Details

sample117.0ms

Algorithm

intervals

Results

43.0ms	256×	body	80	valid
36.0ms	239×	body	80	nan

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize38.0ms

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))
0.5b	(* (log base) (log base))
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite148.0ms

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:

61.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
24.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
19.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
136.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
206.0ms	(* (log base) (log base))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

122 → 122

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1342	2035
3	4402	1998
done	5001	1992

prune642.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
9×	`pow1`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `associate-/r*` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `log-pow` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2))))
5.0ms	(pow (log base) 2)
5.0ms	(pow (log base) 2)
14.0ms	(sqrt (+ (* re re) (* im im)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2))))
215.0ms	(pow (log base) 2)
234.0ms	(pow (log base) 2)
72.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

108 → 108

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	167	2516
1	366	2350
2	916	2199
3	2728	2173
done	5001	2169

prune717.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

24.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
11.0ms	(cbrt base)
14.0ms	(sqrt (+ (* re re) (* im im)))

series699.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
228.0ms	(cbrt base)
284.0ms	(cbrt base)
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

77 → 77

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	116	875
1	229	828
2	552	728
3	1177	707
4	2809	705
done	5002	705

prune576.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
28.8b	(sqrt (+ (* re re) (* im im)))
30.0b	(log (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `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 → 51

Calls

4 calls:

1.0ms	(cbrt base)
1.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(log (+ (* re re) (* im im)))

series918.0ms

Counts

4 → 12

Calls

4 calls:

549.0ms	(cbrt base)
242.0ms	(cbrt base)
44.0ms	(sqrt (+ (* re re) (* im im)))
82.0ms	(log (+ (* re re) (* im im)))

simplify3.7s

Counts

63 → 63

Iterations

Useful iterations: 3 (236.0ms)

Iter	Nodes	Cost
0	85	574
1	171	529
2	341	467
3	716	449
4	1731	449
5	4828	449
done	5000	449

prune569.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 6.6b

regimes959.0ms

Accuracy

58.5% (10.6b remaining)

Error of 17.5b against oracle of 7.0b and baseline of 32.5b

bsearch121.0ms

Steps

Iters	Range		Point
2	2.117882082947689e+145	2.406271033498864e+145	2.1539307017665857e+145
7	-2.7106654859603125e+84	-3.692021070621555e+82	-2.6637756994207938e+84

simplify23.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	45	91
1	63	91
2	67	91
3	68	91
done	68	91

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.4s	8219×	body	80	nan