Details

sample368.0ms

Algorithm

intervals

Results

53.0ms	258×	body	10240	exit
25.0ms	453×	body	80	nan
8.0ms	241×	body	80	valid
2.0ms	19×	body	160	valid

simplify73.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.8b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (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)

series214.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
36.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify131.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (111.0ms)

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

prune339.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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

series135.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (exp (* 2.0 x)))
44.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
53.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify126.0ms

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

prune209.0ms

Filtered

72 candidates to 49 candidates (68.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series148.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
28.0ms	(pow (exp 2.0) (* 1/2 x))
61.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	284	478
1	804	450
2	2586	443
3	5002	441

prune268.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
3.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.9b	(- (exp x) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
44×	`sqrt-prod`
39×	`times-frac`
38×	`unpow-prod-down` `cube-prod`
37×	`add-sqr-sqrt`
36×	`distribute-lft-out`
27×	`add-cube-cbrt`
13×	`associate-/l*`
9×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`pow-pow` `difference-of-squares`
4×	`sum-cubes`
3×	`pow-unpow` `flip3--` `sqrt-pow1` `associate-/r*` `flip--` `distribute-lft-out--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `exp-prod` `exp-to-pow` `frac-2neg` `flip3-+` `pow1/2` `unpow3` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip-+` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 137

Calls

4 calls:

27.0ms	(/ (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
4.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series596.0ms

Counts

4 → 12

Calls

4 calls:

474.0ms	(/ (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
53.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
53.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify98.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	677	2524
1	3327	2375
2	5002	2365

prune429.0ms

Filtered

149 candidates to 76 candidates (51.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

98.1% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.9b

bsearch76.0ms

Steps

Iters	Range		Point
7	2.7581197155588776e-09	1.0392876537738595e-07	7.925407606594412e-09
6	-3.484100988050835e-05	-2.6892755714465704e-06	-1.3070090851707563e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	35
1	41	35

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	6899×	body	10240	exit
406.0ms	12756×	body	80	nan
246.0ms	7397×	body	80	valid
57.0ms	721×	body	160	valid