Details

analyze315.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

sample48.0ms

Algorithm

intervals

Results

26.0ms	113×	body	8192	exit
7.0ms	212×	body	128	valid
2.0ms	17×	body	512	valid
2.0ms	25×	body	256	valid
1.0ms	2×	body	1024	valid
0.0ms	5×	body	128	invalid

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4944	18
1	4944	18

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 12.7b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
0.2b	(/.f64 x (exp.f64 wj))
5.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
9×	`associate-/l*_binary64`
8×	`distribute-lft-out_binary64`
7×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`associate-+r-_binary64` `flip3--_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 91

Calls

3 calls:

14.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))
19.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
61.0ms	(/.f64 x (exp.f64 wj))
78.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

simplify77.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5074	2095

prune83.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Merged error: 0.6b

Counts

102 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(.f64 wj (+.f64 wj (.f64 x -2)))
0.0b	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 35

Calls

2 calls:

6.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
4.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

series110.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
49.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

simplify78.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4951	598
1	4951	598

prune39.0ms

Filtered

28 candidates to 41 candidates (-46.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	36	5	41
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	36	10	46

Merged error: 0.6b

Counts

46 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
10.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
10.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
10.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
5.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
5.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
5.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

series1.7s

Counts

4 → 12

Calls

4 calls:

466.0ms	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
400.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
390.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
398.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5360	1507

prune121.0ms

Filtered

67 candidates to 84 candidates (-25.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	82	12	94

Merged error: 0.6b

Counts

94 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6)
10.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
10.4b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
29.4b	(pow.f64 (pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6) 1/3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`unpow-prod-down_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64`
6×	`pow-unpow_binary64`
5×	`pow1_binary64` `pow-exp_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
3×	`pow-to-exp_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`unpow1/3_binary64`

Counts

4 → 66

Calls

4 calls:

4.0ms	(pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6)
5.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
6.0ms	(pow.f64 (pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6) 1/3)

series2.8s

Counts

4 → 12

Calls

4 calls:

878.0ms	(pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6)
425.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
409.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
1.1s	(pow.f64 (pow.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) 6) 1/3)

simplify90.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4932	1282
1	4932	1282

prune85.0ms

Filtered

60 candidates to 78 candidates (-30.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	79	11	90

Merged error: 0.6b

Counts

90 → 11

regimes62.0ms

Accuracy

60.8% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.0b

bsearch11.0ms

Steps

Iters	Range		Point
5	1.3415442842464698e-14	2.9005038282448894e-14	2.8502121317239544e-14

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	39
1	36	39

end0.0ms

sample1.5s

Algorithm

intervals

Results

885.0ms	3880×	body	8192	exit
238.0ms	6572×	body	128	valid
91.0ms	700×	body	512	valid
58.0ms	701×	body	256	valid
5.0ms	27×	body	1024	valid
4.0ms	83×	body	128	invalid
0.0ms	14×	body	128	overflowed

Details

analyze315.0ms

sample48.0ms

simplify87.0ms

prune4.0ms

localize8.0ms

rewrite46.0ms

series237.0ms

simplify77.0ms

prune83.0ms

localize6.0ms

rewrite14.0ms

series110.0ms

simplify78.0ms

prune39.0ms

localize10.0ms

rewrite30.0ms

series1.7s

simplify64.0ms

prune121.0ms

localize17.0ms

rewrite25.0ms

series2.8s

simplify90.0ms

prune85.0ms

regimes62.0ms

bsearch11.0ms

simplify3.0ms

end0.0ms

sample1.5s

Profiling