Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
3.0ms	18×	body	2560	valid
2.0ms	11×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	17	15
2	24	15
3	29	15
4	33	15
done	33	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.1b	(- (sqrt (+ (* re re) (* im im))) re)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

12.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series249.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

52 → 52

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	106	776
1	230	671
2	706	621
3	2329	596
done	5001	595

prune153.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* 2.0 (+ 0 (pow im 2)))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
26.4b	(sqrt (* 2.0 (+ 0 (pow im 2))))
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite52.0ms

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

Counts

4 → 96

Calls

4 calls:

26.0ms	(/ (sqrt (* 2.0 (+ 0 (pow im 2)))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (* 2.0 (+ 0 (pow im 2))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (sqrt (* 2.0 (+ 0 (pow im 2)))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (* 2.0 (+ 0 (pow im 2))))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

108 → 108

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	200	2506
1	444	2081
2	1238	1963
3	4605	1925
done	5000	1925

prune349.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.3b	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
39×	`sqrt-prod`
37×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `associate-l` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 125

Calls

4 calls:

49.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
23.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
95.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify781.0ms

Counts

137 → 137

Iterations

Useful iterations: done (777.0ms)

Iter	Nodes	Cost
0	248	2920
1	602	2628
2	2056	2460
done	5001	2454

prune375.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (sqrt 2.0)) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.3b	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
48×	`times-frac`
40×	`sqrt-prod`
38×	`add-cube-cbrt`
27×	`associate-r`
12×	`cbrt-prod`
11×	`add-exp-log`
9×	`associate-l` `add-cbrt-cube` `unswap-sqr`
8×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 131

Calls

4 calls:

52.0ms	(* (cbrt (sqrt 2.0)) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
19.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(* (cbrt (sqrt 2.0)) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
98.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify858.0ms

Counts

143 → 143

Iterations

Useful iterations: done (853.0ms)

Iter	Nodes	Cost
0	247	3165
1	603	2876
2	2201	2701
done	5000	2695

prune438.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

regimes202.0ms

Accuracy

67.5% (9.7b remaining)

Error of 17.8b against oracle of 8.1b and baseline of 37.8b

bsearch198.0ms

Steps

Iters	Range		Point
10	5.164511264057817e+108	8.190465964655102e+120	4.065324281963127e+114
7	7.991847353731723e-282	1.110810473879014e-279	1.2766285812733717e-281
8	-6.1566044135874494e-263	-2.025600411185499e-265	-4.7290934126280475e-264
9	-1.0928018917701282e+131	-5.157756317616828e+122	-5.577781367361616e+127

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	110
1	70	110
done	70	110

end0.0ms

sample666.0ms

Algorithm

intervals

Results

200.0ms	6006×	body	80	valid
126.0ms	691×	body	2560	valid
77.0ms	480×	body	1280	valid
74.0ms	314×	body	5120	valid
36.0ms	285×	body	640	valid
12.0ms	135×	body	320	valid
5.0ms	89×	body	160	valid