Details

sample338.0ms

Algorithm

intervals

Results

39.0ms	213×	body	10240	exit
12.0ms	389×	body	80	nan
7.0ms	233×	body	80	valid
2.0ms	25×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize20.0ms

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))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (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)

series213.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
34.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify124.0ms

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

prune335.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize16.0ms

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))
5.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.8b	(- (exp x) 1.0)

rewrite21.0ms

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:

1.0ms	(sqrt (exp (* 2.0 x)))
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)

series139.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(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))
16.0ms	(- (exp x) 1.0)

simplify122.0ms

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

prune230.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))
5.8b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
5.8b	(- (exp x) 1.0)

rewrite28.0ms

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:

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

series151.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
32.0ms	(pow (exp 2.0) (* 1/2 x))
57.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (65.0ms)

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

prune290.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (exp x) 1.0) 3)
0.1b	(cbrt (pow (- (exp x) 1.0) 3))
5.8b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
5.8b	(- (exp x) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`cbrt-prod`
12×	`unpow-prod-down`
11×	`difference-of-squares`
10×	`add-cube-cbrt` `cube-prod`
8×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--` `sqr-pow`
3×	`pow-unpow` `sqrt-prod`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 89

Calls

4 calls:

7.0ms	(pow (- (exp x) 1.0) 3)
7.0ms	(cbrt (pow (- (exp x) 1.0) 3))
13.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
5.0ms	(- (exp x) 1.0)

series131.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (- (exp x) 1.0) 3)
15.0ms	(cbrt (pow (- (exp x) 1.0) 3))
59.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	320	585
1	1165	559
2	5002	549

prune336.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

75.6% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.1b

bsearch52.0ms

Steps

Iters	Range		Point
8	-0.0008391074150366579	-8.849834202292668e-07	-1.2887874422510308e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	40	22

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6739×	body	10240	exit
376.0ms	12781×	body	80	nan
239.0ms	7403×	body	80	valid
57.0ms	711×	body	160	valid