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

Average Error: 6.1 → 1.8

Time: 23.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r32212334 = 2.0;
        double r32212335 = x;
        double r32212336 = y;
        double r32212337 = r32212335 * r32212336;
        double r32212338 = z;
        double r32212339 = t;
        double r32212340 = r32212338 * r32212339;
        double r32212341 = r32212337 + r32212340;
        double r32212342 = a;
        double r32212343 = b;
        double r32212344 = c;
        double r32212345 = r32212343 * r32212344;
        double r32212346 = r32212342 + r32212345;
        double r32212347 = r32212346 * r32212344;
        double r32212348 = i;
        double r32212349 = r32212347 * r32212348;
        double r32212350 = r32212341 - r32212349;
        double r32212351 = r32212334 * r32212350;
        return r32212351;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r32212352 = 2.0;
        double r32212353 = y;
        double r32212354 = x;
        double r32212355 = r32212353 * r32212354;
        double r32212356 = z;
        double r32212357 = t;
        double r32212358 = r32212356 * r32212357;
        double r32212359 = r32212355 + r32212358;
        double r32212360 = a;
        double r32212361 = b;
        double r32212362 = c;
        double r32212363 = r32212361 * r32212362;
        double r32212364 = r32212360 + r32212363;
        double r32212365 = i;
        double r32212366 = r32212362 * r32212365;
        double r32212367 = r32212364 * r32212366;
        double r32212368 = r32212359 - r32212367;
        double r32212369 = r32212352 * r32212368;
        return r32212369;
}

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	6.1
Target	1.8
Herbie	1.8

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

Derivation

1. Initial program 6.1

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

3. Applied associate-*l* 1.8

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

4. Final simplification 1.8

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

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

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