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

Average Error: 6.2 → 1.8

Time: 29.1s

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 r36510403 = 2.0;
        double r36510404 = x;
        double r36510405 = y;
        double r36510406 = r36510404 * r36510405;
        double r36510407 = z;
        double r36510408 = t;
        double r36510409 = r36510407 * r36510408;
        double r36510410 = r36510406 + r36510409;
        double r36510411 = a;
        double r36510412 = b;
        double r36510413 = c;
        double r36510414 = r36510412 * r36510413;
        double r36510415 = r36510411 + r36510414;
        double r36510416 = r36510415 * r36510413;
        double r36510417 = i;
        double r36510418 = r36510416 * r36510417;
        double r36510419 = r36510410 - r36510418;
        double r36510420 = r36510403 * r36510419;
        return r36510420;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r36510421 = 2.0;
        double r36510422 = y;
        double r36510423 = x;
        double r36510424 = r36510422 * r36510423;
        double r36510425 = z;
        double r36510426 = t;
        double r36510427 = r36510425 * r36510426;
        double r36510428 = r36510424 + r36510427;
        double r36510429 = a;
        double r36510430 = b;
        double r36510431 = c;
        double r36510432 = r36510430 * r36510431;
        double r36510433 = r36510429 + r36510432;
        double r36510434 = i;
        double r36510435 = r36510431 * r36510434;
        double r36510436 = r36510433 * r36510435;
        double r36510437 = r36510428 - r36510436;
        double r36510438 = r36510421 * r36510437;
        return r36510438;
}

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	1.8
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 6.2

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

3. Applied associate-*l* 1.8

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

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 2019172 
(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))))