Details

sample31.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.7b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

16.0ms	(+ (* re re) (* im im))
26.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
12.0ms	(sqrt (+ (* re re) (* im im)))

series295.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* re re) (* im im))
203.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
3	2285
2	683
1	262
0	125

prune549.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
29.9b	(log (+ (* re re) (* im im)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
83×	`add-sqr-sqrt`
54×	`sqrt-prod`
53×	`*-un-lft-identity` `add-cube-cbrt`
34×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
19×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`div-sub`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 164

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
53.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
5.0ms	(log (+ (* re re) (* im im)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* re re) (* im im))
200.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
573.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
62.0ms	(log (+ (* re re) (* im im)))

simplify1.8s

Counts

176 → 176

Iterations

Iter	Nodes
done	5001
2	1964
1	586
0	214

prune818.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
1.0b	(sqrt (sqrt (log 10.0)))
1.0b	(sqrt (sqrt (log 10.0)))
29.9b	(log (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
60×	`times-frac`
56×	`add-sqr-sqrt`
52×	`*-un-lft-identity` `add-cube-cbrt`
33×	`cbrt-prod`
18×	`pow1`
10×	`associate-/r*` `log-pow`
8×	`sqrt-pow1`
7×	`add-exp-log`
6×	`associate-/l*`
5×	`add-cbrt-cube`
4×	`rem-sqrt-square` `pow1/2` `add-log-exp`
3×	`log-prod`
2×	`log-div`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `flip-+` `div-inv`

Counts

4 → 142

Calls

4 calls:

8.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
2.0ms	(sqrt (sqrt (log 10.0)))
2.0ms	(sqrt (sqrt (log 10.0)))
5.0ms	(log (+ (* re re) (* im im)))

series100.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
0.0ms	(sqrt (sqrt (log 10.0)))
0.0ms	(sqrt (sqrt (log 10.0)))
100.0ms	(log (+ (* re re) (* im im)))

simplify2.0s

Counts

148 → 148

Iterations

Iter	Nodes
done	5001
4	2124
3	1039
2	495
1	288
0	169

prune937.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.9b

localize94.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
1.0b	(sqrt (cbrt (log 10.0)))
1.6b	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
29.9b	(log (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

29×	`cbrt-prod`
27×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`add-exp-log`
9×	`swap-sqr` `sqrt-prod`
8×	`log-pow`
7×	`add-cbrt-cube` `pow1/3` `associate-r` `associate-l`
4×	`associate-/r*` `times-frac` `add-log-exp` `unswap-sqr`
3×	`log-prod`
2×	`cbrt-undiv` `rem-sqrt-square` `log-div` `sqrt-pow1` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `pow1/2` `rem-log-exp` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 101

Calls

4 calls:

35.0ms	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
4.0ms	(sqrt (cbrt (log 10.0)))
11.0ms	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
5.0ms	(log (+ (* re re) (* im im)))

series85.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
0.0ms	(sqrt (cbrt (log 10.0)))
0.0ms	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
85.0ms	(log (+ (* re re) (* im im)))

simplify2.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	5003
3	2765
2	924
1	327
0	147

prune738.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.9b

regimes1.1s

Accuracy

57.9% (10.1b remaining)

Error of 17.4b against oracle of 7.3b and baseline of 31.4b

bsearch174.0ms

Steps

Iters	Range		Point
8	2.0081831682580294e+141	7.125568374099785e+144	3.466359063004586e+143
9	-1.6938002153937483e+104	-4.084920897753177e+97	-9.68163596973406e+102

simplify12.0ms

Iterations

Iter	Nodes
done	51
1	51
0	40

end0.0ms

sample952.0ms

Algorithm

intervals

Results

747.0ms

8000×

body

valid