Details

sample55.0ms

Algorithm

intervals

Results

33.0ms

256×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

29.0ms	(+ (* re re) (* im im))
53.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
11.0ms	(sqrt (+ (* re re) (* im im)))

series341.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* re re) (* im im))
221.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.1s

Counts

83 → 83

Iterations

Useful iterations: 3 (474.0ms)

Iter	Nodes	Cost
0	125	1357
1	254	1281
2	588	1165
3	1394	1163
4	3509	1163
done	5001	1163

prune402.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
0.6b	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
94×	`log-pow`
91×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
79×	`pow1`
34×	`associate-/r*`
22×	`sqrt-pow1` `pow1/2`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
4×	`cbrt-undiv`
3×	`sqrt-prod`
2×	`rec-exp` `frac-2neg` `flip3-+` `sqrt-div` `1-exp` `clear-num` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `sum-log` `associate-/r/` `inv-pow`

Counts

4 → 208

Calls

4 calls:

17.0ms	(+ (* re re) (* im im))
31.0ms	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
26.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
9.0ms	(sqrt (+ (* re re) (* im im)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* re re) (* im im))
169.0ms	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
215.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

220 → 220

Iterations

Useful iterations: 3 (954.0ms)

Iter	Nodes	Cost
0	246	4499
1	531	3920
2	1078	3575
3	2472	3501
done	5000	3501

prune506.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))) 3))
0.6b	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
0.7b	(pow (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))) 3)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite79.0ms

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-/r*`
5×	`div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`cbrt-undiv` `cube-div` `cube-mult` `sqrt-div` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `clear-num` `rem-cbrt-cube` `flip-+`

Counts

4 → 209

Calls

4 calls:

21.0ms	(cbrt (pow (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))) 3))
11.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
12.0ms	(pow (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))) 3)
9.0ms	(sqrt (+ (* re re) (* im im)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (pow (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))) 3))
195.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
360.0ms	(pow (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))) 3)
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

221 → 221

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	211	4994
1	541	4243
2	1613	3902
done	5001	3897

prune656.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (/ (log 10.0) (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))) 3)
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

204×	`pow1`
156×	`log-pow`
144×	`times-frac`
76×	`unpow-prod-down` `cube-prod`
72×	`pow1/3` `pow-prod-up`
57×	`add-sqr-sqrt`
54×	`add-cube-cbrt` `*-un-lft-identity`
48×	`pow-plus`
40×	`pow-prod-down`
24×	`pow-sqr`
16×	`pow2`
9×	`sqrt-prod`
8×	`pow3`
7×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-exp` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp` `sqr-pow`

Counts

4 → 217

Calls

4 calls:

179.0ms	(pow (/ (log 10.0) (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))) 3)
15.0ms	(sqrt (+ (* re re) (* im im)))
26.0ms	(sqrt (+ (* re re) (* im im)))
17.0ms	(sqrt (+ (* re re) (* im im)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(pow (/ (log 10.0) (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))))) 3)
54.0ms	(sqrt (+ (* re re) (* im im)))
78.0ms	(sqrt (+ (* re re) (* im im)))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

229 → 229

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	201	7370
1	662	6542
2	1820	4176
done	5000	3834

prune600.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.2b

regimes1.2s

Accuracy

57.2% (10.6b remaining)

Error of 18.0b against oracle of 7.5b and baseline of 32.1b

bsearch106.0ms

Steps

Iters	Range		Point
8	9.20494146023971e+137	8.337939306029303e+141	1.2449882138840628e+138
7	-5.792006846201835e+113	-3.7885935661345695e+111	-1.1564076018637175e+112

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	48
1	41	48
done	41	48

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8000×

body

valid