Details

sample112.0ms

Algorithm

intervals

Results

36.0ms	252×	body	80	nan
35.0ms	256×	body	80	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-cbrt-cube` `associate-l` `add-exp-log` `log-pow`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `flip3-+` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

38.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
145.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
227.0ms	(* (log base) (log base))
68.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1677
1	505
0	200

prune971.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

18.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
199.0ms	(* (log base) (log base))
204.0ms	(* (log base) (log base))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
4	4375
3	1741
2	760
1	312
0	130

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-cbrt-cube` `associate-l` `add-exp-log` `log-pow`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `flip3-+` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

33.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
138.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
231.0ms	(* (log base) (log base))
55.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5005
3	4644
2	1469
1	511
0	200

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
6×	`cbrt-prod` `log-prod` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
9.0ms	(sqrt (+ (* re re) (* im im)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
265.0ms	(cbrt base)
274.0ms	(cbrt base)
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
4	2908
3	1307
2	554
1	245
0	116

prune671.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.0b

regimes1.0s

Accuracy

56.7% (10.5b remaining)

Error of 18.0b against oracle of 7.4b and baseline of 31.8b

bsearch533.0ms

Steps

Iters	Range		Point
8	7.494570457068337e+116	1.1262746475157651e+120	3.4996331592827644e+118
9	8.293948122507532e-200	2.3496223720415168e-194	1.8162982431833731e-199
7	-6.856160329593529e-213	-9.104135836411172e-215	-3.5661932702760735e-214
8	-4.792703353650342e+80	-1.5715417821050658e+76	-1.737740429468826e+80

simplify37.0ms

Iterations

Iter	Nodes
done	98
4	98
3	94
2	89
1	85
0	62

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	7931×	body	80	nan
1.4s	8000×	body	80	valid