Details

sample57.0ms

Algorithm

intervals

Results

19.0ms	224×	body	80	nan
18.0ms	256×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16
done	23	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
39.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
102.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
141.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205
done	5001	1205

prune444.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize21.0ms

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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

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-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `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:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
10.0ms	(* (log base) (log base))
13.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
287.0ms	(* (log base) (log base))
147.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify144.0ms

Counts

127 → 127

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4681	599
3	5001	592
done	5001	592

prune413.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
1.0b	(pow (log base) 4)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms	(* (log base) (log base))
3.0ms	(pow (log base) 4)
8.0ms	(sqrt (+ (* re re) (* im im)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
146.0ms	(* (log base) (log base))
160.0ms	(pow (log base) 4)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	319	642
1	1269	568
2	5002	539
done	5002	539

prune435.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
0.7b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-unpow` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`pow2` `pow-pow` `pow-plus` `sqrt-div` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `cube-prod` `flip-+` `sqr-pow`

Counts

4 → 109

Calls

4 calls:

10.0ms	(* (log base) (log base))
9.0ms	(* (log base) (log base))
11.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
8.0ms	(sqrt (+ (* re re) (* im im)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (log base) (log base))
146.0ms	(* (log base) (log base))
145.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	295	610
1	1189	536
2	5001	518
done	5001	518

prune411.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.3b

regimes581.0ms

Accuracy

56.6% (10.8b remaining)

Error of 17.9b against oracle of 7.1b and baseline of 32.0b

bsearch325.0ms

Steps

Iters	Range		Point
9	1.5275481395911593e+86	9.063140559484059e+91	5.168286053687553e+91
8	2.8783829979102853e-268	6.166733511535458e-265	6.665470315389402e-268
9	6.149017774468906e-306	5.393968064642576e-299	9.450669110711002e-302
8	-1.1694514609356496e+58	-5.892119085235431e+53	-1.1518889041005871e+58

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	93
1	83	93
2	84	93
3	84	93
done	84	93

end0.0ms

sample1.6s

Algorithm

intervals

Results

555.0ms	8000×	body	80	valid
539.0ms	7823×	body	80	nan