Details

sample60.0ms

Algorithm

intervals

Results

44.0ms

256×

body

valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	11
1	11
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize33.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
20×	`pow1`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
4×	`associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`sqrt-prod`
2×	`log-div` `flip3-+` `div-sub` `flip-+` `insert-posit16` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 65

Calls

2 calls:

26.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
6.0ms	(sqrt (+ (* re re) (* im im)))

series262.0ms

Counts

2 → 6

Calls

2 calls:

186.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
76.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

71 → 71

Iterations

Iter	Nodes
4	2850
3	1122
2	499
1	228
0	118

prune284.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.8b

localize54.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
31.8b	(log (+ (* re re) (* im im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`*-un-lft-identity` `add-cube-cbrt`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `insert-posit16` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `clear-num` `frac-2neg` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 156

Calls

3 calls:

23.0ms	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
52.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
12.0ms	(log (+ (* re re) (* im im)))

series421.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
215.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
55.0ms	(log (+ (* re re) (* im im)))

simplify5.2s

Counts

165 → 165

Iterations

Iter	Nodes
3	5539
2	1744
1	547
0	208

prune706.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.6b

localize97.0ms

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)))
31.8b	(log (+ (* re re) (* im im)))

rewrite18.0ms

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))
1.0ms	(cbrt (log 10))
9.0ms	(* (cbrt (log 10)) (cbrt (log 10)))
7.0ms	(log (+ (* re re) (* im im)))

series78.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt (log 10))
0.0ms	(cbrt (log 10))
0.0ms	(* (cbrt (log 10)) (cbrt (log 10)))
78.0ms	(log (+ (* re re) (* im im)))

simplify3.3s

Counts

93 → 93

Iterations

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

prune566.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.5b

localize57.0ms

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)))
31.8b	(log (+ (* re re) (* im im)))

rewrite18.0ms

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:

8.0ms	(* (cbrt 1/2) (cbrt 1/2))
2.0ms	(sqrt (sqrt (log 10)))
2.0ms	(sqrt (sqrt (log 10)))
6.0ms	(log (+ (* re re) (* im im)))

series75.0ms

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)))
75.0ms	(log (+ (* re re) (* im im)))

simplify948.0ms

Counts

104 → 104

Iterations

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

prune502.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 8.5b

regimes1.2s

Accuracy

59.5% (9.6b remaining)

Error of 16.6b against oracle of 6.9b and baseline of 30.7b

bsearch232.0ms

Steps

Iters	Range		Point
9	4.7599761429228367e+98	9.416899659600005e+104	5.956366146560391e+103
9	-8.438381893092855e+95	-2.4077790411462946e+90	-1.3496059084460043e+95

simplify10.0ms

Iterations

Iter	Nodes
2	52
1	52
0	43

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.6s

8000×

body

valid