Details

analyze514.0ms

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
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

sample42.0ms

Algorithm

intervals

Results

11.0ms	182×	body	80	valid
6.0ms	27×	body	1280	valid
5.0ms	28×	body	1280	nan
4.0ms	27×	body	640	valid
3.0ms	26×	body	640	nan
2.0ms	16×	body	320	nan
1.0ms	12×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	5×	body	160	nan
0.0ms	9×	body	80	nan

simplify356.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (347.0ms)

Iter	Nodes	Cost
0	5145	18

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: 18.1b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
0.0b	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
1.8b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
5.2b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
67×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
33×	`difference-of-squares_binary64`
19×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
16×	`log-prod_binary64`
8×	`associate--r+_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `flip3--_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
5×	`associate-/l*_binary64`
4×	`log-div_binary64`
3×	`associate--r-_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `associate-/r/_binary64` `div-sub_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 119

Calls

4 calls:

9.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))
22.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
16.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
16.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

series171.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))
57.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
37.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
54.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

simplify101.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5547	2791

prune147.0ms

Filtered

93 candidates to 131 candidates (-40.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	4	132

Merged error: 0.1b

Counts

132 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 y))
0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))
4.0b	(-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y))))
5.2b	(log.f64 (-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
18×	`add-exp-log_binary64`
15×	`difference-of-squares_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
5×	`associate-l_binary64`
4×	`associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`log-prod_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `log-div_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `log-pow_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 1 y))
15.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))
4.0ms	(-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y))))
4.0ms	(log.f64 (-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1 (-.f64 1 y))
25.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))
38.0ms	(-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y))))
56.0ms	(log.f64 (-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5064	2046

prune98.0ms

Filtered

89 candidates to 135 candidates (-51.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	135	4	139

Merged error: 0.1b

Counts

139 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (pow.f64 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))) 3))
0.3b	(pow.f64 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))) 3)
1.8b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
5.2b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
8×	`log-prod_binary64` `unpow-prod-down_binary64` `difference-of-squares_binary64` `cube-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
5×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`times-frac_binary64`
3×	`pow-unpow_binary64`
2×	`flip3--_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-sub_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 84

Calls

4 calls:

2.0ms	(cbrt.f64 (pow.f64 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))) 3))
3.0ms	(pow.f64 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))) 3)
16.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
18.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(cbrt.f64 (pow.f64 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))) 3))
284.0ms	(pow.f64 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))) 3)
37.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
55.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

simplify57.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5126	2407

prune74.0ms

Filtered

59 candidates to 96 candidates (-62.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	96	4	100

Merged error: 0.1b

Counts

100 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(-.f64 y (+.f64 x (.f64 (.f64 x x) 1/2)))
0.0b	(+.f64 x (.f64 (.f64 x x) 1/2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
2×	`diff-log_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `associate-l_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 45

Calls

3 calls:

6.0ms	(.f64 (.f64 x x) 1/2)
6.0ms	(-.f64 y (+.f64 x (.f64 (.f64 x x) 1/2)))
4.0ms	(+.f64 x (.f64 (.f64 x x) 1/2))

series73.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(.f64 (.f64 x x) 1/2)
19.0ms	(-.f64 y (+.f64 x (.f64 (.f64 x x) 1/2)))
34.0ms	(+.f64 x (.f64 (.f64 x x) 1/2))

simplify80.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4951	721
1	4951	721

prune28.0ms

Filtered

34 candidates to 54 candidates (-58.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	54	4	58

Merged error: 0.1b

Counts

58 → 4

regimes79.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.8b

bsearch119.0ms

Steps

Iters	Range		Point
10	3687.9947085081185	3.7802798181751866e+17	47119492.00505001
11	-1694467432.6693075	-1.1400907852749228e-11	-92176554.09175538

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	166	59
1	166	59

end0.0ms

sample1.2s

Algorithm

intervals

Results

270.0ms	5688×	body	80	valid
194.0ms	811×	body	1280	valid
139.0ms	811×	body	640	valid
125.0ms	692×	body	1280	nan
97.0ms	694×	body	640	nan
58.0ms	453×	body	320	valid
42.0ms	412×	body	320	nan
19.0ms	237×	body	160	valid
16.0ms	218×	body	160	nan
12.0ms	364×	body	80	nan

Details

analyze514.0ms

sample42.0ms

simplify356.0ms

prune1.0ms

localize8.0ms

rewrite68.0ms

series171.0ms

simplify101.0ms

prune147.0ms

localize9.0ms

rewrite34.0ms

series128.0ms

simplify76.0ms

prune98.0ms

localize11.0ms

rewrite42.0ms

series434.0ms

simplify57.0ms

prune74.0ms

localize7.0ms

rewrite16.0ms

series73.0ms

simplify80.0ms

prune28.0ms

regimes79.0ms

bsearch119.0ms

simplify6.0ms

end0.0ms

sample1.2s

Profiling