Details

sample328.0ms

Algorithm

intervals

Results

43.0ms	220×	body	10240	exit
12.0ms	407×	body	80	nan
9.0ms	240×	body	80	valid
2.0ms	19×	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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0b	(- (exp (* 2.0 x)) 1.0)
4.0b	(- (exp x) 1.0)

rewrite46.0ms

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:

14.0ms	(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)
7.0ms	(- (exp x) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify127.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (110.0ms)

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

prune339.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (exp x) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`sqrt-prod`
7×	`pow1`
5×	`sqrt-div` `difference-of-squares`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `distribute-lft-out--`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*l/` `flip--` `distribute-lft-out`
1×	`+-commutative` `pow1/2` `associate-*r/` `pow-prod-down` `sum-log`

Counts

4 → 61

Calls

4 calls:

18.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
7.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series450.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
46.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	420	776
1	1462	712
2	5001	694

prune224.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (exp x) 1.0)
4.0b	(- (exp x) 1.0)
4.0b	(- (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:

48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)
17.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)

simplify94.0ms

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

prune241.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
0.0b	(* x (+ 1.0 (* 0.5 x)))
28.0b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-r` `associate-l` `sqrt-prod` `flip-+`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

4.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
7.0ms	(* x (+ 1.0 (* 0.5 x)))
7.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series170.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
67.0ms	(* x (+ 1.0 (* 0.5 x)))
81.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	308	385
1	1305	364
2	5001	352

prune107.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

78.8% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.4b

bsearch41.0ms

Steps

Iters	Range		Point
7	-5.023588783947765e-05	-7.23934040408857e-07	-1.1563998871691034e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6743×	body	10240	exit
379.0ms	12822×	body	80	nan
240.0ms	7450×	body	80	valid
54.0ms	691×	body	160	valid