Details

sample138.0ms

Algorithm

intervals

Results

71.0ms	256×	body	80	valid
46.0ms	207×	body	80	nan

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5174
7	1116
6	232
5	78
4	53
3	39
2	24
1	22
0	18

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize22.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
24×	`times-frac`
22×	`log-pow`
20×	`pow1`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
8×	`sqrt-prod`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`distribute-lft-out`
4×	`associate-/r` `add-cbrt-cube` `sqrt-div` `associate-l*` `add-exp-log`
2×	`log-div` `flip3-+` `div-sub` `swap-sqr` `flip-+` `insert-posit16` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 70

Calls

2 calls:

76.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
60.0ms	(sqrt (+ (* re re) (* im im)))

series197.0ms

Counts

2 → 6

Calls

2 calls:

140.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
4	3029
3	1147
2	518
1	236
0	125

prune393.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log base))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

202×	`sqrt-prod`
194×	`sqrt-pow1`
193×	`*-un-lft-identity`
175×	`pow1`
136×	`log-pow`
100×	`times-frac`
98×	`pow1/2`
81×	`add-sqr-sqrt`
70×	`associate-l`
62×	`distribute-lft-out`
54×	`pow-prod-up`
52×	`sqrt-div` `swap-sqr`
49×	`add-cube-cbrt`
30×	`pow-prod-down` `pow-sqr`
25×	`associate-/l*`
14×	`flip3-+` `associate-r` `flip-+`
9×	`unswap-sqr`
8×	`frac-times` `log-div` `add-cbrt-cube` `div-sub` `add-exp-log`
6×	`pow2` `pow-plus`
4×	`associate-/r` `associate-l/` `associate-*r/` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square`
1×	`cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 311

Calls

4 calls:

929.0ms	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log base))
368.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
105.0ms	(sqrt (+ (* re re) (* im im)))
105.0ms	(sqrt (+ (* re re) (* im im)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log base))
60.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
67.0ms	(sqrt (+ (* re re) (* im im)))
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

323 → 323

Iterations

Iter	Nodes
done	5001
3	2984
2	1116
1	574
0	290

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (/ 1 (log base)))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite995.0ms

Algorithm

rewrite-expression-head

Rules

202×	`sqrt-prod`
175×	`*-un-lft-identity`
95×	`associate-l`
68×	`add-sqr-sqrt`
66×	`sqrt-pow1`
62×	`distribute-lft-out`
59×	`pow1`
52×	`swap-sqr`
34×	`pow1/2`
30×	`associate-r`
29×	`add-cube-cbrt`
28×	`sqrt-div`
26×	`log-pow`
18×	`pow-prod-up`
15×	`add-exp-log`
14×	`times-frac`
12×	`associate-*r/` `unswap-sqr`
11×	`add-cbrt-cube` `pow-prod-down`
10×	`pow-sqr`
8×	`flip3-+` `flip-+`
5×	`prod-exp`
4×	`frac-times` `associate-/r` `insert-posit16` `associate-/l` `add-log-exp`
3×	`un-div-inv` `cbrt-unprod`
2×	`pow2` `rem-sqrt-square` `clear-num` `pow-plus` `div-exp` `associate-l/` `-commutative`
1×	`cbrt-undiv` `rec-exp` `rem-square-sqrt` `frac-2neg` `sqrt-unprod` `1-exp` `div-inv`

Counts

4 → 234

Calls

4 calls:

419.0ms	(* (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (/ 1 (log base)))
380.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
81.0ms	(sqrt (+ (* re re) (* im im)))
95.0ms	(sqrt (+ (* re re) (* im im)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (/ 1 (log base)))
47.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
66.0ms	(sqrt (+ (* re re) (* im im)))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.0s

Counts

246 → 246

Iterations

Iter	Nodes
done	5028
3	3033
2	1149
1	470
0	215

prune975.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.5b

localize78.0ms

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)) (+ (* (log base) (log base)) (* 0 0)))
0.5b	(* (log base) (log base))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

413×	`*-un-lft-identity`
189×	`distribute-lft-out`
182×	`associate-l`
117×	`times-frac`
111×	`pow1`
98×	`log-pow`
88×	`swap-sqr`
44×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
13×	`associate-/r*`
12×	`log-prod`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
8×	`associate-r` `sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`insert-posit16` `add-log-exp`
3×	`flip3-+` `flip-+`
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 → 243

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
343.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
10.0ms	(* (log base) (log base))
76.0ms	(sqrt (+ (* re re) (* im im)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
139.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
266.0ms	(* (log base) (log base))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

255 → 255

Iterations

Iter	Nodes
done	5003
3	3180
2	1185
1	506
0	209

prune741.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.4b

regimes456.0ms

Accuracy

58.5% (9.6b remaining)

Error of 16.8b against oracle of 7.2b and baseline of 30.4b

bsearch571.0ms

Steps

Iters	Range		Point
8	1.3393316766876643e+127	8.442893536612497e+130	1.687660857647486e+127
11	2.3835309502694435e-242	4.669921679618734e-220	1.483347789429306e-239
9	8.289117053169836e-275	1.613341434485956e-267	3.688680909166565e-273
9	-3.505749298226566e+116	-2.1981796775526612e+111	-2.929915037932605e+116

simplify49.0ms

Iterations

Iter	Nodes
done	56
3	56
2	54
1	53
0	45

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.5s	8000×	body	80	valid
2.1s	7974×	body	80	nan