Details

sample276.0ms

Algorithm

intervals

Results

8.0ms	193×	body	80	valid
6.0ms	33×	body	2560	valid
4.0ms	30×	body	1280	valid
3.0ms	102×	body	80	nan
1.0ms	6×	body	5120	valid
1.0ms	9×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

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:

41.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
2.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

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

prune249.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
4.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.0b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
24.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
152.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
186.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (82.0ms)

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

prune489.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.4b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.4b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
45.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
167.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
131.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

745×	`times-frac`
479×	`add-sqr-sqrt`
392×	`*-un-lft-identity`
306×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
43×	`distribute-lft-out--`
38×	`div-inv`
37×	`add-exp-log`
29×	`div-exp`
22×	`associate-/r*`
16×	`add-cbrt-cube`
13×	`associate-/l*`
10×	`1-exp`
8×	`cbrt-undiv` `add-log-exp`
5×	`pow1`
4×	`rec-exp`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `associate-/l/`

Counts

4 → 393

Calls

4 calls:

32.0ms	(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
31.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify89.0ms

Algorithm

egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1632	6452
1	5001	5776

prune390.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.8b

regimes142.0ms

Accuracy

93.5% (1.5b remaining)

Error of 7.2b against oracle of 5.7b and baseline of 29.3b

bsearch124.0ms

Steps

Iters	Range		Point
7	7.8930669794294e+68	1.794276654474529e+70	1.7701741483501238e+70
8	1.1323007768539012e-246	2.166838235984046e-243	1.9220534958503673e-246
8	-2.75227652547193e+57	-2.8729039666377685e+54	-2.237522594933402e+57

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	19
1	39	19
2	39	19

end0.0ms

sample967.0ms

Algorithm

intervals

Results

201.0ms	1059×	body	2560	valid
193.0ms	5874×	body	80	valid
132.0ms	884×	body	1280	valid
86.0ms	2865×	body	80	nan
55.0ms	448×	body	640	valid
30.0ms	117×	body	5120	valid
18.0ms	208×	body	320	valid
7.0ms	126×	body	160	valid