Details

sample1.0s

Algorithm

intervals

Results

785.0ms	247×	body	10240	exit
123.0ms	501×	body	80	nan
87.0ms	256×	body	80	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	54
1	54
0	18

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize497.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (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))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite80.0ms

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:

33.0ms	(/ (* (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))
7.0ms	(sqrt (+ (* re re) (* im im)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
136.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
210.0ms	(* (log base) (log base))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify695.0ms

Counts

116 → 116

Iterations

Iter	Nodes
2	2079
1	701
0	162

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(/ (/ (log (sqrt (+ (* re re) (* im im)))) 1) (log base))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
78×	`add-sqr-sqrt`
77×	`*-un-lft-identity` `add-cube-cbrt`
68×	`log-pow`
57×	`pow1`
22×	`associate-/l*`
16×	`sqrt-pow1` `pow1/2`
10×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`div-inv`
5×	`div-exp` `add-log-exp`
4×	`associate-/r*` `sqrt-div` `div-sub`
3×	`cbrt-undiv` `flip3-+` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `1-exp` `associate-/l/`

Counts

3 → 161

Calls

3 calls:

12.0ms	(+ (* re re) (* im im))
26.0ms	(/ (/ (log (sqrt (+ (* re re) (* im im)))) 1) (log base))
17.0ms	(sqrt (+ (* re re) (* im im)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* re re) (* im im))
128.0ms	(/ (/ (log (sqrt (+ (* re re) (* im im)))) 1) (log base))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

170 → 170

Iterations

Iter	Nodes
3	3004
2	1637
1	943
0	262

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) 1) (log base))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

691×	`times-frac`
514×	`sqrt-pow1`
469×	`pow1`
410×	`log-pow`
275×	`add-sqr-sqrt`
258×	`pow1/2`
243×	`*-un-lft-identity` `add-cube-cbrt`
144×	`pow-prod-up`
80×	`pow-prod-down` `pow-sqr`
79×	`associate-/l*`
72×	`sqrt-prod`
52×	`sqrt-div`
16×	`pow2` `pow-plus` `div-sub`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
13×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`frac-times` `log-div`
6×	`div-inv`
5×	`div-exp`
4×	`associate-/r` `associate-l/` `associate-*r/` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv`
2×	`rem-sqrt-square`
1×	`clear-num` `rem-square-sqrt` `frac-2neg` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 540

Calls

4 calls:

122.0ms	(/ (/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) 1) (log base))
39.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) 1) (log base))
39.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
47.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

552 → 552

Iterations

Iter	Nodes
1	2164
0	621

prune6.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) 1) (/ 1 (log base)))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

130×	`sqrt-pow1`
111×	`add-sqr-sqrt`
106×	`pow1`
99×	`times-frac`
88×	`associate-l`
72×	`sqrt-prod`
69×	`log-pow`
66×	`pow1/2`
61×	`*-un-lft-identity`
55×	`add-cube-cbrt`
37×	`add-exp-log`
36×	`pow-prod-up`
28×	`sqrt-div`
25×	`associate-r`
21×	`pow-prod-down`
20×	`pow-sqr`
18×	`add-cbrt-cube` `unswap-sqr`
15×	`swap-sqr`
14×	`div-exp`
13×	`prod-exp`
8×	`flip3-+` `flip-+`
7×	`1-exp`
5×	`frac-times` `cbrt-unprod`
4×	`pow2` `cbrt-undiv` `pow-plus` `insert-posit16` `add-log-exp`
3×	`rec-exp` `associate-l/` `associate-r/`
2×	`rem-sqrt-square` `*-commutative` `div-inv`
1×	`rem-square-sqrt` `sqrt-unprod` `un-div-inv`

Counts

4 → 250

Calls

4 calls:

129.0ms	(* (/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) 1) (/ 1 (log base)))
43.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) 1) (/ 1 (log base)))
61.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
60.0ms	(sqrt (+ (* re re) (* im im)))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

262 → 262

Iterations

Iter	Nodes
3	4055
2	1924
1	1051
0	277

prune3.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.0b

regimes809.0ms

Accuracy

51.7% (11.5b remaining)

Error of 18.8b against oracle of 7.3b and baseline of 31.1b

bsearch1.9s

Steps

Iters	Range	Point
5	1.3108230826417503e-56	3.3878388801915877e-56	3.3440052807984994e-56
6	-3.066438994183041e-87	-2.4260742374513095e-88	-2.973946629754585e-88
10	-7.898439204912028e+150	-5.815936964035446e+140	-3.723507598105854e+150

Iters

Range

Point

1.3108230826417503e-56

3.3878388801915877e-56

3.3440052807984994e-56

-3.066438994183041e-87

-2.4260742374513095e-88

-2.973946629754585e-88

-7.898439204912028e+150

-5.815936964035446e+140

-3.723507598105854e+150

simplify6.0ms

Iterations

Iter	Nodes
2	36
1	36
0	32

end0.0ms

sample35.4s

Algorithm

intervals

Results

26.9s	7897×	body	10240	exit
5.3s	16210×	body	80	nan
2.2s	8000×	body	80	valid