Details

sample45.0ms

Algorithm

intervals

Results

25.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize39.0ms

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))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

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:

6.0ms	(+ (* re re) (* im im))
36.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
13.0ms	(sqrt (+ (* re re) (* im im)))

series278.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* re re) (* im im))
188.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify839.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1092
1	277
0	125

prune479.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

localize29.0ms

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)))
29.7b	(log (+ (* re re) (* im im)))

rewrite127.0ms

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:

12.0ms	(+ (* re re) (* im im))
78.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
21.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
10.0ms	(log (+ (* re re) (* im im)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* re re) (* im im))
177.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
265.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
71.0ms	(log (+ (* re re) (* im im)))

simplify1.9s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
2	3117
1	605
0	214

prune943.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
29.7b	(log (+ (* re re) (* im im)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
46×	`add-sqr-sqrt` `times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
30×	`add-cbrt-cube`
29×	`associate-l`
26×	`associate-r` `sqrt-prod`
22×	`prod-exp`
19×	`pow1`
12×	`cbrt-unprod`
11×	`div-exp`
8×	`log-pow`
6×	`cbrt-undiv` `add-log-exp`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`rec-exp` `log-prod` `1-exp` `un-div-inv`
2×	`frac-times` `log-div` `flip3-+` `*-commutative` `flip-+` `div-inv`
1×	`+-commutative` `sum-log` `rem-log-exp` `associate-*l/`

Counts

4 → 133

Calls

4 calls:

13.0ms	(+ (* re re) (* im im))
23.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
57.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
5.0ms	(log (+ (* re re) (* im im)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* re re) (* im im))
280.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
219.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
71.0ms	(log (+ (* re re) (* im im)))

simplify3.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	3589
1	633
0	221

prune769.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 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)))
0.5b	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
29.7b	(log (+ (* re re) (* im im)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
131×	`add-sqr-sqrt`
107×	`sqrt-prod`
79×	`*-un-lft-identity` `add-cube-cbrt`
78×	`add-exp-log`
68×	`associate-l`
59×	`add-cbrt-cube`
42×	`pow1`
33×	`associate-r`
31×	`prod-exp` `log-pow`
27×	`div-exp`
22×	`cbrt-unprod`
18×	`cbrt-undiv`
15×	`unswap-sqr`
7×	`associate-/r*`
6×	`frac-times` `associate-*r/`
5×	`1-exp`
4×	`log-div` `pow-prod-down` `associate-l/` `div-inv` `associate-/l` `add-log-exp`
3×	`log-prod`
2×	`flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`clear-num` `frac-2neg` `rem-log-exp`

Counts

4 → 245

Calls

4 calls:

91.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
40.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
115.0ms	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
10.0ms	(log (+ (* re re) (* im im)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
241.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
303.0ms	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
96.0ms	(log (+ (* re re) (* im im)))

simplify1.2s

Counts

257 → 257

Iterations

Iter	Nodes
done	5000
1	953
0	311

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.7b

regimes997.0ms

Accuracy

58.7% (10.3b remaining)

Error of 17.3b against oracle of 7.0b and baseline of 32.0b

bsearch154.0ms

Steps

Iters	Range		Point
10	5.983110960818372e+78	5.424691173039659e+92	5.714402214507161e+91
4	-1.8700852155488777e+100	-1.0341250558666946e+100	-1.3008124389926461e+100

simplify16.0ms

Iterations

Iter	Nodes
done	44
1	44
0	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8000×

body

valid