Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	37×	body	2560	valid
6.0ms	184×	body	80	valid
5.0ms	36×	body	1280	valid
3.0ms	91×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

61.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune225.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
4.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
59.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* b_2 b_2) (* a c))
138.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
168.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune465.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.5b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.1b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
78.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
158.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
127.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
52.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune993.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
0.3b	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.6b	(- (* b_2 b_2) (* a c))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

807×	`times-frac`
516×	`add-sqr-sqrt`
423×	`*-un-lft-identity`
331×	`add-cube-cbrt`
92×	`difference-of-squares`
49×	`sqrt-prod`
48×	`add-exp-log`
46×	`distribute-lft-out--`
41×	`div-inv`
34×	`div-exp`
31×	`associate-/r/`
27×	`associate-/l*`
19×	`associate-/r*`
18×	`add-cbrt-cube`
17×	`flip3--` `flip--`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/` `inv-pow`

Counts

4 → 453

Calls

4 calls:

88.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
51.0ms	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
72.0ms	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
29.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1804	8007
1	5001	7267

prune626.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

regimes171.0ms

Accuracy

93.6% (1.6b remaining)

Error of 7.2b against oracle of 5.6b and baseline of 29.8b

bsearch131.0ms

Steps

Iters	Range		Point
6	2.905752377093217e+53	1.5130510757279288e+54	9.981010889976272e+53
11	4.542165024737633e-308	1.3813418935482828e-285	2.1783833196582517e-298
9	-8.8250320263031e+72	-8.58470807685748e+66	-8.687169645099805e+72

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

195.0ms	5915×	body	80	valid
192.0ms	1059×	body	2560	valid
133.0ms	880×	body	1280	valid
89.0ms	3014×	body	80	nan
58.0ms	461×	body	640	valid
27.0ms	122×	body	5120	valid
21.0ms	213×	body	320	valid
7.0ms	119×	body	160	valid