Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	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

simplify14.0ms

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

localize13.0ms

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)))

rewrite34.0ms

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)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify915.0ms

Counts

52 → 52

Iterations

Useful iterations: done (913.0ms)

Iter	Nodes	Cost
0	106	776
1	230	671
2	707	621
3	2351	596
done	5000	595

prune157.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.3b

localize15.0ms

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)))

rewrite50.0ms

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:

25.0ms	(/ (sqrt (* 2.0 (+ 0 (pow im 2)))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (* 2.0 (+ 0 (pow im 2))))
3.0ms	(sqrt (+ (* re re) (* im im)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (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))))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify569.0ms

Counts

108 → 108

Iterations

Useful iterations: done (566.0ms)

Iter	Nodes	Cost
0	200	2506
1	444	2081
2	1360	1961
done	5000	1958

prune348.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.2b

localize14.0ms

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:

52.0ms	(* (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)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
95.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify644.0ms

Counts

137 → 137

Iterations

Useful iterations: done (640.0ms)

Iter	Nodes	Cost
0	248	2920
1	602	2628
2	2100	2460
done	5001	2454

prune367.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (sqrt 2.0) (sqrt (fabs im))) (/ (sqrt (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.5b	(* (sqrt 2.0) (sqrt (fabs im)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

58×	`sqrt-prod`
54×	`associate-r`
50×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
42×	`times-frac`
36×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
7×	`associate-l` `prod-exp` `cbrt-unprod` `distribute-lft-out`
6×	`pow-prod-down` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-unprod` `flip-+`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`+-commutative` `rem-sqrt-square` `sqrt-undiv` `associate-*r/` `sum-log` `div-inv`

Counts

4 → 126

Calls

4 calls:

53.0ms	(* (* (sqrt 2.0) (sqrt (fabs im))) (/ (sqrt (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
6.0ms	(* (sqrt 2.0) (sqrt (fabs im)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (* (sqrt 2.0) (sqrt (fabs im))) (/ (sqrt (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
39.0ms	(* (sqrt 2.0) (sqrt (fabs im)))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify872.0ms

Counts

138 → 138

Iterations

Useful iterations: done (869.0ms)

Iter	Nodes	Cost
0	239	2663
1	654	2173
2	2579	1984
done	5000	1981

prune341.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.3b

regimes219.0ms

Accuracy

67.4% (9.7b remaining)

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

bsearch170.0ms

Steps

Iters	Range		Point
7	4.7789019538112153e+104	1.591151741636895e+106	1.5729919746509674e+106
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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	94
1	68	94
done	68	94

end0.0ms

sample676.0ms

Algorithm

intervals

Results

204.0ms	6006×	body	80	valid
130.0ms	691×	body	2560	valid
80.0ms	314×	body	5120	valid
75.0ms	480×	body	1280	valid
34.0ms	285×	body	640	valid
12.0ms	135×	body	320	valid
5.0ms	89×	body	160	valid