Details

sample127.0ms

Algorithm

intervals

Results

49.0ms	256×	body	80	valid
36.0ms	264×	body	80	nan

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize59.0ms

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)))
0.6b	(* (log base) (log base))
28.8b	(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:

11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
51.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (log base) (log base))
14.0ms	(sqrt (+ (* re re) (* im im)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
142.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
269.0ms	(* (log base) (log base))
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2906
1	507
0	200

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.9b

localize53.0ms

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))
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite115.0ms

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:

81.0ms	(* (/ 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)))))
8.0ms	(* (log base) (log base))
13.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (/ 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)))))
239.0ms	(* (log base) (log base))
201.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
1	760
0	248

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.9b

localize105.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
28.8b	(sqrt (+ (* re re) (* im im)))
28.8b	(sqrt (+ (* re re) (* im im)))
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

9.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
12.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
49.0ms	(sqrt (+ (* re re) (* im im)))
50.0ms	(sqrt (+ (* re re) (* im im)))
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	2540
2	492
1	155
0	70

prune878.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.9b

localize128.0ms

Local error

Found 4 expressions with local error:

5.0b	(pow (sqrt (+ (* re re) (* im im))) 1/3)
28.8b	(sqrt (+ (* re re) (* im im)))
28.8b	(sqrt (+ (* re re) (* im im)))
28.8b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
6×	`unpow-prod-down` `sqrt-div`
5×	`add-exp-log`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `pow-pow` `flip3-+` `flip-+`
1×	`pow-to-exp` `unpow1/3` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

8.0ms	(pow (sqrt (+ (* re re) (* im im))) 1/3)
12.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))
13.0ms	(sqrt (+ (* re re) (* im im)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(pow (sqrt (+ (* re re) (* im im))) 1/3)
57.0ms	(sqrt (+ (* re re) (* im im)))
50.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
3	3930
2	854
1	251
0	82

prune903.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.9b

regimes902.0ms

Accuracy

58% (10.1b remaining)

Error of 17.5b against oracle of 7.4b and baseline of 31.5b

bsearch329.0ms

Steps

Iters	Range		Point
1	8.61389046210236e+138	9.220036899991912e+138	9.068500290519523e+138
10	1.5616267497116248e-250	6.40875993774134e-237	5.119261304077866e-247
7	-8.033278323680815e-259	-1.3959161768952126e-260	-5.0752943855110864e-260
5	-7.198520720508104e+107	-3.310147475454695e+107	-5.2752545601015594e+107

simplify31.0ms

Iterations

Iter	Nodes
done	88
3	88
2	86
1	76
0	58

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	8087×	body	80	nan
1.5s	8000×	body	80	valid