Details

sample325.0ms

Algorithm

intervals

Results

38.0ms	196×	body	10240	exit
12.0ms	427×	body	80	nan
8.0ms	230×	body	80	valid
2.0ms	30×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 5.1b

localize19.0ms

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))
5.6b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp x) 1.0)

rewrite45.0ms

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:

13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify128.0ms

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

prune340.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.7b	(- (exp x) 1.0)
5.7b	(- (exp x) 1.0)
5.7b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-log-exp`
7×	`difference-of-squares`
6×	`sqrt-prod`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`

Counts

4 → 60

Calls

4 calls:

7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)
4.0ms	(- (exp x) 1.0)
4.0ms	(- (exp x) 1.0)

series94.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)
13.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)

simplify95.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	156	394
1	399	367
2	1035	363
3	2831	363
4	5002	363

prune264.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.1b	(* (exp x) (exp x))
5.6b	(- (* (exp x) (exp x)) (* 1.0 1.0))
5.6b	(- (exp (* 2.0 x)) 1.0)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`exp-prod`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-log-exp`
7×	`difference-of-squares`
6×	`add-exp-log`
5×	`distribute-lft-out`
4×	`pow-prod-down` `associate-/r` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`flip3--` `swap-sqr` `associate-r` `associate-l` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

24.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
8.0ms	(* (exp x) (exp x))
7.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)

series120.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
14.0ms	(* (exp x) (exp x))
25.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	415	859
1	1790	771
2	5002	753

prune306.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (* 2 x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
0.1b	(/ (- (exp (* 2 x)) (* 1.0 1.0)) (+ (exp x) 1.0))
5.6b	(- (exp (* 2.0 x)) 1.0)
5.6b	(- (exp (* 2 x)) (* 1.0 1.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
197×	`*-un-lft-identity`
169×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
54×	`difference-of-squares`
29×	`distribute-lft-out`
26×	`associate-/r*`
24×	`distribute-lft-out--`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 223

Calls

4 calls:

23.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (* 2 x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
13.0ms	(/ (- (exp (* 2 x)) (* 1.0 1.0)) (+ (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
3.0ms	(- (exp (* 2 x)) (* 1.0 1.0))

series171.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (* 2 x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
38.0ms	(/ (- (exp (* 2 x)) (* 1.0 1.0)) (+ (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp (* 2 x)) (* 1.0 1.0))

simplify114.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	931	4060
1	3886	3925
2	5002	3924

prune602.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes28.0ms

Accuracy

74.2% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.1b

bsearch50.0ms

Steps

Iters	Range		Point
7	-7.817435050815358e-11	-4.7780558611076405e-12	-7.542564620677507e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6622×	body	10240	exit
382.0ms	12573×	body	80	nan
245.0ms	7347×	body	80	valid
57.0ms	760×	body	160	valid