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

Average Error: 6.1 → 1.5

Time: 35.3s

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 r515480 = 2.0;
        double r515481 = x;
        double r515482 = y;
        double r515483 = r515481 * r515482;
        double r515484 = z;
        double r515485 = t;
        double r515486 = r515484 * r515485;
        double r515487 = r515483 + r515486;
        double r515488 = a;
        double r515489 = b;
        double r515490 = c;
        double r515491 = r515489 * r515490;
        double r515492 = r515488 + r515491;
        double r515493 = r515492 * r515490;
        double r515494 = i;
        double r515495 = r515493 * r515494;
        double r515496 = r515487 - r515495;
        double r515497 = r515480 * r515496;
        return r515497;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r515498 = 2.0;
        double r515499 = x;
        double r515500 = y;
        double r515501 = r515499 * r515500;
        double r515502 = z;
        double r515503 = t;
        double r515504 = r515502 * r515503;
        double r515505 = r515501 + r515504;
        double r515506 = a;
        double r515507 = b;
        double r515508 = c;
        double r515509 = r515507 * r515508;
        double r515510 = r515506 + r515509;
        double r515511 = i;
        double r515512 = r515508 * r515511;
        double r515513 = r515510 * r515512;
        double r515514 = r515505 - r515513;
        double r515515 = r515498 * r515514;
        return r515515;
}

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	1.5
Herbie	1.5

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

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* 1.5

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

4. Final simplification 1.5

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

Reproduce

herbie shell --seed 2019323 
(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))))