Details

sample48.0ms

Algorithm

intervals

Results

29.0ms

256×

body

valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	10

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize135.0ms

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))
30.4b	(sqrt (+ (* re re) (* im im)))

rewrite161.0ms

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-+` `insert-posit16`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 77

Calls

3 calls:

18.0ms	(+ (* re re) (* im im))
104.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
34.0ms	(sqrt (+ (* re re) (* im im)))

series373.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* re re) (* im im))
249.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
76.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5003
3	2340
2	688
1	265
0	128

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.6b

localize117.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 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)))
31.6b	(log (+ (* re re) (* im im)))

rewrite620.0ms

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` `insert-posit16` `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 → 168

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
468.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
73.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
15.0ms	(log (+ (* re re) (* im im)))

series810.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* re re) (* im im))
258.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
377.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
122.0ms	(log (+ (* re re) (* im im)))

simplify4.8s

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
2	1925
1	589
0	218

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize271.0ms

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)))
31.6b	(log (+ (* re re) (* im im)))

rewrite118.0ms

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` `insert-posit16` `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 → 105

Calls

4 calls:

54.0ms	(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (log 10.0)) (cbrt (log 10.0)))))
6.0ms	(sqrt (cbrt (log 10.0)))
37.0ms	(* (cbrt (log 10.0)) (cbrt (log 10.0)))
15.0ms	(log (+ (* re re) (* im im)))

series94.0ms

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)))
94.0ms	(log (+ (* re re) (* im im)))

simplify5.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	5002
3	2737
2	910
1	333
0	151

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.4b

localize174.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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)))
31.6b	(log (+ (* re re) (* im im)))

rewrite434.0ms

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/` `insert-posit16` `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 → 211

Calls

4 calls:

163.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
121.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
89.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
25.0ms	(log (+ (* re re) (* im im)))

series1.7s

Counts

4 → 12

Calls

4 calls:

449.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
809.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
370.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
95.0ms	(log (+ (* re re) (* im im)))

simplify5.5s

Counts

223 → 223

Iterations

Iter	Nodes
done	5001
2	2307
1	681
0	273

prune2.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.3b

regimes2.3s

Accuracy

54.8% (11.0b remaining)

Error of 18.4b against oracle of 7.4b and baseline of 31.8b

bsearch378.0ms

Steps

Iters	Range		Point
8	1.0202913897586463e+104	3.251572119276446e+106	2.2624206856873828e+105
3	1.3373501688296423e-158	1.7803579200561248e-158	1.475790091087918e-158
8	-3.147576329037351e-256	-6.1523601201211696e-260	-4.892315061161181e-257
11	-2.7312467666666225e+116	-7.171553699074835e+91	-8.915974928248364e+114

simplify50.0ms

Iterations

Iter	Nodes
done	69
1	69
0	55

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8000×

body

valid