Details

sample130.0ms

Algorithm

intervals

Results

59.0ms	256×	body	80	valid
34.0ms	250×	body	80	nan

simplify14.0ms

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: 34.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (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))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite94.0ms

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:

42.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
28.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
117.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
232.0ms	(* (log base) (log base))
56.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2887
1	507
0	200

prune858.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.1b

localize46.0ms

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	(* (log base) (log base))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
20×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`log-pow`
6×	`log-prod` `associate-/r*` `swap-sqr`
4×	`unpow-prod-down` `sqrt-div` `associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `flip-+` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`pow2` `pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

55.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2))))
3.0ms	(pow (log base) 2)
8.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2))))
300.0ms	(pow (log base) 2)
278.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

125 → 125

Iterations

Iter	Nodes
done	5002
2	2617
1	499
0	203

prune1.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.8b

localize57.0ms

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)
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

47.0ms	(/ (+ (* (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)
12.0ms	(sqrt (+ (* re re) (* im im)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2))))
241.0ms	(pow (log base) 2)
277.0ms	(pow (log base) 2)
61.0ms	(sqrt (+ (* re re) (* im im)))

simplify786.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1524
1	406
0	167

prune970.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.8b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
8×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-plus`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 91

Calls

4 calls:

38.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
66.0ms	(sqrt (+ (* re re) (* im im)))
73.0ms	(sqrt (+ (* re re) (* im im)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1548
1	360
0	125

prune759.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 7.7b

regimes1.6s

Accuracy

57.8% (10.5b remaining)

Error of 17.2b against oracle of 6.7b and baseline of 31.7b

bsearch313.0ms

Steps

Iters	Range		Point
8	5.32879288388449e+97	2.5678194040371354e+101	2.190589872393484e+99
8	-1.2509693448545742e+92	-1.767245734559518e+88	-9.737457083335623e+91

simplify1.2s

Iterations

Iter	Nodes
done	5000
10	4509
9	3287
8	2284
7	1423
6	919
5	622
4	351
3	119
2	71
1	61
0	44

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.4s	7964×	body	80	nan