Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
3.0ms	17×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	3×	body	320	valid
2.0ms	8×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	23	15
done	23	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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:

2.0ms	(+ (* re re) (* im im))
10.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
167.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

63 → 63

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	108	888
1	272	774
2	845	698
3	2784	673
done	5001	672

prune192.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
7×	`pow1`
4×	`add-exp-log` `cbrt-prod` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div` `associate-*r/`
1×	`pow1/3`

Counts

4 → 59

Calls

4 calls:

11.0ms	(cbrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(cbrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
41.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify967.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (309.0ms)

Iter	Nodes	Cost
0	118	1065
1	267	925
2	719	866
3	2208	845
done	5001	845

prune293.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.6b

localize24.0ms

Local error

Found 4 expressions with local error:

28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	207	680
3	459	656
4	1009	656
5	2577	656
done	5000	656

prune359.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.6b

localize19.0ms

Local error

Found 4 expressions with local error:

3.0b	(exp (log (+ (* re re) (* im im))))
13.1b	(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
28.5b	(sqrt (exp (log (+ (* re re) (* im im)))))
29.6b	(log (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(exp (log (+ (* re re) (* im im))))
19.0ms	(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (exp (log (+ (* re re) (* im im)))))
3.0ms	(log (+ (* re re) (* im im)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(exp (log (+ (* re re) (* im im))))
50.0ms	(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (exp (log (+ (* re re) (* im im)))))
53.0ms	(log (+ (* re re) (* im im)))

simplify940.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (270.0ms)

Iter	Nodes	Cost
0	113	1127
1	227	903
2	574	799
3	1692	791
done	5001	791

prune217.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.6b

regimes456.0ms

Accuracy

56.3% (9.5b remaining)

Error of 26.4b against oracle of 16.9b and baseline of 38.6b

bsearch78.0ms

Steps

Iters	Range		Point
7	1.8684288122828866e+141	1.487546070235645e+143	6.674516804324248e+142
9	-1.6545147340030671e-295	-6.515465488001152e-301	-6.580886374598778e-301

simplify3.0ms

Iterations

Useful iterations: done (3.0ms)

Iter	Nodes	Cost
0	34	52
1	45	52
done	45	50

end0.0ms

sample694.0ms

Algorithm

intervals

Results

211.0ms	5999×	body	80	valid
135.0ms	657×	body	2560	valid
84.0ms	524×	body	1280	valid
72.0ms	295×	body	5120	valid
39.0ms	308×	body	640	valid
13.0ms	142×	body	320	valid
5.0ms	75×	body	160	valid