Details

sample111.0ms

Algorithm

intervals

Results

40.0ms	256×	body	80	valid
37.0ms	228×	body	80	nan

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune34.0ms

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)))

rewrite102.0ms

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:

49.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (+ (* (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))
237.0ms	(* (log base) (log base))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

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: 7.0b

localize66.0ms

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)))

rewrite34.0ms

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))
8.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (log base) (log base))
207.0ms	(* (log base) (log base))
228.0ms	(* (log base) (log base))
69.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1287
1	220
0	89

prune893.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.0b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
8×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`cbrt-prod` `sqrt-prod`
2×	`pow2` `pow-plus` `sqrt-div` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+`

Counts

4 → 98

Calls

4 calls:

1.0ms	(cbrt base)
8.0ms	(* (log base) (log base))
11.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(cbrt base)
200.0ms	(* (log base) (log base))
199.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1375
1	253
0	105

prune828.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.6b	(cbrt (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
8×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `pow-plus` `sqrt-div` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `pow3` `rem-cbrt-cube` `flip-+`

Counts

4 → 97

Calls

4 calls:

8.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))
139.0ms	(cbrt (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
13.0ms	(sqrt (+ (* re re) (* im im)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (log base) (log base))
172.0ms	(* (log base) (log base))
184.0ms	(cbrt (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1295
1	230
0	98

prune552.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 6.9b

regimes1.1s

Accuracy

58.8% (10.4b remaining)

Error of 17.5b against oracle of 7.1b and baseline of 32.3b

bsearch218.0ms

Steps

Iters	Range		Point
9	4.21314112800409e+88	2.5535742070497435e+96	2.5848905970927477e+95
7	-5.7639100580615025e+107	-3.4845569108032984e+105	-1.4362714021925781e+107

simplify30.0ms

Iterations

Iter	Nodes
done	66
3	66
2	64
1	56
0	43

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.0s	7699×	body	80	nan
1.2s	8000×	body	80	valid