Details

analyze258.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample252.0ms

Algorithm

intervals

Results

217.0ms	70×	body	1280	valid
10.0ms	37×	body	640	valid
9.0ms	28×	body	2560	valid
5.0ms	29×	body	320	valid
3.0ms	76×	body	80	valid
2.0ms	16×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 52.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.8b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
18.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series90.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
46.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
18.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify91.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4835	862
1	4835	862

prune62.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
22.3b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
13×	`add-exp-log_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow1_binary64`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

3 → 69

Calls

3 calls:

5.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

series88.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(*.f64 3/40 (pow.f64 x 5))
28.0ms	(*.f64 (pow.f64 x 3) 1/6)
29.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5028	1008

prune58.0ms

Filtered

50 candidates to 78 candidates (-56.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Merged error: 0b

Counts

82 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.4b	(/.f64 1/8 (pow.f64 x 3))
7.8b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`
13×	`unpow-prod-down_binary64` `cube-prod_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `sum-log_binary64`
4×	`diff-log_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `log-div_binary64` `associate-+r+_binary64` `frac-sub_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 123

Calls

4 calls:

20.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
24.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
22.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
27.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
31.0ms	(/.f64 1/8 (pow.f64 x 3))
41.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5445	2608

prune98.0ms

Filtered

80 candidates to 135 candidates (-68.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	135	4	139

Merged error: 0b

Counts

139 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/16 (pow.f64 x 5))
0.4b	(/.f64 1/8 (pow.f64 x 3))
9.7b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
16.4b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 1/16 (pow.f64 x 5))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
35.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
40.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 1/16 (pow.f64 x 5))
23.0ms	(/.f64 1/8 (pow.f64 x 3))
42.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
27.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify100.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4879	3605
1	4879	3605

prune171.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	171	4	175

Merged error: 0b

Counts

175 → 4

regimes22.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.5b

bsearch34.0ms

Steps

Iters	Range		Point
9	7.581530169793224e-06	954.2672973039676	0.9582019973612633
9	-5.194840675490605	-4.341877876899752e-09	-1.0916889627380748

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2339×	body	1280	valid
437.0ms	1567×	body	640	valid
267.0ms	800×	body	2560	valid
134.0ms	805×	body	320	valid
92.0ms	2092×	body	80	valid
39.0ms	397×	body	160	valid

Details

analyze258.0ms

sample252.0ms

simplify12.0ms

prune1.0ms

localize6.0ms

rewrite18.0ms

series90.0ms

simplify91.0ms

prune62.0ms

localize9.0ms

rewrite19.0ms

series88.0ms

simplify79.0ms

prune58.0ms

localize10.0ms

rewrite75.0ms

series121.0ms

simplify64.0ms

prune98.0ms

localize12.0ms

rewrite91.0ms

series123.0ms

simplify100.0ms

prune171.0ms

regimes22.0ms

bsearch34.0ms

simplify5.0ms

end0.0ms

sample2.2s

Profiling