Details

sample94.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
30.0ms	239×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize46.0ms

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)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
31.3b	(sqrt (+ (* re re) (* im im)))

rewrite103.0ms

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:

63.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
13.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
129.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
254.0ms	(* (log base) (log base))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

122 → 122

Iterations

Useful iterations: done (2.3s)

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

prune848.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(pow (log base) 2)
0.5b	(* (log base) (log base))
31.3b	(sqrt (+ (* re re) (* im im)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
157×	`add-sqr-sqrt`
156×	`*-un-lft-identity`
154×	`add-cube-cbrt`
141×	`sqrt-prod`
24×	`associate-/l*`
20×	`pow1`
18×	`sqrt-div`
16×	`associate-/r/`
12×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`div-inv`
7×	`log-pow`
6×	`log-prod` `swap-sqr` `associate-/r*`
4×	`unpow-prod-down` `associate-r` `associate-l` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `pow-unpow` `distribute-lft-in` `div-exp`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 261

Calls

4 calls:

118.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(pow (log base) 2)
15.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
183.0ms	(pow (log base) 2)
208.0ms	(* (log base) (log base))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.8s

Counts

273 → 273

Iterations

Useful iterations: 2 (987.0ms)

Iter	Nodes	Cost
0	417	14712
1	1025	13461
2	4965	12859
done	5000	12859

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
31.3b	(sqrt (+ (* re re) (* im im)))

rewrite225.0ms

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/` `un-div-inv` `*-commutative`

Counts

4 → 141

Calls

4 calls:

194.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
9.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
9.0ms	(sqrt (+ (* re re) (* im im)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
228.0ms	(pow (log base) 2)
217.0ms	(pow (log base) 2)
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.6s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	235	5185
1	710	4859
2	4143	4124
done	5000	4124

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
31.3b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
9.0ms	(sqrt (+ (* re re) (* im im)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
227.0ms	(cbrt base)
193.0ms	(cbrt base)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.7s

Counts

77 → 77

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	116	875
1	246	828
2	770	730
3	3896	709
done	5001	705

prune708.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 7.3b

regimes812.0ms

Accuracy

57.8% (10.4b remaining)

Error of 17.9b against oracle of 7.5b and baseline of 32.2b

bsearch462.0ms

Steps

Iters	Range		Point
4	1.0359064072202984e+135	1.4158385550386766e+135	1.0477792868396227e+135
9	6.537455865500771e-218	7.40486894182865e-213	3.064979836205642e-217
7	-4.657824840852224e-248	-2.841058930922235e-249	-2.5119673460865214e-248
10	-8.857830348421293e+161	-1.626953607814572e+151	-2.1066157852653055e+151

simplify14.0ms

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

sample4.6s

Algorithm

intervals

Results

2.4s	8139×	body	80	nan
1.3s	8000×	body	80	valid