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

Average Error: 6.2 → 1.8

Time: 25.8s

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 r18399522 = 2.0;
        double r18399523 = x;
        double r18399524 = y;
        double r18399525 = r18399523 * r18399524;
        double r18399526 = z;
        double r18399527 = t;
        double r18399528 = r18399526 * r18399527;
        double r18399529 = r18399525 + r18399528;
        double r18399530 = a;
        double r18399531 = b;
        double r18399532 = c;
        double r18399533 = r18399531 * r18399532;
        double r18399534 = r18399530 + r18399533;
        double r18399535 = r18399534 * r18399532;
        double r18399536 = i;
        double r18399537 = r18399535 * r18399536;
        double r18399538 = r18399529 - r18399537;
        double r18399539 = r18399522 * r18399538;
        return r18399539;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r18399540 = 2.0;
        double r18399541 = y;
        double r18399542 = x;
        double r18399543 = r18399541 * r18399542;
        double r18399544 = z;
        double r18399545 = t;
        double r18399546 = r18399544 * r18399545;
        double r18399547 = r18399543 + r18399546;
        double r18399548 = a;
        double r18399549 = b;
        double r18399550 = c;
        double r18399551 = r18399549 * r18399550;
        double r18399552 = r18399548 + r18399551;
        double r18399553 = i;
        double r18399554 = r18399550 * r18399553;
        double r18399555 = r18399552 * r18399554;
        double r18399556 = r18399547 - r18399555;
        double r18399557 = r18399540 * r18399556;
        return r18399557;
}

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 2019171 
(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))))