Details

sample401.0ms

Algorithm

intervals

Results

35.0ms	182×	body	10240	exit
27.0ms	244×	body	80	valid
12.0ms	377×	body	80	nan
2.0ms	22×	body	160	valid

simplify70.0ms

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: 4.0b

localize13.0ms

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))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp x) 1.0)

rewrite107.0ms

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:

28.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
45.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series183.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
23.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify119.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (106.0ms)

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

prune324.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(sqrt (exp (* 2.0 x)))
4.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.4b	(- (exp x) 1.0)

rewrite37.0ms

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (exp (* 2.0 x)))
21.0ms	(sqrt (exp (* 2.0 x)))
43.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify102.0ms

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

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(pow (exp 2.0) (* 1/2 x))
4.4b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.4b	(- (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:

3.0ms	(sqrt (exp (* 2.0 x)))
5.0ms	(pow (exp 2.0) (* 1/2 x))
31.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series113.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (exp (* 2.0 x)))
26.0ms	(pow (exp 2.0) (* 1/2 x))
53.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
13.0ms	(- (exp x) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (60.0ms)

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

prune287.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.1b	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
4.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.4b	(- (exp x) 1.0)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

83×	`sqrt-pow1`
75×	`sqrt-prod`
58×	`add-sqr-sqrt`
28×	`pow1`
23×	`*-un-lft-identity`
21×	`add-log-exp`
17×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
13×	`exp-prod` `exp-to-pow` `pow-prod-up`
9×	`associate-r` `associate-l` `pow-prod-down` `pow-sqr` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`difference-of-squares`
3×	`distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

5.0ms	(sqrt (exp (* 2.0 x)))
34.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
18.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
13.0ms	(- (exp x) 1.0)

series103.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (exp (* 2.0 x)))
26.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
43.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
13.0ms	(- (exp x) 1.0)

simplify225.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	280	774
1	984	713
2	4935	689
3	5001	689

prune324.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

97.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.7b

bsearch99.0ms

Steps

Iters	Range		Point
9	2.0513987020488157e-07	0.5429513389937057	5.717344166834741e-06
9	-0.000702289593969892	-1.5317450828987306e-09	-3.2646702564599914e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	35
1	51	35

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	6675×	body	10240	exit
393.0ms	12885×	body	80	nan
242.0ms	7439×	body	80	valid
55.0ms	698×	body	160	valid