 = r481358 - r481366;
        double r481368 = r481351 * r481367;
        return r481368;
}

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

Target

Original	6.4
Target	1.9
Herbie	1.9

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

1. Initial program 6.4

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

3. Applied associate-*l* 1.9

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

4. Simplified 1.9

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

5. Final simplification 1.9

   \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))