Details

sample40.0ms

Algorithm

intervals

Results

27.0ms

256×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	11
1	11
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

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:

10.0ms	(+ (* re re) (* im im))
42.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
13.0ms	(sqrt (+ (* re re) (* im im)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* re re) (* im im))
191.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify805.0ms

Counts

86 → 86

Iterations

Iter	Nodes
3	2233
2	714
1	264
0	128

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
30.8b	(log (+ (* re re) (* im im)))

rewrite76.0ms

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:

10.0ms	(+ (* re re) (* im im))
34.0ms	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
24.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
6.0ms	(log (+ (* re re) (* im im)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* re re) (* im im))
206.0ms	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
276.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
63.0ms	(log (+ (* re re) (* im im)))

simplify5.3s

Counts

180 → 180

Iterations

Iter	Nodes
3	6539
2	1959
1	583
0	218

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (log 10))
1.0b	(cbrt (log 10))
1.6b	(* (cbrt (log 10)) (cbrt (log 10)))
30.8b	(log (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`pow1`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`swap-sqr` `log-pow`
8×	`pow1/3`
7×	`associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`log-prod`
2×	`log-div` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `flip3-+` `pow-plus` `rem-log-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 87

Calls

4 calls:

1.0ms	(cbrt (log 10))
2.0ms	(cbrt (log 10))
18.0ms	(* (cbrt (log 10)) (cbrt (log 10)))
11.0ms	(log (+ (* re re) (* im im)))

series63.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt (log 10))
0.0ms	(cbrt (log 10))
0.0ms	(* (cbrt (log 10)) (cbrt (log 10)))
63.0ms	(log (+ (* re re) (* im im)))

simplify3.6s

Counts

93 → 93

Iterations

Iter	Nodes
5	6009
4	1803
3	814
2	415
1	208
0	99

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.7b

localize80.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt 1/2) (cbrt 1/2))
1.0b	(sqrt (sqrt (log 10)))
1.0b	(sqrt (sqrt (log 10)))
30.8b	(log (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`sqrt-prod`
18×	`pow1`
17×	`*-un-lft-identity` `add-cube-cbrt`
16×	`cbrt-prod`
8×	`sqrt-pow1`
7×	`add-exp-log`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`rem-sqrt-square` `add-cbrt-cube` `pow1/2` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`log-prod` `log-pow`
2×	`log-div` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `flip3-+` `pow-plus` `rem-log-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 98

Calls

4 calls:

14.0ms	(* (cbrt 1/2) (cbrt 1/2))
3.0ms	(sqrt (sqrt (log 10)))
4.0ms	(sqrt (sqrt (log 10)))
20.0ms	(log (+ (* re re) (* im im)))

series55.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(* (cbrt 1/2) (cbrt 1/2))
0.0ms	(sqrt (sqrt (log 10)))
0.0ms	(sqrt (sqrt (log 10)))
55.0ms	(log (+ (* re re) (* im im)))

simplify817.0ms

Counts

104 → 104

Iterations

Iter	Nodes
4	2050
3	871
2	460
1	234
0	120

prune1.7s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 6.7b

regimes870.0ms

Accuracy

56.5% (10.4b remaining)

Error of 17.4b against oracle of 7.0b and baseline of 30.8b

bsearch455.0ms

Steps

Iters	Range		Point
8	3.807534648988377e+65	1.3176703569903367e+68	6.734502278787053e+66
9	6.507846128246995e-219	9.274384512239978e-214	4.071831069248947e-214
6	1.382421543513226e-246	9.34993854108783e-246	8.145199547234516e-246
8	2.5258242951023844e-302	3.185418417846864e-299	3.259709475737078e-301
8	-3.560522852506786e-274	-3.1594605666812263e-277	-2.5387418282241494e-275
2	-1.2889734826068362e+36	-1.1593995580640188e+36	-1.272776742038984e+36

simplify22.0ms

Iterations

Iter	Nodes
2	87
1	87
0	71

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.2s

8000×

body

valid