Details

sample412.0ms

Algorithm

intervals

Results

59.0ms	206×	body	10240	exit
10.0ms	375×	body	80	nan
9.0ms	241×	body	80	valid
1.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

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))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp x) 1.0)

rewrite100.0ms

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:

28.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
42.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp x) 1.0)

series208.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
63.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify122.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (109.0ms)

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

prune328.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.6b	(- (exp x) 1.0)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

32.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
16.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series442.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
43.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
52.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	420	776
1	1462	712
2	5001	694

prune230.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.1b	(pow (sqrt (exp (* 2.0 x))) 3)
4.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.6b	(- (exp x) 1.0)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

64.0ms	(- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
6.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series199.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (+ (exp (* 2.0 x)) 1.0) (* (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
49.0ms	(pow (sqrt (exp (* 2.0 x))) 3)
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	379	661
1	1487	605
2	5002	597

prune295.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
0.1b	(pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
4.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.6b	(- (exp x) 1.0)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

20.0ms	(cbrt (pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
24.0ms	(pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series223.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
110.0ms	(pow (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	374	825
1	1419	759
2	5001	749

prune249.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

76.4% (0.8b remaining)

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

bsearch38.0ms

Steps

Iters	Range		Point
8	-5.931762247777049e-05	-2.2707086624102254e-09	-2.429265889646968e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6750×	body	10240	exit
368.0ms	12617×	body	80	nan
232.0ms	7426×	body	80	valid
51.0ms	702×	body	160	valid