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

sample41.0ms

Algorithm

intervals

Results

14.0ms	201×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	21×	body	640	valid
4.0ms	16×	body	1280	valid
2.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

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: 24.6b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

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))

1.3b

(+.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)

20.6b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

23.0ms

(/.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))

36.0ms

(+.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)))

series687.0ms

Counts

3 → 9

Calls

3 calls:

283.0ms

(/.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))

340.0ms

(+.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)

64.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify128.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4944	5261
1	4944	5261

prune201.0ms

Filtered

91 candidates to 120 candidates (-31.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Merged error: 6.3b

Counts

121 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
2.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.6b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite121.0ms

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:

20.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
14.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
41.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
28.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series847.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
62.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
283.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
340.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

simplify173.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4992	13438
1	4992	13438

prune481.0ms

Filtered

199 candidates to 307 candidates (-54.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	305	2	307
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	307	8	315

Merged error: 6.3b

Counts

315 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
2.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.6b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac_binary64`
152×	`*-un-lft-identity_binary64`
117×	`add-sqr-sqrt_binary64`
90×	`associate-r_binary64`
76×	`add-cube-cbrt_binary64`
22×	`distribute-lft-out_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/r/_binary64` `cbrt-prod_binary64`
10×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-inv_binary64`
5×	`associate-/l*_binary64`
4×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64`
2×	`cbrt-div_binary64` `associate-/l/_binary64` `cube-div_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `associate-r/_binary64` `pow1/3_binary64` `sqr-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `unpow3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 191

Calls

4 calls:

30.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
44.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
29.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series1.0s

Counts

4 → 12

Calls

4 calls:

332.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
56.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
285.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
336.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

simplify136.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5070	7828

prune338.0ms

Filtered

134 candidates to 203 candidates (-51.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	202	9	211

Merged error: 6.3b

Counts

211 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.4b	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.4b	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
7.4b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

90×	`*-un-lft-identity_binary64`
64×	`times-frac_binary64`
56×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`
17×	`associate-/r*_binary64` `distribute-lft-out_binary64`
12×	`add-exp-log_binary64` `associate-/l*_binary64`
10×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `sqrt-div_binary64`
3×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-flip_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `inv-pow_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 157

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
14.0ms	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
41.0ms	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series656.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
142.0ms	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
117.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
341.0ms	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

simplify104.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4954	5085
1	4954	5085

prune263.0ms

Filtered

103 candidates to 169 candidates (-64.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	169	9	178

Merged error: 6.3b

Counts

178 → 9

regimes135.0ms

Accuracy

7.4% (5.7b remaining)

Error of 11.8b against oracle of 6.1b and baseline of 12.2b

bsearch102.0ms

Steps

Iters	Range		Point
6	3.642117896536635e+211	1.5693363691217388e+212	1.3588989434573756e+212
8	6.043586340655682e+81	2.2813786649102605e+86	1.0405905765331085e+86
8	1.2340678290696518e+40	1.3987077847067637e+43	1.5251724157134815e+41

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	157
1	86	157

end0.0ms

sample1.1s

Algorithm

intervals

Results

369.0ms	6382×	body	80	valid
177.0ms	8000×	pre	80	true
146.0ms	504×	body	1280	valid
126.0ms	560×	body	640	valid
62.0ms	376×	body	320	valid
22.0ms	178×	body	160	valid

Details

analyze128.0ms

sample41.0ms

simplify80.0ms

prune3.0ms

localize13.0ms

rewrite78.0ms

series687.0ms

simplify128.0ms

prune201.0ms

localize15.0ms

rewrite121.0ms

series847.0ms

simplify173.0ms

prune481.0ms

localize16.0ms

rewrite125.0ms

series1.0s

simplify136.0ms

prune338.0ms

localize19.0ms

rewrite82.0ms

series656.0ms

simplify104.0ms

prune263.0ms

regimes135.0ms

bsearch102.0ms

simplify5.0ms

end0.0ms

sample1.1s

Profiling