Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	252×	body	80	nan
17.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize19.0ms

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))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

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)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify584.0ms

Counts

122 → 122

Iterations

Useful iterations: done (580.0ms)

Iter	Nodes	Cost
0	200	2451
1	441	2259
2	1349	2035
done	5001	2023

prune519.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
12×	`log-prod`
9×	`sqrt-prod`
8×	`add-exp-log` `unpow-prod-down`
6×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-r` `log-pow` `add-cbrt-cube`
4×	`associate-l` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

9.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
1.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
154.0ms	(pow (log base) 2)
156.0ms	(pow (log base) 2)
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

99 → 99

Iterations

Useful iterations: 3 (731.0ms)

Iter	Nodes	Cost
0	132	1182
1	266	1069
2	732	945
3	2609	924
done	5001	924

prune441.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`log-prod`
11×	`log-pow`
10×	`associate-r`
9×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
8×	`associate-l` `add-cbrt-cube`
6×	`swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow`
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 → 103

Calls

4 calls:

9.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
5.0ms	(* (log base) (log base))
1.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
152.0ms	(* (log base) (log base))
170.0ms	(pow (log base) 4)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

115 → 115

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	166	1352
1	325	1188
2	1024	1071
3	3533	1037
done	5000	1037

prune515.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `unpow-prod-down`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
8×	`cbrt-prod`
6×	`add-exp-log` `pow-unpow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod` `log-pow` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `pow-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `unpow2`

Counts

4 → 68

Calls

4 calls:

1.0ms	(pow (log base) 2)
1.0ms	(cbrt (pow (log base) 6))
1.0ms	(pow (log base) 6)
4.0ms	(sqrt (+ (* re re) (* im im)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(pow (log base) 2)
155.0ms	(cbrt (pow (log base) 6))
196.0ms	(pow (log base) 6)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify857.0ms

Counts

80 → 80

Iterations

Useful iterations: 3 (226.0ms)

Iter	Nodes	Cost
0	112	687
1	235	602
2	506	529
3	1746	467
done	5001	467

prune347.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.8b

regimes464.0ms

Accuracy

46.4% (13.3b remaining)

Error of 20.3b against oracle of 7.0b and baseline of 31.8b

bsearch324.0ms

Steps

Iters	Range		Point
6	675314123564825.6	4177447709703034.0	4130730593743547.5
10	2.166909288086334e-67	1.0283107515010361e-54	2.1974199628881544e-67
7	6.964284502474888e-208	4.246380689010823e-206	5.367728923838159e-207
10	-1.4120878331876276e+156	-4.0852822163078115e+137	-7.599046967462505e+146

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	156
1	93	156
done	93	156

end0.0ms

sample1.4s

Algorithm

intervals

Results

538.0ms	8000×	body	80	valid
537.0ms	7885×	body	80	nan