Details

analyze117.0ms

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	212×	body	80	valid
6.0ms	22×	body	1280	valid
5.0ms	256×	pre	80	true
5.0ms	10×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify122.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5064	43

prune4.0ms

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: 22.4b

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))

0.4b

(+.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)

20.5b

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

rewrite100.0ms

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` `insert-posit16` `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 → 114

Calls

3 calls:

29.0ms

(/.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))

46.0ms

(+.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)))

series1.2s

Counts

3 → 9

Calls

3 calls:

419.0ms

(/.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))

451.0ms

(+.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)

342.0ms

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

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	549	768
1	549	768
0	67	69
1	67	69
0	549	768
1	549	768
0	67	69
1	67	69
0	71	45
1	71	45
0	796	1398
1	796	1398
0	117	528
1	117	528
0	796	1398
1	796	1398
0	117	528
1	117	528
0	56	33
1	56	33
0	743	1371
1	743	1371
0	112	528
1	112	528
0	743	1371
1	743	1371
0	112	528
1	112	528
0	53	33
1	53	33

simplify65.0ms

Counts

123 → 123

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	645	5737
1	645	5737

prune217.0ms

Filtered

101 candidates to 123 candidates (-21.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	10	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 10.2b

Counts

124 → 10

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 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))))
0.4b	(+.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)

rewrite105.0ms

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` `insert-posit16` `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 → 133

Calls

4 calls:

13.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
29.0ms	(/.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))
22.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
34.0ms	(+.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)

series1.6s

Counts

4 → 12

Calls

4 calls:

314.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
460.0ms	(/.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))
369.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
493.0ms	(+.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)

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	849	1449
1	849	1449
0	123	528
1	123	528
0	849	1449
1	849	1449
0	123	528
1	123	528
0	53	27
1	53	27
0	595	831
1	595	831
0	70	75
1	70	75
0	595	831
1	595	831
0	70	75
1	70	75
0	28	3
1	28	3
0	790	1422
1	790	1422
0	118	528
1	118	528
0	790	1422
1	790	1422
0	118	528
1	118	528
0	51	27
1	51	27
0	500	552
1	500	552
0	49	51
1	49	51
0	500	552
1	500	552
0	49	51
1	49	51
0	82	45
1	82	45

simplify59.0ms

Counts

145 → 145

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	611	4741
1	611	4741

prune221.0ms

Filtered

112 candidates to 145 candidates (-29.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	145	10	155

Merged error: 10.2b

Counts

155 → 10

localize16.0ms

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)
0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.4b	(+.f64 (cbrt.f64 (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)
11.2b	(cbrt.f64 (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))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
26×	`cbrt-prod_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
20×	`unpow-prod-down_binary64` `cube-prod_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out_binary64`
5×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `insert-posit16` `pow-exp_binary64`
3×	`pow-unpow_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`sqr-pow_binary64` `cube-div_binary64` `unswap-sqr_binary64` `frac-times_binary64` `unpow3_binary64` `associate-*l/_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 141

Calls

4 calls:

28.0ms	(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)
25.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
22.0ms	(+.f64 (cbrt.f64 (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)
12.0ms	(cbrt.f64 (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))

series1.4s

Counts

4 → 12

Calls

4 calls:

557.0ms	(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)
369.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
228.0ms	(+.f64 (cbrt.f64 (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)
215.0ms	(cbrt.f64 (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))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	278	2092
1	278	2092
0	210	1729
1	210	1729
0	278	2092
1	278	2092
0	210	1729
1	210	1729
0	1	3
1	1	3
0	328	2119
1	328	2119
0	222	1729
1	222	1729
0	328	2119
1	328	2119
0	222	1729
1	222	1729
0	1	3
1	1	3
0	595	831
1	595	831
0	70	75
1	70	75
0	595	831
1	595	831
0	70	75
1	70	75
0	28	3
1	28	3
0	937	1655
1	937	1655
0	203	1213
1	203	1213
0	937	1655
1	937	1655
0	203	1213
1	203	1213
0	23	15
1	23	15

simplify112.0ms

Counts

153 → 153

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5013	5813

prune322.0ms

Filtered

92 candidates to 153 candidates (-66.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	154	9	163

Merged error: 10.2b

Counts

163 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.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))))
0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.4b	(+.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)
2.6b	(log.f64 (+.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))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
20×	`times-frac_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
17×	`add-cube-cbrt_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/r_binary64` `cbrt-unprod_binary64` `log-prod_binary64` `associate-/r/_binary64` `associate-l_binary64` `prod-exp_binary64` `insert-posit16` `frac-times_binary64` `associate-l/_binary64`
3×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`associate-*r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `log-div_binary64`
1×	`pow-prod-down_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 108

Calls

4 calls:

30.0ms	(/.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))))
22.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
30.0ms	(+.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)
29.0ms	(log.f64 (+.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))

series1.9s

Counts

4 → 12

Calls

4 calls:

469.0ms	(/.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))))
374.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
501.0ms	(+.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)
534.0ms	(log.f64 (+.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))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	908	1611
1	908	1611
0	137	1212
1	137	1212
0	908	1611
1	908	1611
0	137	1212
1	137	1212
0	36	44
1	36	44
0	849	1449
1	849	1449
0	121	522
1	121	522
0	849	1449
1	849	1449
0	121	522
1	121	522
0	53	27
1	53	27
0	595	831
1	595	831
0	70	75
1	70	75
0	595	831
1	595	831
0	70	75
1	70	75
0	28	3
1	28	3
0	790	1422
1	790	1422
0	116	522
1	116	522
0	790	1422
1	790	1422
0	116	522
1	116	522
0	51	27
1	51	27

simplify61.0ms

Counts

120 → 120

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	556	4742
1	556	4742

prune177.0ms

Filtered

94 candidates to 120 candidates (-27.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	118	11	129

Merged error: 10.2b

Counts

129 → 11

regimes149.0ms

Accuracy

0% (0.3b remaining)

Error of 12.3b against oracle of 12.0b and baseline of 12.3b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	47
1	35	47

end0.0ms

sample1.1s

Algorithm

intervals

Results

344.0ms	6367×	body	80	valid
174.0ms	8000×	pre	80	true
146.0ms	511×	body	1280	valid
123.0ms	559×	body	640	valid
57.0ms	352×	body	320	valid
25.0ms	211×	body	160	valid

Details

analyze117.0ms

sample39.0ms

simplify122.0ms

prune4.0ms

localize13.0ms

rewrite100.0ms

series1.2s

simplify65.0ms

prune217.0ms

localize13.0ms

rewrite105.0ms

series1.6s

simplify59.0ms

prune221.0ms

localize16.0ms

rewrite94.0ms

series1.4s

simplify112.0ms

prune322.0ms

localize16.0ms

rewrite116.0ms

series1.9s

simplify61.0ms

prune177.0ms

regimes149.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample1.1s

Profiling