Details

sample111.0ms

Algorithm

intervals

Results

54.0ms	256×	body	80	valid
36.0ms	207×	body	80	nan

simplify1.8s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize30.0ms

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)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 65

Calls

2 calls:

31.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series197.0ms

Counts

2 → 6

Calls

2 calls:

138.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
4	4376
3	1336
2	524
1	233
0	123

prune364.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.5b

localize25.0ms

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)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

194×	`sqrt-pow1`
175×	`pow1`
136×	`log-pow`
100×	`times-frac`
98×	`pow1/2`
81×	`add-sqr-sqrt`
72×	`sqrt-prod`
54×	`pow-prod-up`
52×	`sqrt-div`
49×	`*-un-lft-identity` `add-cube-cbrt`
30×	`pow-prod-down` `pow-sqr`
25×	`associate-/l*`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
9×	`associate-r` `associate-l` `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 → 266

Calls

4 calls:

142.0ms	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log base))
51.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (log base))
61.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
45.0ms	(sqrt (+ (* re re) (* im im)))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

278 → 278

Iterations

Iter	Nodes
done	5001
3	2848
2	1070
1	572
0	286

prune715.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.5b

localize40.0ms

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)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
66×	`add-sqr-sqrt` `sqrt-pow1`
58×	`pow1`
34×	`pow1/2` `associate-l`
28×	`*-un-lft-identity` `sqrt-div`
27×	`add-cube-cbrt`
25×	`associate-r` `log-pow`
18×	`pow-prod-up`
15×	`swap-sqr` `add-exp-log`
14×	`times-frac`
12×	`unswap-sqr`
11×	`add-cbrt-cube` `pow-prod-down`
10×	`pow-sqr`
8×	`flip3-+` `flip-+`
5×	`prod-exp`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`associate-*r/` `cbrt-unprod`
2×	`pow2` `rem-sqrt-square` `pow-plus` `div-exp` `associate-l/` `-commutative`
1×	`cbrt-undiv` `rec-exp` `rem-square-sqrt` `sqrt-unprod` `1-exp` `un-div-inv` `div-inv`

Counts

4 → 178

Calls

4 calls:

61.0ms	(* (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (/ 1 (log base)))
38.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (/ 1 (log base)))
55.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
45.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

190 → 190

Iterations

Iter	Nodes
done	5002
3	2596
2	1072
1	460
0	207

prune620.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.5b

localize39.0ms

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)))

rewrite75.0ms

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×	`insert-posit16` `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 → 114

Calls

4 calls:

13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
43.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
12.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
145.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))
216.0ms	(* (log base) (log base))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5004
3	2717
2	1087
1	492
0	204

prune646.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.4b

regimes757.0ms

Accuracy

58.5% (9.6b remaining)

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

bsearch411.0ms

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

simplify7.0ms

Iterations

Iter	Nodes
done	44
1	44
0	39

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	7974×	body	80	nan
1.8s	8000×	body	80	valid