Details

sample57.0ms

Algorithm

intervals

Results

15.0ms	200×	body	80	valid
8.0ms	18×	body	2560	valid
6.0ms	16×	body	1280	valid
4.0ms	8×	body	5120	valid
2.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

16.0ms	(+ (* re re) (* im im))
52.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
55.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (+ (* re re) (* im im)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* re re) (* im im))
275.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
78.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
64.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

63 → 63

Iterations

Useful iterations: done (998.0ms)

Iter	Nodes	Cost
0	108	888
1	293	782
2	1331	698
done	5001	682

prune486.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (+ (* re re) (* im im))) re)
0.3b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
26.6b	(sqrt (* 2.0 (+ (* im im) 0)))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite228.0ms

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

Counts

4 → 109

Calls

4 calls:

78.0ms	(- (sqrt (+ (* re re) (* im im))) re)
110.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
15.0ms	(sqrt (+ (* re re) (* im im)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (sqrt (+ (* re re) (* im im))) re)
311.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
71.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

121 → 121

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	212	2952
1	472	2509
2	2195	2366
done	5000	2346

prune903.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (+ (* re re) (* im im))) re)
0.3b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(* (sqrt 2.0) (fabs im))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite219.0ms

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-l` `add-log-exp` `difference-of-squares`
4×	`sqrt-div`
3×	`associate-r` `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:

78.0ms	(- (sqrt (+ (* re re) (* im im))) re)
94.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
27.0ms	(* (sqrt 2.0) (fabs im))
15.0ms	(sqrt (+ (* re re) (* im im)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (sqrt (+ (* re re) (* im im))) re)
268.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
62.0ms	(* (sqrt 2.0) (fabs im))
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts

99 → 99

Iterations

Useful iterations: 2 (509.0ms)

Iter	Nodes	Cost
0	192	1649
1	477	1497
2	2534	1367
done	5002	1367

prune759.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (+ (* re re) (* im im))) re)
0.3b	(/ (* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (fabs im)))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

78.0ms	(- (sqrt (+ (* re re) (* im im))) re)
159.0ms	(/ (* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
90.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (fabs im)))
15.0ms	(sqrt (+ (* re re) (* im im)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (sqrt (+ (* re re) (* im im))) re)
304.0ms	(/ (* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
70.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (fabs im)))
77.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

105 → 105

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	203	2536
1	570	2317
2	2893	1741
done	5000	1549

prune722.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

regimes524.0ms

Accuracy

55.9% (13.1b remaining)

Error of 20.9b against oracle of 7.8b and baseline of 37.6b

bsearch218.0ms

Steps

Iters	Range		Point
9	2.828406465914494e-47	6.594228604770262e-42	1.7351403959562423e-43
6	-9.002982014462326e+138	-9.457886154583405e+137	-6.439772273490177e+138

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	56
1	43	56
done	43	56

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	5996×	body	80	valid
458.0ms	668×	body	2560	valid
243.0ms	308×	body	5120	valid
209.0ms	491×	body	1280	valid
96.0ms	286×	body	640	valid
37.0ms	155×	body	320	valid
15.0ms	96×	body	160	valid