Details

sample174.0ms

Algorithm

intervals

Results

85.0ms	256×	body	80	valid
58.0ms	245×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	22
1	22
0	18

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
20×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
12×	`log-prod`
10×	`associate-l` `log-pow`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `flip3-+` `times-frac` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `associate-/l`

Counts

4 → 104

Calls

4 calls:

22.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms	(* (log base) (log base))
30.0ms	(sqrt (+ (* re re) (* im im)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
144.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
196.0ms	(* (log base) (log base))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify8.2s

Counts

116 → 116

Iterations

Iter	Nodes
3	11790
2	1707
1	417
0	162

prune572.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.8b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

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:

8.0ms	(+ (* re re) (* im im))
25.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ (* re re) (* im im))
140.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify705.0ms

Counts

86 → 86

Iterations

Iter	Nodes
3	2244
2	713
1	268
0	133

prune328.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ 1 (log base))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
26×	`times-frac`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
17×	`pow1` `add-exp-log`
16×	`associate-r`
11×	`add-cbrt-cube`
10×	`log-pow`
6×	`associate-l` `add-log-exp`
4×	`associate-/r*` `div-exp` `prod-exp` `insert-posit16`
3×	`sqrt-prod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 107

Calls

4 calls:

17.0ms	(+ (* re re) (* im im))
7.0ms	(/ 1 (log base))
27.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
13.0ms	(sqrt (+ (* re re) (* im im)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* re re) (* im im))
230.0ms	(/ 1 (log base))
103.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (log base)))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

119 → 119

Iterations

Iter	Nodes
3	2989
2	1142
1	352
0	152

prune509.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ 1/2 (/ (log base) (log (+ (* re re) (* im im)))))
0.3b	(/ (log base) (log (+ (* re re) (* im im))))
30.5b	(log (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
72×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
47×	`pow1`
43×	`log-pow`
24×	`associate-/r*`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`log-prod`
2×	`log-div` `clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`+-commutative` `sum-log` `rem-log-exp` `associate-/r/`

Counts

4 → 163

Calls

4 calls:

7.0ms	(+ (* re re) (* im im))
8.0ms	(/ 1/2 (/ (log base) (log (+ (* re re) (* im im)))))
12.0ms	(/ (log base) (log (+ (* re re) (* im im))))
12.0ms	(log (+ (* re re) (* im im)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* re re) (* im im))
131.0ms	(/ 1/2 (/ (log base) (log (+ (* re re) (* im im)))))
123.0ms	(/ (log base) (log (+ (* re re) (* im im))))
68.0ms	(log (+ (* re re) (* im im)))

simplify2.7s

Counts

175 → 175

Iterations

Iter	Nodes
3	5022
2	1641
1	558
0	227

prune967.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 8.8b

regimes480.0ms

Accuracy

60.3% (9.2b remaining)

Error of 16.5b against oracle of 7.2b and baseline of 30.5b

bsearch299.0ms

Steps

Iters	Range		Point
10	1.5006927183611262e+96	2.4511133739659252e+112	1.945423092678915e+111
9	-1.396677438673827e+115	-3.745082354651661e+109	-4.0303141568877995e+114

simplify6.0ms

Iterations

Iter	Nodes
2	26
1	26
0	23

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	7955×	body	80	nan
1.8s	8000×	body	80	valid