Details

sample160.0ms

Algorithm

intervals

Results

22.0ms	196×	body	80	valid
13.0ms	23×	body	2560	valid
10.0ms	21×	body	1280	valid
4.0ms	7×	body	5120	valid
2.0ms	4×	body	640	valid
1.0ms	5×	body	320	valid

simplify101.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	75
5	75
4	73
3	64
2	50
1	41
0	12

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize60.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1`
6×	`*-un-lft-identity`
5×	`sqrt-prod` `add-log-exp`
4×	`sqrt-div` `add-cube-cbrt`
3×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--`

Counts

3 → 46

Calls

3 calls:

26.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
41.0ms	(- (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (+ (* re re) (* im im)))

series402.0ms

Counts

3 → 9

Calls

3 calls:

271.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
75.0ms	(- (sqrt (+ (* re re) (* im im))) re)
56.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

55 → 55

Iterations

Iter	Nodes
4	4761
3	1991
2	823
1	426
0	109

prune589.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.3b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `insert-posit16`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares`

Counts

4 → 130

Calls

4 calls:

37.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
55.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
12.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
88.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
52.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.5s

Counts

142 → 142

Iterations

Iter	Nodes
4	6297
3	1963
2	883
1	504
0	141

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* (+ (* im im) 0) 2.0)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (* (+ (* im im) 0) 2.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
8×	`pow1` `sqrt-div`
7×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-l/` `insert-posit16` `associate-/l`
3×	`sqrt-pow1`
2×	`pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sum-log` `frac-2neg` `div-exp` `pow-prod-down` `div-inv`

Counts

4 → 100

Calls

4 calls:

33.0ms	(/ (sqrt (* (+ (* im im) 0) 2.0)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
35.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (* (+ (* im im) 0) 2.0))

series482.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (sqrt (* (+ (* im im) 0) 2.0)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
74.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
54.0ms	(sqrt (+ (* re re) (* im im)))
54.0ms	(sqrt (* (+ (* im im) 0) 2.0))

simplify1.5s

Counts

112 → 112

Iterations

Iter	Nodes
3	3701
2	1568
1	783
0	201

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.3b	(/ (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

104×	`sqrt-prod`
91×	`*-un-lft-identity`
88×	`times-frac`
78×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
48×	`associate-r`
14×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `associate-/l*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+` `insert-posit16`
3×	`associate-l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 171

Calls

4 calls:

94.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
54.0ms	(/ (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
268.0ms	(/ (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
88.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify997.0ms

Counts

183 → 183

Iterations

Iter	Nodes
2	2832
1	1162
0	271

prune2.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.1b

regimes355.0ms

Accuracy

69.3% (9.3b remaining)

Error of 16.8b against oracle of 7.5b and baseline of 37.8b

bsearch188.0ms

Steps

Iters	Range		Point
4	1.6614623208655807e+111	2.310891359266851e+111	2.2094180720166524e+111
4	1.0526647032619268e-288	1.7669848660662517e-288	1.0730314248253915e-288
8	-9.687258947367738e-245	-1.5584770251340243e-249	-1.7322803508780655e-249
8	-6.584011051733632e+134	-1.1458450209363985e+130	-9.534169287773102e+132

simplify44.0ms

Iterations

Iter	Nodes
2	60
1	60
0	47

end0.0ms

sample2.9s

Algorithm

intervals

Results

866.0ms	5994×	body	80	valid
561.0ms	673×	body	2560	valid
528.0ms	293×	body	640	valid
402.0ms	504×	body	1280	valid
268.0ms	301×	body	5120	valid
54.0ms	160×	body	320	valid
16.0ms	75×	body	160	valid