Details

sample112.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
36.0ms	263×	body	80	nan

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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)))
0.5b	(* (log base) (log base))
27.1b	(sqrt (+ (* re re) (* im im)))

rewrite66.0ms

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:

11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
29.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
136.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
188.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1692
1	505
0	200

prune905.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.1b	(sqrt (+ (* re re) (* im im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

45.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
19.0ms	(* (log base) (log base))
12.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
225.0ms	(* (log base) (log base))
217.0ms	(* (log base) (log base))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
3	3292
2	1290
1	433
0	182

prune981.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(cbrt (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
0.6b	(* (* (log base) (log base)) (* (log base) (log base)))
27.1b	(sqrt (+ (* re re) (* im im)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

129×	`pow1`
37×	`pow-prod-up`
24×	`pow-prod-down`
23×	`pow-sqr`
19×	`pow-plus`
18×	`add-sqr-sqrt` `log-prod` `add-cbrt-cube` `add-exp-log`
17×	`*-un-lft-identity`
15×	`distribute-rgt-in` `distribute-lft-in` `add-cube-cbrt`
14×	`pow2`
9×	`prod-exp` `cbrt-unprod`
7×	`swap-sqr`
6×	`log-pow`
5×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `pow3` `rem-cbrt-cube` `flip-+`

Counts

4 → 136

Calls

4 calls:

8.0ms	(* (log base) (log base))
124.0ms	(cbrt (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
36.0ms	(* (* (log base) (log base)) (* (log base) (log base)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series666.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (log base) (log base))
198.0ms	(cbrt (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))
224.0ms	(* (* (log base) (log base)) (* (log base) (log base)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

148 → 148

Iterations

Iter	Nodes
done	5001
3	3107
2	1316
1	441
0	145

prune787.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.1b	(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

42.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
11.0ms	(* (log base) (log base))
11.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
199.0ms	(* (log base) (log base))
203.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
3	3292
2	1290
1	433
0	182

prune735.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 5.0b

regimes957.0ms

Accuracy

55.4% (11.3b remaining)

Error of 18.1b against oracle of 6.8b and baseline of 32.0b

bsearch294.0ms

Steps

Iters	Range		Point
8	7.690537674537789e+54	4.241385736755644e+58	4.884463756615851e+57
11	-733100.9210806559	-4.535667315572071e-15	-2039.492255936365

simplify18.0ms

Iterations

Iter	Nodes
done	52
1	52
0	41

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	7937×	body	80	nan
1.6s	8000×	body	80	valid