Details

sample75.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
24.0ms	228×	body	80	nan

simplify10.0ms

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: 31.4b

localize72.0ms

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)))

rewrite86.0ms

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:

53.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
106.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
199.0ms	(* (log base) (log base))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1677
1	505
0	200

prune981.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.0b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* re re) (* im im)))
48.0ms	(sqrt (+ (* re re) (* im im)))
60.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
5	3274
4	992
3	429
2	195
1	91
0	38

prune884.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.0b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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

series744.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
283.0ms	(cbrt base)
303.0ms	(cbrt base)
45.0ms	(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

prune749.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 6.9b

localize92.0ms

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)))

rewrite54.0ms

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:

8.0ms	(* (log base) (log base))
15.0ms	(* (log base) (log base))
15.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (log base) (log base))
212.0ms	(* (log base) (log base))
235.0ms	(* (log base) (log base))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

135 → 135

Iterations

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

prune756.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 6.9b

regimes1.0s

Accuracy

58.8% (10.4b remaining)

Error of 17.5b against oracle of 7.2b and baseline of 32.3b

bsearch596.0ms

Steps

Iters	Range		Point
9	4.21314112800409e+88	2.5535742070497435e+96	2.3916742676221853e+96
10	-1.5321938689221141e+128	-1.1914452388573492e+118	-1.2570017619609752e+125

simplify23.0ms

Iterations

Iter	Nodes
done	70
4	70
3	66
2	61
1	57
0	43

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.7s	7699×	body	80	nan
1.2s	8000×	body	80	valid