Details

sample74.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
23.0ms	244×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune8.0ms

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: 32.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
11.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
5.0ms	(sqrt (+ (* re re) (* im im)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
30.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
16.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.1s

Counts

122 → 122

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	203	2483
1	457	2344
2	1325	2034
3	4941	1990
done	5000	1990

prune270.0ms

Filtered

86 candidates to 122 candidates (-41.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 6.9b

Counts

123 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

30.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
5.0ms	(sqrt (+ (* re re) (* im im)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
16.0ms	(pow (log base) 2)
16.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

152 → 152

Iterations

Useful iterations: 2 (606.0ms)

Iter	Nodes	Cost
0	240	5261
1	669	4903
2	2085	4093
done	5001	4093

prune399.0ms

Filtered

90 candidates to 152 candidates (-68.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	148	18	166

Merged error: 6.9b

Counts

166 → 18

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (* 2 (log (cbrt base))))
0.5b	(cbrt base)
0.5b	(cbrt base)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
18×	`cbrt-prod`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
4×	`associate-l` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `log-pow` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

8.0ms	(* (log base) (* 2 (log (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (log base) (* 2 (log (cbrt base))))
24.0ms	(cbrt base)
24.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts

92 → 92

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	163	1074
1	356	992
2	837	871
3	2401	832
done	5001	831

prune189.0ms

Filtered

55 candidates to 92 candidates (-67.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	2	14	16
Picked	1	0	1
Done	0	1	1
Total	91	19	110

Merged error: 6.9b

Counts

110 → 19

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt base)
0.5b	(cbrt (pow (* (* (log (cbrt base)) 2) (log base)) 3))
0.7b	(pow (* (* (log (cbrt base)) 2) (log base)) 3)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `cbrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `sqrt-prod` `cbrt-unprod` `rem-cube-cbrt`
2×	`cube-mult` `unpow-prod-down` `pow1/3` `sqrt-div` `unpow3` `cube-prod` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `rem-cbrt-cube` `flip-+`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt base)
3.0ms	(cbrt (pow (* (* (log (cbrt base)) 2) (log base)) 3))
7.0ms	(pow (* (* (log (cbrt base)) 2) (log base)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt base)
58.0ms	(cbrt (pow (* (* (log (cbrt base)) 2) (log base)) 3))
73.0ms	(pow (* (* (log (cbrt base)) 2) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (789.0ms)

Iter	Nodes	Cost
0	137	965
1	298	815
2	851	722
3	4357	695
done	5000	695

prune140.0ms

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	2	15	17
Picked	0	1	1
Done	0	1	1
Total	79	20	99

Merged error: 6.9b

Counts

99 → 20

regimes656.0ms

Accuracy

57.4% (10.6b remaining)

Error of 17.8b against oracle of 7.2b and baseline of 32.1b

bsearch160.0ms

Steps

Iters	Range		Point
5	1.8171784245322648e+37	6.43616546702885e+37	6.316251233561299e+37
9	1.9980346609717805e-204	2.9831774035161146e-199	4.7115991876438505e-204
7	-2.410271475432134e-307	2.8466800401792686e-308	-2.8820882891916374e-308
6	-1.1149114536052807e+61	-7.527714714268046e+59	-2.0752208244632336e+60

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	128
1	57	128
done	57	128

end0.0ms

sample2.1s

Algorithm

intervals

Results

770.0ms	8000×	body	80	valid
740.0ms	7896×	body	80	nan

Details

sample74.0ms

simplify5.0ms

prune8.0ms

localize19.0ms

rewrite31.0ms

series75.0ms

simplify3.1s

prune270.0ms

localize24.0ms

rewrite48.0ms

series73.0ms

simplify1.6s

prune399.0ms

localize26.0ms

rewrite20.0ms

series116.0ms

simplify2.9s

prune189.0ms

localize32.0ms

rewrite17.0ms

series162.0ms

simplify2.4s

prune140.0ms

regimes656.0ms

bsearch160.0ms

simplify4.0ms

end0.0ms

sample2.1s

Profiling