Details

sample138.0ms

Algorithm

intervals

Results

15.0ms	32×	body	2560	valid
14.0ms	177×	body	80	valid
5.0ms	11×	body	5120	valid
5.0ms	15×	body	1280	valid
3.0ms	12×	body	640	valid
2.0ms	8×	body	320	valid
0.0ms	1×	body	160	valid

simplify115.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	17	15
2	24	15
3	30	15
4	35	15
done	35	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite173.0ms

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:

47.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
103.0ms	(- (sqrt (+ (* re re) (* im im))) re)
19.0ms	(sqrt (+ (* re re) (* im im)))

series416.0ms

Counts

3 → 9

Calls

3 calls:

268.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
82.0ms	(- (sqrt (+ (* re re) (* im im))) re)
65.0ms	(sqrt (+ (* re re) (* im im)))

simplify622.0ms

Counts

52 → 52

Iterations

Useful iterations: done (619.0ms)

Iter	Nodes	Cost
0	106	776
1	242	675
2	1007	621
done	5000	598

prune215.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
27.4b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (* 2.0 (+ (* im im) 0)))

rewrite181.0ms

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:

84.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
67.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
83.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
73.0ms	(sqrt (+ (* re re) (* im im)))
51.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

simplify1.2s

Counts

108 → 108

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	198	2506
1	463	2091
2	2078	1954
done	5000	1936

prune524.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.4b

localize21.0ms

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)))
1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite383.0ms

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:

202.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
84.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
69.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
128.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
79.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

137 → 137

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	248	2920
1	652	2642
2	4031	2472
done	5001	2468

prune607.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (sqrt (fabs im)))
1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

64.0ms	(/ (sqrt (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(* (sqrt 2.0) (sqrt (fabs im)))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (sqrt (fabs im)) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
57.0ms	(* (sqrt 2.0) (sqrt (fabs im)))
72.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

139 → 139

Iterations

Useful iterations: 2 (385.0ms)

Iter	Nodes	Cost
0	216	2727
1	478	2438
2	2167	2345
done	5002	2345

prune604.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

regimes258.0ms

Accuracy

55.2% (13.1b remaining)

Error of 20.9b against oracle of 7.8b and baseline of 36.9b

bsearch143.0ms

Steps

Iters	Range		Point
9	1.9585635812996623e+65	6.751285631647885e+73	6.594840577856812e+73
5	-1.1599915936277108e-82	-4.556869025404441e-83	-5.4785539535281515e-83

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	37	54
1	50	52
done	50	52

end0.0ms

sample2.4s

Algorithm

intervals

Results

860.0ms	687×	body	2560	valid
478.0ms	5967×	body	80	valid
309.0ms	516×	body	1280	valid
251.0ms	304×	body	5120	valid
111.0ms	282×	body	640	valid
34.0ms	164×	body	320	valid
11.0ms	80×	body	160	valid