Details

sample56.0ms

Algorithm

intervals

Results

17.0ms	250×	body	80	nan
17.0ms	256×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 32.0b

localize20.0ms

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

rewrite76.0ms

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:

38.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
154.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

122 → 122

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1342	2035
3	4402	1998
done	5001	1992

prune446.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

localize25.0ms

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

rewrite102.0ms

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:

74.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
3.0ms	(pow (log base) 2)
8.0ms	(sqrt (+ (* re re) (* im im)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
88.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms	(pow (log base) 2)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify999.0ms

Counts

116 → 116

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	225	2560
1	551	2351
2	1700	2090
done	5001	2065

prune452.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

10.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	205	680
3	444	656
4	1114	656
5	3182	656
done	5001	656

prune480.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (- (* (pow 0.0 3) 0.0) (pow (log base) 4)))
0.5b	(pow (log base) 2)
1.0b	(pow (log base) 4)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `times-frac`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `add-cbrt-cube`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `associate-/r/` `log-pow` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `flip--` `div-inv` `unpow2`

Counts

4 → 83

Calls

4 calls:

64.0ms	(/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (- (* (pow 0.0 3) 0.0) (pow (log base) 4)))
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 4)
8.0ms	(sqrt (+ (* re re) (* im im)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (- (* (pow 0.0 3) 0.0) (pow (log base) 4)))
147.0ms	(pow (log base) 2)
168.0ms	(pow (log base) 4)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

95 → 95

Iterations

Useful iterations: 3 (826.0ms)

Iter	Nodes	Cost
0	180	1952
1	442	1752
2	1231	1604
3	4713	1583
done	5000	1583

prune409.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.5b

regimes507.0ms

Accuracy

44.4% (17.7b remaining)

Error of 18.0b against oracle of 0.3b and baseline of 32.2b

bsearch295.0ms

Steps

Iters	Range		Point
8	1.7355649689124848e+106	8.777746745010686e+110	3.283081512447869e+107
7	1.010971308202633e-239	1.977027620513521e-237	1.6845120982883925e-238
8	-7.823120959143482e-241	-2.3169923828202224e-244	-1.056135040441818e-243
8	-7.169178603400426e+84	-1.169629697327831e+81	-2.941271494123403e+82

simplify10.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	65	177
1	78	175
2	81	175
done	81	175

end0.0ms

sample1.6s

Algorithm

intervals

Results

553.0ms	8023×	body	80	nan
542.0ms	8000×	body	80	valid