Details

analyze128.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample38.0ms

Algorithm

intervals

Results

11.0ms	201×	body	80	valid
6.0ms	22×	body	1280	valid
5.0ms	256×	pre	80	true
5.0ms	21×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5300	43

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 25.0b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.1b	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.4b	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
22.4b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 142

Calls

4 calls:

12.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
22.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
33.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
15.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
279.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
336.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
62.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

simplify120.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4998	5811
1	4998	5811

prune246.0ms

Filtered

114 candidates to 154 candidates (-35.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	11	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	11	155

Merged error: 5.8b

Counts

155 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
1.4b	(+.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`associate-/l/_binary64` `associate-/r*_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`div-inv_binary64`
2×	`associate-*r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `div-sub_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 129

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
26.0ms	(/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
17.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
26.0ms	(+.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

series763.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
290.0ms	(/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
71.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
340.0ms	(+.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

simplify78.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5288	4223

prune188.0ms

Filtered

100 candidates to 141 candidates (-41.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	141	11	152

Merged error: 5.8b

Counts

152 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.1b	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3)
1.3b	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))
1.7b	(-.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 1)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
21×	`associate-r_binary64`
19×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
5×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `div-inv_binary64`
2×	`unswap-sqr_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `pow-pow_binary64` `difference-of-sqr-1_binary64` `sqr-pow_binary64` `cube-div_binary64` `+-commutative_binary64` `flip--_binary64` `unpow3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 116

Calls

4 calls:

18.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
23.0ms	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3)
18.0ms	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))
24.0ms	(-.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 1)

series40.0s

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
14.7s	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3)
25.1s	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))
209.0ms	(-.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 1)

simplify108.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5329	4849

prune375.0ms

Filtered

83 candidates to 128 candidates (-54.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	126	13	139

Merged error: 5.8b

Counts

139 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3)
1.3b	(log.f64 (exp.f64 (+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))))
1.3b	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))
1.7b	(-.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 1)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`add-log-exp_binary64` `times-frac_binary64`
6×	`pow1_binary64`
5×	`log-pow_binary64`
4×	`distribute-lft-out_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `exp-prod_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-inv_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `difference-of-sqr-1_binary64` `sqr-pow_binary64` `cube-div_binary64` `exp-sum_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 88

Calls

4 calls:

25.0ms	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3)
18.0ms	(log.f64 (exp.f64 (+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))))
16.0ms	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))
24.0ms	(-.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 1)

series1.1min

Counts

4 → 12

Calls

4 calls:

14.6s	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3)
25.1s	(log.f64 (exp.f64 (+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))))
24.6s	(+.f64 1 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 3))
205.0ms	(-.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) 1)

simplify97.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5911	4561

prune227.0ms

Filtered

63 candidates to 100 candidates (-58.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	99	14	113

Merged error: 5.8b

Counts

113 → 14

regimes208.0ms

Accuracy

13% (5.9b remaining)

Error of 12.1b against oracle of 6.2b and baseline of 13.0b

bsearch99.0ms

Steps

Iters	Range		Point
7	2.627148353075517e+196	2.3544056438917118e+198	4.8907958261153134e+197
7	2.3178362635135812e+165	4.602373943295915e+166	4.552813519470753e+166
7	2.683126051482656e+89	5.685184401348611e+91	7.158130970526724e+89

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	222
1	106	222

end0.0ms

sample1.0s

Algorithm

intervals

Results

331.0ms	6275×	body	80	valid
159.0ms	8000×	pre	80	true
147.0ms	547×	body	1280	valid
129.0ms	609×	body	640	valid
60.0ms	375×	body	320	valid
20.0ms	194×	body	160	valid

Details

analyze128.0ms

sample38.0ms

simplify81.0ms

prune3.0ms

localize15.0ms

rewrite88.0ms

series706.0ms

simplify120.0ms

prune246.0ms

localize14.0ms

rewrite85.0ms

series763.0ms

simplify78.0ms

prune188.0ms

localize21.0ms

rewrite87.0ms

series40.0s

simplify108.0ms

prune375.0ms

localize28.0ms

rewrite86.0ms

series1.1min

simplify97.0ms

prune227.0ms

regimes208.0ms

bsearch99.0ms

simplify5.0ms

end0.0ms

sample1.0s

Profiling