Details

sample76.0ms

Algorithm

intervals

Results

26.0ms	203×	body	80	valid
15.0ms	21×	body	2560	valid
11.0ms	12×	body	5120	valid
9.0ms	12×	body	1280	valid
3.0ms	5×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `sqrt-prod` `flip-+` `insert-posit16`
3×	`sqrt-pow1`
2×	`+-commutative` `sum-log` `pow1/2` `associate-*r/`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

10.0ms	(+ (* re re) (* im im))
40.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(sqrt (+ (* re re) (* im im)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* re re) (* im im))
75.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
234.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	5003
3	3012
2	815
1	280
0	112

prune346.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (* (* im im) 2.0))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`pow1`
9×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div` `insert-posit16` `associate-/l*`
3×	`pow-prod-down`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

58.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
38.0ms	(- (sqrt (+ (* re re) (* im im))) re)
20.0ms	(sqrt (* (* im im) 2.0))
13.0ms	(sqrt (+ (* re re) (* im im)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
63.0ms	(- (sqrt (+ (* re re) (* im im))) re)
64.0ms	(sqrt (* (* im im) 2.0))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
3	3325
2	1005
1	402
0	199

prune680.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs im) (/ (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
0.4b	(/ (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

156×	`sqrt-prod`
142×	`add-sqr-sqrt`
112×	`times-frac`
99×	`*-un-lft-identity`
71×	`add-cube-cbrt`
60×	`associate-r`
28×	`difference-of-squares`
14×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
7×	`pow1`
6×	`sqrt-div` `associate-/l*` `add-log-exp`
5×	`unswap-sqr`
4×	`associate-/r/` `insert-posit16`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

4 → 200

Calls

4 calls:

125.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
45.0ms	(/ (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
56.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
205.0ms	(/ (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
82.0ms	(- (sqrt (+ (* re re) (* im im))) re)
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

212 → 212

Iterations

Iter	Nodes
done	5001
2	2371
1	720
0	296

prune906.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (fabs im) (sqrt 2.0))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `times-frac`
7×	`pow1`
6×	`associate-r` `add-log-exp` `difference-of-squares`
4×	`sqrt-div` `insert-posit16`
3×	`associate-l` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 91

Calls

4 calls:

55.0ms	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
10.0ms	(* (fabs im) (sqrt 2.0))
37.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
55.0ms	(* (fabs im) (sqrt 2.0))
64.0ms	(- (sqrt (+ (* re re) (* im im))) re)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	5007
2	1648
1	468
0	197

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

regimes648.0ms

Accuracy

63% (10.6b remaining)

Error of 18.3b against oracle of 7.7b and baseline of 36.4b

bsearch294.0ms

Steps

Iters	Range		Point
10	12461.173664998358	8322112628852838.0	8235632211164311.0
10	7.578145392669126e-173	6.368480921027092e-162	1.3001999503965804e-165
6	-3.505749298226566e+116	-2.552279280824353e+115	-1.4891181159633834e+116

simplify20.0ms

Iterations

Iter	Nodes
done	50
1	50
0	40

end0.0ms

sample3.0s

Algorithm

intervals

Results

957.0ms	6025×	body	80	valid
590.0ms	711×	body	2560	valid
564.0ms	275×	body	640	valid
353.0ms	488×	body	1280	valid
247.0ms	294×	body	5120	valid
50.0ms	145×	body	320	valid
14.0ms	62×	body	160	valid