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

Average Error: 6.2 → 1.6

Time: 6.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r768374 = 2.0;
        double r768375 = x;
        double r768376 = y;
        double r768377 = r768375 * r768376;
        double r768378 = z;
        double r768379 = t;
        double r768380 = r768378 * r768379;
        double r768381 = r768377 + r768380;
        double r768382 = a;
        double r768383 = b;
        double r768384 = c;
        double r768385 = r768383 * r768384;
        double r768386 = r768382 + r768385;
        double r768387 = r768386 * r768384;
        double r768388 = i;
        double r768389 = r768387 * r768388;
        double r768390 = r768381 - r768389;
        double r768391 = r768374 * r768390;
        return r768391;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r768392 = 2.0;
        double r768393 = x;
        double r768394 = y;
        double r768395 = r768393 * r768394;
        double r768396 = z;
        double r768397 = t;
        double r768398 = r768396 * r768397;
        double r768399 = r768395 + r768398;
        double r768400 = a;
        double r768401 = b;
        double r768402 = c;
        double r768403 = r768401 * r768402;
        double r768404 = r768400 + r768403;
        double r768405 = i;
        double r768406 = r768402 * r768405;
        double r768407 = r768404 * r768406;
        double r768408 = r768399 - r768407;
        double r768409 = r768392 * r768408;
        return r768409;
}

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	6.2
Target	1.6
Herbie	1.6

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

Derivation

1. Initial program 6.2

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

3. Applied associate-*l* 1.6

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

4. Final simplification 1.6

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

Reproduce

herbie shell --seed 2020034 
(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))))