Details

analyze123.0ms

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

12.0ms	209×	body	80	valid
7.0ms	17×	body	1280	valid
5.0ms	256×	pre	80	true
5.0ms	20×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5221	29

prune5.0ms

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: 23.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.0b	(/.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))
1.2b	(+.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)))

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:

10.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
24.0ms	(/.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)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
73.0ms	(/.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))
97.0ms	(+.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)
19.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

simplify51.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4968	3892
1	4968	3892

prune176.0ms

Filtered

114 candidates to 154 candidates (-35.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	146	8	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	8	155

Merged error: 4.1b

Counts

155 → 8

localize13.0ms

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 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
2.1b	(.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)))))
3.8b	(+.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)

rewrite124.0ms

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:

15.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
21.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
39.0ms	(.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)))))
31.0ms	(+.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)

series228.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
42.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
74.0ms	(.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)))))
96.0ms	(+.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)

simplify94.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5049	8873

prune353.0ms

Filtered

199 candidates to 307 candidates (-54.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	301	6	307
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	307	8	315

Merged error: 4.1b

Counts

315 → 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))))
1.2b	(+.f64 (log.f64 (exp.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)
2.1b	(.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)))))
3.3b	(log.f64 (exp.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)))))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac_binary64`
277×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
132×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
46×	`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`
14×	`flip3-+_binary64` `flip-+_binary64`
11×	`div-inv_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
6×	`log-prod_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`log-pow_binary64`
4×	`associate-/r_binary64` `associate-l*_binary64`
3×	`cbrt-unprod_binary64` `associate-+l+_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`div-sub_binary64` `exp-to-pow_binary64` `frac-times_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `exp-prod_binary64` `-commutative_binary64`

Counts

4 → 275

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))))
6.0ms	(+.f64 (log.f64 (exp.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)
42.0ms	(.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)))))
3.0ms	(log.f64 (exp.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)))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
94.0ms	(+.f64 (log.f64 (exp.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)
73.0ms	(.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)))))
77.0ms	(log.f64 (exp.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)))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5016	8705

prune344.0ms

Filtered

187 candidates to 287 candidates (-53.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	287	8	295

Merged error: 4.1b

Counts

295 → 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))))
0.1b	(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))
2.1b	(.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)))))
3.8b	(+.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)

rewrite140.0ms

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:

23.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
29.0ms	(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))
39.0ms	(.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)))))
31.0ms	(+.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)

series306.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
94.0ms	(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))
75.0ms	(.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)))))
96.0ms	(+.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)

simplify85.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4993	9182
1	4993	9182

prune568.0ms

Filtered

186 candidates to 290 candidates (-55.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	285	5	290
Fresh	4	2	6
Picked	1	0	1
Done	1	0	1
Total	291	7	298

Merged error: 4.1b

Counts

298 → 7

regimes236.0ms

Accuracy

1.9% (6.3b remaining)

Error of 12.1b against oracle of 5.8b and baseline of 12.2b

bsearch104.0ms

Steps

Iters	Range		Point
8	6.427001180233014e+254	1.101813803539734e+258	1.6308915972802799e+255
7	2.42269300389632e+209	1.6710815416988815e+211	1.6459537248978528e+211
8	1.6977211707142244e+91	1.5790889752041876e+95	3.0611776262030834e+92

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	139
1	89	139

end0.0ms

sample1.1s

Algorithm

intervals

Results

369.0ms	6379×	body	80	valid
171.0ms	8000×	pre	80	true
146.0ms	507×	body	1280	valid
123.0ms	534×	body	640	valid
63.0ms	362×	body	320	valid
24.0ms	218×	body	160	valid

Details

analyze123.0ms

sample39.0ms

simplify53.0ms

prune5.0ms

localize13.0ms

rewrite88.0ms

series197.0ms

simplify51.0ms

prune176.0ms

localize13.0ms

rewrite124.0ms

series228.0ms

simplify94.0ms

prune353.0ms

localize15.0ms

rewrite89.0ms

series288.0ms

simplify90.0ms

prune344.0ms

localize15.0ms

rewrite140.0ms

series306.0ms

simplify85.0ms

prune568.0ms

regimes236.0ms

bsearch104.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling