Details

sample84.0ms

Algorithm

intervals

Results

30.0ms	252×	body	80	nan
28.0ms	256×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize43.0ms

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))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite77.0ms

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:

40.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
19.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
143.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
223.0ms	(* (log base) (log base))
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2887
1	507
0	200

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))
10.0ms	(sqrt (+ (* re re) (* im im)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
254.0ms	(* (log base) (log base))
220.0ms	(* (log base) (log base))
55.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	1836
1	314
0	130

prune888.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.1b

localize56.0ms

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))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

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:

13.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
22.0ms	(sqrt (+ (* re re) (* im im)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (log base) (log base))
251.0ms	(* (log base) (log base))
206.0ms	(* (log base) (log base))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify962.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1287
1	220
0	89

prune763.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
0.6b	(cbrt base)
28.9b	(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)))

series849.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt base)
269.0ms	(cbrt base)
235.0ms	(cbrt base)
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
4	2439
3	864
2	331
1	130
0	60

prune530.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 7.0b

regimes913.0ms

Accuracy

56.5% (10.6b remaining)

Error of 18.0b against oracle of 7.4b and baseline of 31.8b

bsearch383.0ms

Steps

Iters	Range		Point
5	1.2618939617618823e+110	3.936034324239634e+110	2.1310417422961706e+110
6	6.92543355188382e-187	3.260368270748403e-186	7.657991494094246e-187
7	-6.856160329593529e-213	-9.104135836411172e-215	-3.5661932702760735e-214
8	-4.792703353650342e+80	-1.5715417821050658e+76	-1.737740429468826e+80

simplify46.0ms

Iterations

Iter	Nodes
done	71
1	71
0	55

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.6s	7931×	body	80	nan
1.4s	8000×	body	80	valid