Details

sample28.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize35.0ms

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))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite85.0ms

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:

24.0ms	(+ (* re re) (* im im))
44.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
13.0ms	(sqrt (+ (* re re) (* im im)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* re re) (* im im))
247.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

83 → 83

Iterations

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

prune567.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize48.0ms

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)))
29.3b	(log (+ (* re re) (* im im)))

rewrite166.0ms

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:

13.0ms	(+ (* re re) (* im im))
90.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
41.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
11.0ms	(log (+ (* re re) (* im im)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* re re) (* im im))
163.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
270.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
73.0ms	(log (+ (* re re) (* im im)))

simplify1.9s

Counts

176 → 176

Iterations

Iter	Nodes
done	5001
2	1964
1	586
0	214

prune942.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
0.4b	(* (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)))
29.3b	(log (+ (* re re) (* im im)))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod`
112×	`times-frac`
107×	`add-sqr-sqrt`
69×	`*-un-lft-identity` `add-cube-cbrt`
56×	`associate-l`
42×	`pow1`
33×	`associate-r`
31×	`log-pow`
21×	`add-exp-log`
20×	`add-cbrt-cube`
12×	`unswap-sqr`
10×	`sqrt-div`
7×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`frac-times` `associate-*r/`
4×	`log-div` `pow-prod-down` `associate-l/` `div-inv` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `log-prod` `div-exp`
2×	`flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`clear-num` `frac-2neg` `rem-log-exp`

Counts

4 → 207

Calls

4 calls:

107.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
75.0ms	(* (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)))
6.0ms	(log (+ (* re re) (* im im)))

series1.4s

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
717.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
295.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
74.0ms	(log (+ (* re re) (* im im)))

simplify2.4s

Counts

219 → 219

Iterations

Iter	Nodes
done	5000
2	2307
1	679
0	269

prune1.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.6b

localize84.0ms

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)))
29.3b	(log (+ (* re re) (* im im)))

rewrite59.0ms

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:

29.0ms	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
2.0ms	(sqrt (cbrt (log 10.0)))
18.0ms	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
6.0ms	(log (+ (* re re) (* im im)))

series75.0ms

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)))
74.0ms	(log (+ (* re re) (* im im)))

simplify2.3s

Counts

107 → 107

Iterations

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

prune692.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.6b

regimes1.3s

Accuracy

57.6% (10.6b remaining)

Error of 17.9b against oracle of 7.3b and baseline of 32.2b

bsearch183.0ms

Steps

Iters	Range		Point
11	1.9646879743348034e+113	1.0349113110676533e+135	9.926501183114803e+132
8	-4.064102892713862e+80	-4.4571909682776797e+76	-3.9812501718676645e+79

simplify63.0ms

Iterations

Iter	Nodes
done	108
5	108
4	99
3	79
2	66
1	58
0	43

end0.0ms

sample1.0s

Algorithm

intervals

Results

793.0ms

8000×

body

valid