Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

sample35.0ms

Algorithm

intervals

Results

8.0ms	211×	body	80	valid
3.0ms	19×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	34×	body	80	invalid
1.0ms	5×	body	1280	valid
1.0ms	7×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

prune4.0ms

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: 23.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
1.7b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
16.3b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`flip3--_binary64` `flip--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l/_binary64` `frac-times_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 79

Calls

3 calls:

11.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
9.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
14.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

series103.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
55.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
38.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	6015	1085

prune217.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	13	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Merged error: 3.7b

Counts

89 → 13

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
1.7b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
2.6b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac_binary64`
323×	`*-un-lft-identity_binary64`
321×	`add-sqr-sqrt_binary64`
113×	`add-cube-cbrt_binary64`
104×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
15×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `div-sub_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 274

Calls

3 calls:

9.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
61.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
30.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
55.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
46.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

simplify105.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5092	5477

prune256.0ms

Filtered

170 candidates to 283 candidates (-66.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	8	4	12
Picked	0	1	1
Done	0	0	0
Total	283	13	296

Merged error: 3.5b

Counts

296 → 13

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
1.7b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
2.7b	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 119

Calls

3 calls:

9.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
4.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
19.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))

series104.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
58.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
35.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))

simplify44.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5068	1606

prune124.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	128	13	141

Merged error: 3.5b

Counts

141 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a t))
0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t))))
0.8b	(/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))
8.2b	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

1444×	`times-frac_binary64`
1187×	`add-sqr-sqrt_binary64`
1146×	`*-un-lft-identity_binary64`
905×	`cbrt-prod_binary64`
516×	`add-cube-cbrt_binary64`
373×	`associate-r_binary64`
315×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
78×	`add-exp-log_binary64`
46×	`associate-/r*_binary64`
44×	`associate-/r/_binary64`
36×	`add-cbrt-cube_binary64`
30×	`cbrt-undiv_binary64` `div-exp_binary64`
27×	`cbrt-unprod_binary64` `prod-exp_binary64`
25×	`flip3--_binary64` `flip--_binary64`
20×	`div-inv_binary64`
16×	`cbrt-div_binary64`
14×	`unswap-sqr_binary64`
13×	`associate-l_binary64`
8×	`associate-/l*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
5×	`frac-times_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`associate-/l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/3_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 907

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 a t))
164.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t))))
25.0ms	(/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))
5.0ms	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))))

series199.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (-.f64 a t))
52.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t))))
60.0ms	(/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))
62.0ms	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))))

simplify183.0ms

Algorithm

egg-herbie

Counts

919 → 919

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5562	27998

prune633.0ms

Filtered

592 candidates to 919 candidates (-55.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	918	1	919
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	920	12	932

Merged error: 3.5b

Counts

932 → 12

regimes523.0ms

Accuracy

22.1% (5.8b remaining)

Error of 10.1b against oracle of 4.3b and baseline of 11.8b

bsearch42.0ms

Steps

Iters	Range		Point
6	1.2303149456591255e-172	1.4193958836417344e-171	4.1647360198308445e-172
6	-2.1642703937079366e-225	-1.440747164798236e-226	-2.1231586582406398e-225

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	47
1	83	47

end0.0ms

sample1.0s

Algorithm

intervals

Results

484.0ms	6532×	body	80	valid
78.0ms	521×	body	640	valid
50.0ms	277×	body	1280	valid
49.0ms	1224×	body	80	invalid
47.0ms	397×	body	320	valid
18.0ms	252×	body	160	valid
5.0ms	21×	body	2560	valid

Details

analyze1.2s

sample35.0ms

simplify64.0ms

prune4.0ms

localize9.0ms

rewrite36.0ms

series103.0ms

simplify42.0ms

prune217.0ms

localize16.0ms

rewrite123.0ms

series112.0ms

simplify105.0ms

prune256.0ms

localize11.0ms

rewrite38.0ms

series104.0ms

simplify44.0ms

prune124.0ms

localize17.0ms

rewrite297.0ms

series199.0ms

simplify183.0ms

prune633.0ms

regimes523.0ms

bsearch42.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling