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

Average Error: 6.3 → 2.2

Time: 9.6s

Precision: 64

Math

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

↓

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r634351 = 2.0;
        double r634352 = x;
        double r634353 = y;
        double r634354 = r634352 * r634353;
        double r634355 = z;
        double r634356 = t;
        double r634357 = r634355 * r634356;
        double r634358 = r634354 + r634357;
        double r634359 = a;
        double r634360 = b;
        double r634361 = c;
        double r634362 = r634360 * r634361;
        double r634363 = r634359 + r634362;
        double r634364 = r634363 * r634361;
        double r634365 = i;
        double r634366 = r634364 * r634365;
        double r634367 = r634358 - r634366;
        double r634368 = r634351 * r634367;
        return r634368;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r634369 = 2.0;
        double r634370 = x;
        double r634371 = y;
        double r634372 = r634370 * r634371;
        double r634373 = z;
        double r634374 = t;
        double r634375 = r634373 * r634374;
        double r634376 = r634372 + r634375;
        double r634377 = a;
        double r634378 = b;
        double r634379 = c;
        double r634380 = r634378 * r634379;
        double r634381 = r634377 + r634380;
        double r634382 = i;
        double r634383 = r634379 * r634382;
        double r634384 = r634381 * r634383;
        double r634385 = cbrt(r634384);
        double r634386 = r634385 * r634385;
        double r634387 = r634386 * r634385;
        double r634388 = r634376 - r634387;
        double r634389 = r634369 * r634388;
        return r634389;
}

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	6.3
Target	1.9
Herbie	2.2

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

Derivation

1. Initial program 6.3

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

5. Applied add-cube-cbrt 2.2

   \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}}\right)\]

6. Final simplification 2.2

   \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

Reproduce

herbie shell --seed 2019322 
(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))))