Details

sample134.0ms

Algorithm

intervals

Results

46.0ms	245×	body	80	nan
45.0ms	256×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize50.0ms

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))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite115.0ms

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:

67.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
13.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
128.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
214.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts

122 → 122

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	200	2451
1	508	2278
2	2910	2043
done	5001	2023

prune742.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

177.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
7.0ms	(pow (log base) 2)
6.0ms	(pow (log base) 2)
17.0ms	(sqrt (+ (* re re) (* im im)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
204.0ms	(pow (log base) 2)
239.0ms	(pow (log base) 2)
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.0s

Counts

152 → 152

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	235	5236
1	732	4984
2	4758	4432
done	5001	4432

prune965.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.1b

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)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-r`
16×	`add-exp-log`
14×	`pow1`
11×	`times-frac` `add-cbrt-cube`
9×	`associate-l`
6×	`log-prod`
5×	`prod-exp` `log-pow`
4×	`unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

120.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
25.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(pow (log base) 2)
13.0ms	(sqrt (+ (* re re) (* im im)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
132.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
212.0ms	(pow (log base) 2)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.5s

Counts

116 → 116

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	225	2560
1	632	2395
2	4108	2097
done	5002	2097

prune767.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(pow (log base) 2)
30.0ms	(sqrt (+ (* re re) (* im im)))
17.0ms	(sqrt (+ (* re re) (* im im)))
18.0ms	(sqrt (+ (* re re) (* im im)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(pow (log base) 2)
59.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

76 → 76

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	74	788
1	199	683
2	573	618
3	1802	597
done	5000	595

prune432.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.1b

regimes454.0ms

Accuracy

56.3% (10.6b remaining)

Error of 18.2b against oracle of 7.5b and baseline of 31.9b

bsearch407.0ms

Steps

Iters	Range		Point
8	1.3384996682255767e+79	5.534655914889903e+81	2.8370135832712205e+81
6	-6.556144523483021e-194	-8.06907841245328e-195	-1.503775902899962e-194
7	-9.754799411550227e-147	-3.902000578888293e-149	-4.0151649728280815e-149
7	-2.3279816661292167e+123	-4.323535679707538e+121	-4.600208406875213e+121

simplify31.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	48	118
1	60	116
2	66	116
3	68	116
done	68	116

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.1s	7978×	body	80	nan