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

Average Error: 20.7 → 3.4

Time: 8.1s

Precision: binary64

Math

\[\]

↓

\[\]

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double VAR;
	if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= -8.772159371079582e+301)) {
		VAR = ((double) (((double) (b / ((double) (z * c)))) + ((double) (((double) (9.0 * ((double) (y * ((double) (x / ((double) (z * c)))))))) - ((double) (4.0 * ((double) (a * ((double) (t / c))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= -1.5562810163873928e-297)) {
			VAR_1 = ((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c))));
		} else {
			double VAR_2;
			if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= 3.3798607097195475e+22)) {
				VAR_2 = ((double) (((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) + b)) / z)) - ((double) (4.0 * ((double) (t * a)))))) / c));
			} else {
				double VAR_3;
				if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= 1.246074611410355e+302)) {
					VAR_3 = ((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c))));
				} else {
					VAR_3 = ((double) (((double) (b / ((double) (z * c)))) + ((double) (((double) (9.0 * ((double) (y * ((double) (1.0 / ((double) (c * ((double) (z / x)))))))))) - ((double) (4.0 * ((double) (t * ((double) (a / c))))))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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

Target

Original	20.7
Target	15.0
Herbie	3.4

\[\]

Derivation

1. Split input into 4 regimes

2. if (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -8.7721593710795818e301

   1. Initial program 60.4

      \[\]

   2. Simplified 22.9

      \[\leadsto \]

   3. Taylor expanded around 0 26.7

      \[\leadsto \]

   4. Simplified 8.8

      \[\leadsto \]
   5. Using strategy rm

   6. Applied add-cube-cbrt 9.5

      \[\leadsto \]

   7. Applied *-un-lft-identity 9.5

      \[\leadsto \]

   8. Applied times-frac 9.5

      \[\leadsto \]

   9. Applied associate-*r* 13.1

      \[\leadsto \]

   10. Simplified 13.1

       \[\leadsto \]

   11. Taylor expanded around 0 15.2

       \[\leadsto \]

   12. Simplified 13.6

       \[\leadsto \]

   if -8.7721593710795818e301 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -1.5562810163873928e-297 or 3.37986070971954747e22 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 1.24607461141035502e302

   1. Initial program 0.6

      \[\]

   if -1.5562810163873928e-297 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 3.37986070971954747e22

   1. Initial program 19.4

      \[\]

   2. Simplified 0.8

      \[\leadsto \]
   3. Using strategy rm

   4. Applied associate-*r* 0.8

      \[\leadsto \]

   if 1.24607461141035502e302 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))

   1. Initial program 63.1

      \[\]

   2. Simplified 26.7

      \[\leadsto \]

   3. Taylor expanded around 0 30.4

      \[\leadsto \]

   4. Simplified 15.4

      \[\leadsto \]
   5. Using strategy rm

   6. Applied clear-num 15.4

      \[\leadsto \]

   7. Simplified 10.3

      \[\leadsto \]
3. Recombined 4 regimes into one program.

4. Final simplification 3.4

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.1001567408041051e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))