Details

sample333.0ms

Algorithm

intervals

Results

40.0ms	208×	body	10240	exit
14.0ms	441×	body	80	nan
7.0ms	239×	body	80	valid
2.0ms	23×	body	160	valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

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: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.7b	(- (exp x) 1.0)

rewrite34.0ms

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)
6.0ms	(- (exp x) 1.0)

series198.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
54.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

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

prune336.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
0.2b	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
4.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.7b	(- (exp x) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
67×	`sqrt-prod`
62×	`times-frac`
39×	`difference-of-squares`
29×	`add-cube-cbrt`
25×	`distribute-lft-out--`
9×	`associate-/l*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `associate-/r*`
4×	`flip3--` `flip--`
3×	`rem-sqrt-square`
2×	`sub-neg` `diff-log` `associate-/r/` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 140

Calls

4 calls:

7.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
12.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
92.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	461	1817
1	1462	1748
2	5001	1701

prune376.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.2b	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
4.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.7b	(- (exp x) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
49×	`sqrt-prod`
45×	`times-frac`
39×	`difference-of-squares`
25×	`distribute-lft-out--`
21×	`add-cube-cbrt`
9×	`associate-/l*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 125

Calls

4 calls:

6.0ms	(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
12.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
7.0ms	(- (exp x) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
89.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
49.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify141.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	421	1634
1	1269	1578
2	4858	1561
3	5002	1561

prune391.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
0.2b	(/ (cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)) (- (exp x) 1.0))
4.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.7b	(- (exp x) 1.0)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

231×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
152×	`times-frac`
144×	`cbrt-prod`
103×	`sqrt-prod`
81×	`difference-of-squares`
65×	`add-cube-cbrt`
55×	`distribute-lft-out--`
54×	`unpow-prod-down` `cube-prod`
27×	`associate-/l*`
8×	`add-log-exp`
6×	`add-exp-log` `cube-mult` `unpow3` `distribute-lft-out` `sqr-pow`
5×	`pow1` `associate-/r*` `add-cbrt-cube`
4×	`flip3--` `flip--`
3×	`rem-sqrt-square`
2×	`cube-div` `sub-neg` `cbrt-div` `diff-log` `associate-/r/` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 247

Calls

4 calls:

7.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
20.0ms	(/ (cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)) (- (exp x) 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
89.0ms	(/ (cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)) (- (exp x) 1.0))
50.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	583	3981
1	2109	3783
2	5003	3761

prune494.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes35.0ms

Accuracy

77.5% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.3b

bsearch45.0ms

Steps

Iters	Range		Point
8	-1.7517139813340076e-05	-2.816372011292524e-10	-2.9277154484540503e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	29
1	43	29

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	6824×	body	10240	exit
375.0ms	12951×	body	80	nan
232.0ms	7440×	body	80	valid
50.0ms	685×	body	160	valid