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

Average Error: 6.7 → 1.9

Time: 20.2s

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 r572522 = 2.0;
        double r572523 = x;
        double r572524 = y;
        double r572525 = r572523 * r572524;
        double r572526 = z;
        double r572527 = t;
        double r572528 = r572526 * r572527;
        double r572529 = r572525 + r572528;
        double r572530 = a;
        double r572531 = b;
        double r572532 = c;
        double r572533 = r572531 * r572532;
        double r572534 = r572530 + r572533;
        double r572535 = r572534 * r572532;
        double r572536 = i;
        double r572537 = r572535 * r572536;
        double r572538 = r572529 - r572537;
        double r572539 = r572522 * r572538;
        return r572539;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r572540 = 2.0;
        double r572541 = x;
        double r572542 = y;
        double r572543 = r572541 * r572542;
        double r572544 = z;
        double r572545 = t;
        double r572546 = r572544 * r572545;
        double r572547 = r572543 + r572546;
        double r572548 = a;
        double r572549 = b;
        double r572550 = c;
        double r572551 = r572549 * r572550;
        double r572552 = r572548 + r572551;
        double r572553 = i;
        double r572554 = r572553 * r572550;
        double r572555 = r572552 * r572554;
        double r572556 = r572547 - r572555;
        double r572557 = r572540 * r572556;
        return r572557;
}

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	6.7
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 6.7

   \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
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 2019235 
(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))))