Details

sample118.0ms

Algorithm

intervals

Results

50.0ms	256×	body	80	valid
39.0ms	254×	body	80	nan

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	724
1	23	724
done	23	724

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite69.0ms

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×	`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 → 110

Calls

4 calls:

30.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
19.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
140.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
256.0ms	(* (log base) (log base))
455.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	200	57418
1	507	54670
2	2887	53704
done	5000	53336

prune918.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.6b

localize72.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
58×	`times-frac`
53×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`pow1`
32×	`associate-r` `associate-l` `sqrt-prod`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/`

Counts

4 → 174

Calls

4 calls:

77.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
7.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
226.0ms	(* (log base) (log base))
175.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

186 → 186

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	248	114078
1	760	107429
done	5000	103263

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.5b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
0.6b	(cbrt base)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

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

series822.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt base)
275.0ms	(cbrt base)
234.0ms	(cbrt base)
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

60 → 60

Iterations

Useful iterations: 3 (270.0ms)

Iter	Nodes	Cost
0	60	12173
1	130	10684
2	331	10567
3	864	10087
4	2439	10087
done	5000	10087

prune749.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.5b

localize141.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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×	`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 → 123

Calls

4 calls:

7.0ms	(* (log base) (log base))
7.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(* (log base) (log base))
240.0ms	(* (log base) (log base))
241.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

135 → 135

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	89	29120
1	220	24406
2	1287	23620
done	5000	23170

prune1.1s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 6.5b

regimes1.1s

Accuracy

56.1% (10.8b remaining)

Error of 18.3b against oracle of 7.4b and baseline of 32.1b

bsearch274.0ms

Steps

Iters	Range		Point
7	1.8841348729660574e+121	5.2212346753812574e+122	2.3548449389898907e+121
7	-2.269236330710186e-224	-9.546083620373119e-226	-9.727151345646149e-225
7	-6.958408011851449e-171	-1.5264122711685816e-172	-8.321374673661263e-172
3	-2.330089513821311e+99	-1.8288702712188364e+99	-2.2763645328108957e+99

simplify20.0ms

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	53	2319
1	69	2319
done	69	2319

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	7946×	body	80	nan
1.4s	8000×	body	80	valid