Details

analyze330.0ms

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample31.0ms

Algorithm

intervals

Results

9.0ms	205×	body	80	valid
4.0ms	16×	body	2560	valid
4.0ms	18×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	5×	body	5120	valid
2.0ms	8×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	157	23
1	157	23

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 37.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`sqrt-pow1_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

6.0ms	(+.f64 (.f64 re re) (.f64 im im))
11.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series3.0s

Counts

4 → 12

Calls

4 calls:

550.0ms	(+.f64 (.f64 re re) (.f64 im im))
904.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
893.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
673.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	1371	596
1	1371	596
0	1371	596
1	1371	596
0	4858	14
1	4858	14
0	1866	659
1	1866	659
0	1866	659
1	1866	659
0	4858	14
1	4858	14
0	1977	1265
1	1977	1265
0	1977	1265
1	1977	1265
0	4954	19
1	4954	19
0	1398	282
1	1398	282
0	1398	282
1	1398	282
0	1	3
1	1	3

simplify199.0ms

Counts

69 → 69

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	4923	1122
1	4923	1122

prune128.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	60	9	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	10	70

Merged error: 29.9b

Counts

70 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3)
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
20.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-*r/_binary64` `pow-pow_binary64` `cube-div_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 89

Calls

4 calls:

22.0ms	(pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3)
16.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
9.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3))
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series3.0s

Counts

4 → 12

Calls

4 calls:

964.0ms	(pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3)
874.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
236.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))) 3))
884.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	1371	596
1	1371	596
0	1371	596
1	1371	596
0	4858	14
1	4858	14
0	256	1855
1	256	1855
0	256	1855
1	256	1855
0	5000	19
0	1866	659
1	1866	659
0	1866	659
1	1866	659
0	4858	14
1	4858	14
0	2166	1410
1	2166	1410
0	2166	1410
1	2166	1410
0	7	60
1	7	60

simplify92.0ms

Counts

101 → 101

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5010	2226

prune79.0ms

Filtered

61 candidates to 101 candidates (-65.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	99	12	111

Merged error: 29.9b

Counts

111 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (.f64 2 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.7b	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`pow1_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64` `exp-sum_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64` `difference-of-squares_binary64` `log-div_binary64` `insert-posit16` `sqrt-div_binary64` `exp-prod_binary64`
3×	`flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 66

Calls

4 calls:

16.0ms	(sqrt.f64 (.f64 2 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
11.0ms	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series3.1s

Counts

4 → 12

Calls

4 calls:

817.0ms	(sqrt.f64 (.f64 2 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))))
875.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
744.0ms	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
664.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	1371	596
1	1371	596
0	1371	596
1	1371	596
0	4858	14
1	4858	14
0	1923	1208
1	1923	1208
0	1923	1208
1	1923	1208
0	10	45
1	10	45
0	1866	659
1	1866	659
0	1866	659
1	1866	659
0	4858	14
1	4858	14
0	2037	1543
1	2037	1543
0	2037	1543
1	2037	1543
0	11	60
1	11	60

simplify159.0ms

Counts

78 → 78

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	4867	1449
1	4867	1449

prune69.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	77	13	90

Merged error: 29.9b

Counts

90 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.1b	(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))))
29.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1_binary64` `add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64` `exp-prod_binary64`
6×	`add-log-exp_binary64` `sqrt-prod_binary64` `sqrt-div_binary64`
5×	`sqrt-pow1_binary64`
4×	`log-prod_binary64` `associate-*r/_binary64` `log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-sum_binary64` `insert-posit16`
3×	`pow1/2_binary64` `flip3--_binary64` `flip--_binary64`
2×	`pow-prod-down_binary64` `exp-diff_binary64` `difference-of-squares_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`

Counts

4 → 67

Calls

4 calls:

11.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
13.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
14.0ms	(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series3.2s

Counts

4 → 12

Calls

4 calls:

872.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
865.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
803.0ms	(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))))
667.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	1371	596
1	1371	596
0	1371	596
1	1371	596
0	4858	14
1	4858	14
0	2034	1549
1	2034	1549
0	2034	1549
1	2034	1549
0	10	51
1	10	51
0	1866	659
1	1866	659
0	1866	659
1	1866	659
0	4858	14
1	4858	14
0	1977	1265
1	1977	1265
0	1977	1265
1	1977	1265
0	4954	19
1	4954	19

simplify188.0ms

Counts

79 → 79

Iterations

Useful iterations: 0 (159.0ms)

Iter	Nodes	Cost
0	4890	1458
1	4890	1458

prune62.0ms

Filtered

58 candidates to 79 candidates (-36.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	76	16	92

Merged error: 29.9b

Counts

92 → 16

regimes394.0ms

Accuracy

90.6% (0.7b remaining)

Error of 31.3b against oracle of 30.5b and baseline of 38.5b

bsearch46.0ms

Steps

Iters	Range		Point
7	3.665974490482107e-79	1.7175647994339747e-77	7.75134375027333e-79
9	-7.513536215220485e+159	-2.1126182320254652e+150	-1.3296453913418618e+154

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	65	81
1	65	81

end0.0ms

sample1.0s

Algorithm

intervals

Results

273.0ms	5979×	body	80	valid
194.0ms	721×	body	2560	valid
105.0ms	473×	body	1280	valid
102.0ms	8000×	pre	80	true
99.0ms	312×	body	5120	valid
48.0ms	285×	body	640	valid
17.0ms	133×	body	320	valid
8.0ms	97×	body	160	valid

Details

analyze330.0ms

sample31.0ms

simplify33.0ms

prune2.0ms

localize10.0ms

rewrite34.0ms

series3.0s

simplify199.0ms

prune128.0ms

localize22.0ms

rewrite61.0ms

series3.0s

simplify92.0ms

prune79.0ms

localize16.0ms

rewrite46.0ms

series3.1s

simplify159.0ms

prune69.0ms

localize13.0ms

rewrite46.0ms

series3.2s

simplify188.0ms

prune62.0ms

regimes394.0ms

bsearch46.0ms

simplify7.0ms

end0.0ms

sample1.0s

Profiling