Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	199×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	16×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8
done	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

30.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Counts

33 → 33

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	141	198
1	358	186
2	866	182
3	2557	181
4	5001	181
done	5001	181

prune107.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
4.5b	(exp (log (+ (sqrt (+ (* re re) (* im im))) re)))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

30.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
22.0ms	(exp (log (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series137.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
52.0ms	(exp (log (+ (sqrt (+ (* re re) (* im im))) re)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Counts

54 → 54

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	178	353
1	429	329
2	957	309
3	2722	301
4	5001	301
done	5001	301

prune158.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
4.8b	(pow E (log (+ (sqrt (+ (* re re) (* im im))) re)))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

30.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
22.0ms	(pow E (log (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series240.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
155.0ms	(pow E (log (+ (sqrt (+ (* re re) (* im im))) re)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	270	500
1	742	477
2	2186	459
3	5002	456
done	5002	456

prune194.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (+ (* re re) (* im im))) re)
5.1b	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
22.4b	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

39.0ms	(- (sqrt (+ (* re re) (* im im))) re)
31.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
42.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
11.0ms	(sqrt (+ (* re re) (* im im)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
201.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
79.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify41.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	369	696
1	1474	620
2	5001	611
done	5001	611

prune207.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

regimes256.0ms

Accuracy

57.7% (11.1b remaining)

Error of 24.8b against oracle of 13.7b and baseline of 39.9b

bsearch162.0ms

Steps

Iters	Range		Point
8	3.978686766170509e+64	1.2964566837885159e+67	1.2853826560442209e+67
4	7.427089056077598e-281	1.0961453402580365e-280	8.200231256875078e-281
8	-1.1187802841012395e-302	-7.079793537090769e-307	-1.4887498402374675e-304
10	-8.496526014238052e+204	-3.0851033949965913e+189	-3.1409156883208723e+189

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	34
1	64	34
done	64	34

end0.0ms

sample699.0ms

Algorithm

intervals

Results

190.0ms	6026×	body	80	valid
131.0ms	688×	body	2560	valid
77.0ms	499×	body	1280	valid
63.0ms	281×	body	5120	valid
44.0ms	294×	body	640	valid
12.0ms	139×	body	320	valid
4.0ms	73×	body	160	valid