Details

sample409.0ms

Algorithm

intervals

Results

57.0ms	186×	body	10240	exit
13.0ms	444×	body	80	nan
8.0ms	238×	body	80	valid
1.0ms	18×	body	160	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp x) 1.0)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

30.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
45.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series208.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
63.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify121.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune329.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (exp (* 2.0 x)))
0.1b	(sqrt (exp (* 2.0 x)))
3.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.9b	(- (exp x) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-pow1`
5×	`difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
5.0ms	(sqrt (exp (* 2.0 x)))
18.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series112.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (exp (* 2.0 x)))
26.0ms	(sqrt (exp (* 2.0 x)))
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify103.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5001	361

prune206.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp 2.0) (* 1/2 x))
0.1b	(sqrt (exp (* 2.0 x)))
3.9b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
3.9b	(- (exp x) 1.0)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-log-exp`
7×	`add-cube-cbrt` `difference-of-squares`
6×	`pow1` `sqrt-prod`
5×	`unpow-prod-down`
4×	`add-exp-log` `exp-prod` `pow-pow` `add-cbrt-cube`
3×	`sqrt-pow1` `sqr-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `exp-to-pow` `pow1/2` `pow-exp`

Counts

4 → 66

Calls

4 calls:

5.0ms	(pow (exp 2.0) (* 1/2 x))
5.0ms	(sqrt (exp (* 2.0 x)))
29.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
11.0ms	(- (exp x) 1.0)

series125.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (exp 2.0) (* 1/2 x))
27.0ms	(sqrt (exp (* 2.0 x)))
55.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	243	428
1	686	409
2	2418	406
3	5002	404

prune264.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0)) 3))
0.1b	(sqrt (exp (* 2.0 x)))
3.9b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
3.9b	(- (exp x) 1.0)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
26×	`cbrt-prod`
19×	`difference-of-squares`
16×	`unpow-prod-down` `*-un-lft-identity`
12×	`sqrt-prod`
10×	`cube-prod`
9×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
3×	`flip3--` `sqrt-pow1` `flip--`
2×	`cube-div` `sub-neg` `cbrt-div` `diff-log`
1×	`cube-mult` `rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `pow1/3` `unpow3` `rem-cbrt-cube`

Counts

4 → 85

Calls

4 calls:

32.0ms	(cbrt (pow (- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0)) 3))
3.0ms	(sqrt (exp (* 2.0 x)))
32.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series151.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (pow (- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0)) 3))
23.0ms	(sqrt (exp (* 2.0 x)))
56.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify118.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	321	760
1	1056	752
2	4432	747
3	5001	747

prune310.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

97.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 3.2b

bsearch88.0ms

Steps

Iters	Range		Point
7	3.852731749716052e-11	2.2756628391411034e-09	4.626269415052568e-10
9	-5.8848704152608634e-05	-2.0012008038825942e-10	-8.128074973713997e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	37
1	46	37

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6416×	body	10240	exit
392.0ms	12703×	body	80	nan
259.0ms	7391×	body	80	valid
58.0ms	741×	body	160	valid