Details

sample133.0ms

Algorithm

intervals

Results

61.0ms	265×	body	80	nan
44.0ms	256×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5174
7	1116
6	232
5	78
4	53
3	39
2	24
1	22
0	18

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.9b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`associate-/r*` `sqrt-div`
3×	`flip3-+` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 77

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
32.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* re re) (* im im))
155.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5003
3	2220
2	686
1	269
0	133

prune598.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(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-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

5.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
11.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
55.0ms	(sqrt (+ (* re re) (* im im)))
52.0ms	(sqrt (+ (* re re) (* im im)))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
4	3626
3	1040
2	341
1	149
0	72

prune543.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.9b

localize63.0ms

Local error

Found 4 expressions with local error:

26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

9.0ms	(sqrt (+ (* re re) (* im im)))
14.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
5	3254
4	995
3	435
2	196
1	92
0	39

prune577.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.9b

localize51.0ms

Local error

Found 4 expressions with local error:

26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

10.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
5	3254
4	995
3	435
2	196
1	92
0	39

prune543.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.9b

regimes709.0ms

Accuracy

56% (10.3b remaining)

Error of 17.3b against oracle of 7.0b and baseline of 30.4b

bsearch468.0ms

Steps

Iters	Range		Point
9	3.5627589106734345e+99	6.741762871954432e+106	2.1214141144086502e+101
6	-9.98405984174964e-304	-1.146206375811988e-304	-4.64950550008063e-304
7	-2.1551503804424012e-194	-1.00806654500884e-195	-1.610831336314797e-195
8	-1.0537521384392173e+77	-2.9102656186225933e+72	-3.912111704121843e+74

simplify35.0ms

Iterations

Iter	Nodes
done	52
1	52
0	45

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.3s	7972×	body	80	nan
1.7s	8000×	body	80	valid