Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	199×	body	80	valid
7.0ms	21×	body	2560	valid
5.0ms	11×	body	5120	valid
4.0ms	14×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	640	valid
0.0ms	3×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	24	15
done	24	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

24.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
42.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
26.0ms	(sqrt (+ (* re re) (* im im)))

series412.0ms

Counts

3 → 9

Calls

3 calls:

290.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
54.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
68.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.6s

Counts

49 → 49

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	99	722
1	243	617
2	642	569
3	1604	542
4	4024	537
done	5000	537

prune244.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
30.1b	(sqrt (* (* im im) 2.0))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite212.0ms

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-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div` `associate-/l*`
3×	`pow-prod-down`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 106

Calls

4 calls:

71.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
93.0ms	(- (sqrt (+ (* re re) (* im im))) re)
27.0ms	(sqrt (* (* im im) 2.0))
16.0ms	(sqrt (+ (* re re) (* im im)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
82.0ms	(- (sqrt (+ (* re re) (* im im))) re)
71.0ms	(sqrt (* (* im im) 2.0))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

118 → 118

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	195	2643
1	393	2410
2	1018	2314
3	2860	2285
done	5002	2279

prune511.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(* (fabs im) (sqrt 2.0))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

93.0ms	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
10.0ms	(* (fabs im) (sqrt 2.0))
42.0ms	(- (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (+ (* re re) (* im im)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (* (fabs im) (sqrt 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(* (fabs im) (sqrt 2.0))
78.0ms	(- (sqrt (+ (* re re) (* im im))) re)
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	193	1652
1	449	1480
2	1618	1364
done	5000	1333

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (+ (* re re) (* im im))) re)
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

43.0ms	(- (sqrt (+ (* re re) (* im im))) re)
79.0ms	(- (sqrt (+ (* re re) (* im im))) re)
14.0ms	(sqrt (+ (* re re) (* im im)))
14.0ms	(sqrt (+ (* re re) (* im im)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (sqrt (+ (* re re) (* im im))) re)
68.0ms	(- (sqrt (+ (* re re) (* im im))) re)
59.0ms	(sqrt (+ (* re re) (* im im)))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

72 → 72

Iterations

Useful iterations: 4 (760.0ms)

Iter	Nodes	Cost
0	64	962
1	137	842
2	328	782
3	767	762
4	1986	758
done	5000	758

prune461.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.1b

regimes313.0ms

Accuracy

50.2% (14.6b remaining)

Error of 22.6b against oracle of 8.0b and baseline of 37.4b

bsearch280.0ms

Steps

Iters	Range		Point
9	9.208203168852366e-97	6.460632185244904e-91	4.202834506095947e-94
3	9.630645247606357e-160	1.1174213342480038e-159	9.727118253535962e-160
8	2.419960472709144e-207	1.9603440090509578e-204	1.2802976578175363e-204
8	1.1317114056863307e-247	4.201890819355548e-245	5.124751274050741e-246
9	-1.703715759581658e-137	-4.0504560254265596e-144	-4.2156616274993736e-144
2	-5.449253800430163e+114	-4.7106032971479507e+114	-5.330091552844717e+114

simplify39.0ms

Iterations

Useful iterations: done (39.0ms)

Iter	Nodes	Cost
0	53	132
1	67	125
2	70	107
3	73	107
done	73	106

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	5987×	body	80	valid
332.0ms	702×	body	2560	valid
209.0ms	496×	body	1280	valid
146.0ms	288×	body	5120	valid
79.0ms	297×	body	640	valid
30.0ms	160×	body	320	valid
9.0ms	70×	body	160	valid