Details

analyze137.0ms

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

sample39.0ms

Algorithm

intervals

Results

11.0ms	202×	body	80	valid
6.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
4.0ms	17×	body	640	valid
3.0ms	18×	body	320	valid
0.0ms	4×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5446	29

prune7.0ms

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: 24.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 alpha beta) (*.f64 2.0 i))
0.1b	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) 2.0))
2.0b	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) 2.0)) 1.0)
21.0b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac_binary64`
48×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-/r/_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`add-log-exp_binary64` `distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
4×	`pow1_binary64` `frac-times_binary64` `sum-log_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `+-commutative_binary64` `associate-l/_binary64`
1×	`associate-+l+_binary64`

Counts

4 → 124

Calls

4 calls:

7.0ms	(+.f64 (+.f64 alpha beta) (*.f64 2.0 i))
23.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) 2.0))
34.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) 2.0)) 1.0)
15.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (+.f64 alpha beta) (*.f64 2.0 i))
89.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) 2.0))
112.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)) 2.0)) 1.0)
25.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5737	3711

prune241.0ms

Filtered

102 candidates to 136 candidates (-33.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	9	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Merged error: 7.1b

Counts

137 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
1.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))
3.7b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 295

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
21.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
41.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))
29.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0)

series275.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
51.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
90.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))
113.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4981	8907
1	4981	8907

prune479.0ms

Filtered

198 candidates to 307 candidates (-55.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	307	9	316

Merged error: 7.1b

Counts

316 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
0.3b	(/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))))
1.3b	(.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))))
3.7b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))) 1.0)

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

1713×	`times-frac_binary64`
1199×	`*-un-lft-identity_binary64`
879×	`add-sqr-sqrt_binary64`
658×	`add-cube-cbrt_binary64`
272×	`associate-r_binary64`
170×	`distribute-lft-out_binary64`
110×	`associate-/r*_binary64`
99×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
76×	`associate-/r/_binary64`
62×	`add-exp-log_binary64`
43×	`div-inv_binary64`
37×	`flip3-+_binary64` `flip-+_binary64`
33×	`div-exp_binary64`
32×	`add-cbrt-cube_binary64`
15×	`cbrt-undiv_binary64`
10×	`prod-exp_binary64`
7×	`pow1_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `inv-pow_binary64` `un-div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 833

Calls

4 calls:

21.0ms	(/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
37.0ms	(/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))))
88.0ms	(.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))))
46.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))) 1.0)

series296.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
51.0ms	(/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))))
85.0ms	(.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))))
117.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))) 1.0)

simplify170.0ms

Algorithm

egg-herbie

Counts

845 → 845

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5184	28777

prune1.8s

Filtered

458 candidates to 845 candidates (-84.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	845	0	845
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	845	9	854

Merged error: 7.1b

Counts

854 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
0.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0) 3))
1.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))
3.7b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac_binary64`
275×	`*-un-lft-identity_binary64`
196×	`add-sqr-sqrt_binary64`
133×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
27×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-/r/_binary64`
21×	`associate-/l*_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`cbrt-prod_binary64`
11×	`div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/r_binary64` `associate-l*_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64`
2×	`cbrt-div_binary64` `cube-div_binary64` `div-sub_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `rem-cbrt-cube_binary64` `associate-r/_binary64` `pow1/3_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 278

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
34.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0) 3))
40.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))
31.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0)

series370.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (.f64 2.0 i))))
114.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0) 3))
90.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))))
115.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) (+.f64 2.0 (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))) 1.0)

simplify81.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5075	9219

prune485.0ms

Filtered

186 candidates to 290 candidates (-55.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	282	8	290
Fresh	5	2	7
Picked	0	1	1
Done	1	0	1
Total	288	11	299

Merged error: 7.1b

Counts

299 → 11

regimes340.0ms

Accuracy

15.2% (5.6b remaining)

Error of 11.4b against oracle of 5.9b and baseline of 12.4b

bsearch34.0ms

Steps

Iters	Range		Point
7	2.490290781953067e+179	9.236066902371333e+180	6.636178679578833e+179

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms

sample1.1s

Algorithm

intervals

Results

365.0ms	6345×	body	80	valid
179.0ms	8000×	pre	80	true
151.0ms	514×	body	1280	valid
139.0ms	622×	body	640	valid
56.0ms	337×	body	320	valid
20.0ms	182×	body	160	valid

Details

analyze137.0ms

sample39.0ms

simplify51.0ms

prune7.0ms

localize17.0ms

rewrite85.0ms

series234.0ms

simplify47.0ms

prune241.0ms

localize14.0ms

rewrite125.0ms

series275.0ms

simplify80.0ms

prune479.0ms

localize16.0ms

rewrite273.0ms

series296.0ms

simplify170.0ms

prune1.8s

localize17.0ms

rewrite144.0ms

series370.0ms

simplify81.0ms

prune485.0ms

regimes340.0ms

bsearch34.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling