Details

sample148.0ms

Algorithm

intervals

Results

69.0ms	304×	body	80	nan
41.0ms	256×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize31.0ms

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))
0.6b	(* (log base) (log base))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite122.0ms

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:

55.0ms	(/ (+ (* (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))
15.0ms	(* (log base) (log base))
29.0ms	(sqrt (+ (* re re) (* im im)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
125.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
214.0ms	(* (log base) (log base))
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1677
1	505
0	200

prune883.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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))
12.0ms	(* (log base) (log base))
11.0ms	(sqrt (+ (* re re) (* im im)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
197.0ms	(* (log base) (log base))
211.0ms	(* (log base) (log base))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
4	4375
3	1741
2	760
1	312
0	130

prune905.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

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:

15.0ms	(* (log base) (log base))
10.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (log base) (log base))
197.0ms	(* (log base) (log base))
198.0ms	(* (log base) (log base))
56.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

135 → 135

Iterations

Iter	Nodes
done	5004
4	2406
3	1004
2	512
1	218
0	89

prune870.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.0b

localize89.0ms

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)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
6×	`cbrt-prod` `log-prod` `add-cbrt-cube` `associate-l` `add-exp-log`
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:

17.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
10.0ms	(sqrt (+ (* re re) (* im im)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
240.0ms	(cbrt base)
199.0ms	(cbrt base)
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
4	2908
3	1307
2	554
1	245
0	116

prune547.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 7.0b

regimes1.3s

Accuracy

57.9% (10.4b remaining)

Error of 17.5b against oracle of 7.1b and baseline of 31.8b

bsearch201.0ms

Steps

Iters	Range		Point
8	8.204377162192618e+67	1.198070884819284e+71	1.1752879004201556e+71
9	-1.5811037545328982e+61	-1.4401165640648994e+52	-8.113334361781796e+60

simplify17.0ms

Iterations

Iter	Nodes
done	67
4	67
3	63
2	58
1	54
0	40

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.2s	8039×	body	80	nan