Details

sample396.0ms

Algorithm

intervals

Results

60.0ms	225×	body	10240	exit
14.0ms	418×	body	80	nan
8.0ms	242×	body	80	valid
2.0ms	21×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.5b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.2b	(- (exp x) 1.0)

rewrite101.0ms

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:

38.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
27.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
18.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp x) 1.0)

series199.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify119.0ms

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

prune326.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
0.5b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
4.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.2b	(- (exp x) 1.0)

rewrite107.0ms

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:

51.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
21.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
19.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series235.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
79.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 1))
50.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (36.0ms)

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

prune378.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
0.5b	(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
4.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.2b	(- (exp x) 1.0)

rewrite105.0ms

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:

51.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
21.0ms	(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
81.0ms	(sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify139.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (30.0ms)

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

prune391.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`add-log-exp` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r`
4×	`associate-*r/` `prod-exp`
3×	`cbrt-undiv` `sum-log` `div-inv`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `flip3-+` `frac-add` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`

Counts

4 → 221

Calls

4 calls:

27.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
66.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
10.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))

series275.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
70.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
62.0ms	(/ (pow x 2) (sqrt 2.0))
54.0ms	(/ x (sqrt 2.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	723	1889
1	3042	1708
2	5001	1694

prune469.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes59.0ms

Accuracy

78.2% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.4b

bsearch49.0ms

Steps

Iters	Range		Point
9	-0.04331797882383785	-1.989428328455626e-07	-8.403797957856243e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	31
1	45	31

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6689×	body	10240	exit
377.0ms	12775×	body	80	nan
233.0ms	7444×	body	80	valid
55.0ms	694×	body	160	valid