Details

sample344.0ms

Algorithm

intervals

Results

39.0ms	198×	body	10240	exit
13.0ms	434×	body	80	nan
8.0ms	236×	body	80	valid
3.0ms	24×	body	160	valid

simplify72.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

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))
5.1b	(- (exp (* 2.0 x)) 1.0)
5.1b	(- (exp x) 1.0)

rewrite35.0ms

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:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify127.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (112.0ms)

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

prune351.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.1b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.1b	(- (exp x) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`sqrt-prod` `add-log-exp`
5×	`pow1` `add-cube-cbrt` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-pow1` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `exp-to-pow` `flip3-+` `pow1/2` `sum-log` `flip-+`

Counts

4 → 60

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
6.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series130.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
41.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
53.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify128.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	209	434
1	530	405
2	1324	402
3	3833	401
4	5001	401

prune239.0ms

Pruning

4 alts after pruning (4 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	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.1b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
5.1b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
6.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
7.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series143.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (exp (* 2.0 x)))
42.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
58.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	256	459
1	652	431
2	1842	424
3	5001	422

prune284.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x))))) (sqrt 1.0))
0.0b	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
5.1b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
5.1b	(- (exp x) 1.0)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
69×	`sqrt-prod`
58×	`add-sqr-sqrt`
27×	`pow1`
22×	`add-log-exp`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
13×	`pow-prod-up`
12×	`exp-prod` `exp-to-pow`
9×	`associate-r` `associate-l` `pow-prod-down` `pow-sqr` `unswap-sqr`
7×	`difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
2×	`sub-neg` `unpow-prod-down` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `sqr-pow`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 131

Calls

4 calls:

13.0ms	(+ (* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x))))) (sqrt 1.0))
13.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
7.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series137.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x))))) (sqrt 1.0))
28.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
52.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	371	956
1	1271	815
2	5002	790

prune394.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes31.0ms

Accuracy

73.3% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.9b

bsearch42.0ms

Steps

Iters	Range		Point
6	-9.565599748882727e-17	-1.0649830446260068e-17	-5.555651763911567e-17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	28
1	42	28

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6661×	body	10240	exit
390.0ms	12605×	body	80	nan
239.0ms	7407×	body	80	valid
55.0ms	699×	body	160	valid