Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

26.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms	(sqrt (+ (* re re) (* im im)))

series172.0ms

Counts

2 → 6

Calls

2 calls:

132.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.8s

Counts

69 → 69

Iterations

Useful iterations: 3 (193.0ms)

Iter	Nodes	Cost
0	116	1191
1	222	1120
2	451	1046
3	877	1032
4	1959	1032
5	4637	1032
done	5000	1032

prune184.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
107×	`add-sqr-sqrt`
78×	`sqrt-prod`
66×	`*-un-lft-identity`
61×	`log-pow`
60×	`add-cube-cbrt`
52×	`pow1`
46×	`associate-r`
27×	`add-exp-log`
25×	`associate-l`
17×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`div-inv` `add-log-exp`
2×	`log-div` `rec-exp` `flip3-+` `1-exp` `div-sub` `flip-+`
1×	`frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 194

Calls

3 calls:

57.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
29.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series382.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
207.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

203 → 203

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	238	4455
1	588	4003
2	1564	3528
3	3972	3512
done	5000	3416

prune403.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
46×	`add-sqr-sqrt` `times-frac`
40×	`prod-exp`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
31×	`associate-l`
29×	`sqrt-prod` `add-cbrt-cube`
26×	`associate-r`
20×	`div-exp`
19×	`pow1`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
9×	`log-pow`
6×	`cbrt-undiv`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`un-div-inv` `add-log-exp`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `flip3-+` `associate-*l/` `flip-+`

Counts

3 → 135

Calls

3 calls:

59.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
28.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series382.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
203.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

144 → 144

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	205	3101
1	476	2539
2	1193	1930
3	2679	1920
done	5001	1920

prune300.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
0.8b	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
94×	`log-pow`
79×	`pow1`
64×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
62×	`cbrt-prod`
56×	`unpow-prod-down` `cube-prod`
22×	`sqrt-pow1` `pow1/2`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv`
4×	`sqrt-div` `associate-/r*` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`cbrt-undiv` `cube-div` `cube-mult` `log-div` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

4 → 211

Calls

4 calls:

12.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
25.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
11.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
8.0ms	(sqrt (+ (* re re) (* im im)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
134.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
230.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify807.0ms

Counts

223 → 223

Iterations

Useful iterations: done (794.0ms)

Iter	Nodes	Cost
0	218	5082
1	552	4329
2	1599	3978
done	5000	3867

prune362.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 6.9b

regimes974.0ms

Accuracy

57.7% (10.2b remaining)

Error of 17.8b against oracle of 7.6b and baseline of 31.8b

bsearch89.0ms

Steps

Iters	Range		Point
10	9.511609313434486e+66	1.6770313419776726e+82	1.9498916237070175e+80
8	-3.265571337685236e+43	-5.264462161218697e+40	-6.312992236024164e+42

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	60
1	46	60
2	52	60
3	55	60
done	55	60

end0.0ms

sample511.0ms

Algorithm

intervals

Results

328.0ms

8000×

body

valid