Details

sample89.0ms

Algorithm

intervals

Results

37.0ms	256×	body	80	valid
22.0ms	241×	body	80	nan

simplify40.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (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))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-cbrt-cube` `associate-l` `add-exp-log` `log-pow`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `flip3-+` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 114

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
96.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
13.0ms	(* (log base) (log base))
13.0ms	(sqrt (+ (* re re) (* im im)))

series808.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
228.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
279.0ms	(* (log base) (log base))
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1676
1	510
0	204

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.4b

localize111.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
30×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod` `swap-sqr` `log-pow`
12×	`associate-r` `associate-l`
10×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`insert-posit16` `add-log-exp`
3×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 127

Calls

4 calls:

29.0ms	(* (log base) (log base))
17.0ms	(* (log base) (log base))
13.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series821.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(* (log base) (log base))
239.0ms	(* (log base) (log base))
238.0ms	(* (log base) (log base))
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify6.0s

Counts

139 → 139

Iterations

Iter	Nodes
done	5006
4	2465
3	985
2	501
1	221
0	91

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.3b

localize160.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
28.3b	(sqrt (+ (* re re) (* im im)))
29.5b	(log (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`log-prod` `sqrt-prod`
2×	`log-div` `flip3-+` `pow1/3` `sqrt-div` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

4 → 55

Calls

4 calls:

2.0ms	(cbrt base)
2.0ms	(cbrt base)
11.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(log (+ (* re re) (* im im)))

series792.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(cbrt base)
316.0ms	(cbrt base)
53.0ms	(sqrt (+ (* re re) (* im im)))
124.0ms	(log (+ (* re re) (* im im)))

simplify3.8s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
4	1627
3	714
2	347
1	177
0	88

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

localize271.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(cbrt (+ (* re re) (* im im)))
29.3b	(cbrt (+ (* re re) (* im im)))
29.3b	(cbrt (+ (* re re) (* im im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

21.0ms	(sqrt (+ (* re re) (* im im)))
13.0ms	(cbrt (+ (* re re) (* im im)))
13.0ms	(cbrt (+ (* re re) (* im im)))
14.0ms	(cbrt (+ (* re re) (* im im)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (* re re) (* im im)))
186.0ms	(cbrt (+ (* re re) (* im im)))
196.0ms	(cbrt (+ (* re re) (* im im)))
188.0ms	(cbrt (+ (* re re) (* im im)))

simplify5.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5002
4	3940
3	1044
2	333
1	144
0	67

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.3b

regimes2.4s

Accuracy

59.4% (10.0b remaining)

Error of 17.7b against oracle of 7.6b and baseline of 32.3b

bsearch293.0ms

Steps

Iters	Range		Point
6	5.071112687032584e+85	6.766392302206487e+86	4.348498385315215e+86
11	-2.4334994185842963e+101	-2.852849138622092e+70	-5.096763843336727e+82

simplify72.0ms

Iterations

Iter	Nodes
done	69
4	69
3	65
2	60
1	58
0	44

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
1.4s	7906×	body	80	nan