Details

sample322.0ms

Algorithm

intervals

Results

23.0ms	331×	body	80	nan
16.0ms	241×	body	80	valid
13.0ms	202×	body	80	overflowed
3.0ms	21×	body	160	valid

simplify69.0ms

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: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.8b	(- (exp (* 2.0 x)) 1.0)
5.0b	(- (exp x) 1.0)

rewrite54.0ms

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:

15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
23.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series196.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (106.0ms)

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

prune321.0ms

Pruning

5 alts after pruning (5 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 (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
5.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.0b	(- (exp x) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

1.0ms	(sqrt (exp (* 2.0 x)))
18.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
8.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.0ms	(- (exp x) 1.0)

series415.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (exp (* 2.0 x)))
330.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (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)

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	401	724
1	1381	672
2	5002	655

prune228.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
0.1b	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
5.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.0b	(- (exp x) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

12.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
12.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
10.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series236.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
46.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
50.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	357	1065
1	1371	995
2	5001	983

prune252.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
5.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.0b	(- (exp x) 1.0)
5.0b	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`add-log-exp`
9×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `cube-prod`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `flip3--` `sqrt-pow1` `diff-log` `flip--` `distribute-lft-out--`
1×	`cube-mult` `pow-to-exp` `exp-prod` `exp-to-pow` `distribute-rgt-out--` `pow1/2` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)
5.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
50.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)
101.0ms	(- (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	360	623
1	1444	550
2	5001	542

prune311.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

75.1% (0.9b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 3.6b

bsearch46.0ms

Steps

Iters	Range		Point
8	-0.001896135941054132	-3.774608270569166e-06	-8.25354992509483e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	22
1	33	22

end0.0ms

sample2.1s

Algorithm

intervals

Results

773.0ms	12246×	body	80	nan
491.0ms	7360×	body	80	valid
429.0ms	6523×	body	80	overflowed
99.0ms	760×	body	160	valid