Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Average Error: 5.7 → 0.8

Time: 13.3s

Precision: binary64

Math

\[\]

↓

\[\]

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * 18.0)) * y)) * z)) * t)) - ((double) (((double) (a * 4.0)) * t)))) + ((double) (b * c)))) - ((double) (((double) (x * 4.0)) * i)))) - ((double) (((double) (j * 27.0)) * k))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double VAR;
	if ((((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * 18.0)) * y)) * z)) * t)) - ((double) (t * ((double) (a * 4.0)))))) + ((double) (b * c)))) - ((double) (((double) (x * 4.0)) * i)))) <= -inf.0)) {
		VAR = ((double) (((double) (x * ((double) (18.0 * ((double) (y * ((double) (z * t)))))))) + ((double) (((double) (b * c)) - ((double) (((double) (j * ((double) (27.0 * k)))) + ((double) (4.0 * ((double) (((double) (t * a)) + ((double) (x * i))))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * 18.0)) * y)) * z)) * t)) - ((double) (t * ((double) (a * 4.0)))))) + ((double) (b * c)))) - ((double) (((double) (x * 4.0)) * i)))) <= 1.1019728281780955e+308)) {
			VAR_1 = ((double) (((double) (((double) (((double) (b * c)) + ((double) (((double) (t * ((double) (z * ((double) (x * ((double) (18.0 * y)))))))) - ((double) (t * ((double) (a * 4.0)))))))) - ((double) (((double) (x * 4.0)) * i)))) - ((double) (k * ((double) (j * 27.0))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (((double) (b * c)) + ((double) (((double) (((double) sqrt(((double) (x * ((double) (((double) (z * t)) * ((double) (18.0 * y)))))))) * ((double) sqrt(((double) (x * ((double) (((double) (z * t)) * ((double) (18.0 * y)))))))))) - ((double) (t * ((double) (a * 4.0)))))))) - ((double) (((double) (x * 4.0)) * i)))) - ((double) (k * ((double) (j * 27.0))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Bits error versus j

Bits error versus k

Target

Original	5.7
Target	1.4
Herbie	0.8

\[\]

Derivation

1. Split input into 3 regimes

2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0

   1. Initial program 64.0

      \[\]

   2. Simplified 5.4

      \[\leadsto \]

   if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 1.1019728281780955e308

   1. Initial program 0.3

      \[\]
   2. Using strategy rm

   3. Applied *-un-lft-identity 0.3

      \[\leadsto \]

   4. Applied associate-*r* 0.3

      \[\leadsto \]

   5. Simplified 0.4

      \[\leadsto \]

   if 1.1019728281780955e308 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

   1. Initial program 62.8

      \[\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 63.0

      \[\leadsto \]

   4. Simplified 63.2

      \[\leadsto \]

   5. Simplified 4.4

      \[\leadsto \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))