Details

sample47.0ms

Algorithm

intervals

Results

20.0ms

273×

body

valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	72	15
done	72	15

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
25.3b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

14.0ms	(+ (* y.re y.re) (* y.im y.im))
14.0ms	(- (* x.im y.re) (* x.re y.im))
47.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* y.re y.re) (* y.im y.im))
69.0ms	(- (* x.im y.re) (* x.re y.im))
172.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: 2 (343.0ms)

Iter	Nodes	Cost
0	102	1120
1	320	1097
2	1796	983
done	5000	983

prune421.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 25.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
15.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

12.0ms	(- (* x.im y.re) (* x.re y.im))
49.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* x.im y.re) (* x.re y.im))
204.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
59.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

98 → 98

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	121	1814
1	313	1682
2	1219	1576
done	5000	1574

prune856.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (- (* x.im y.re) (* x.re y.im)) 3)
0.5b	(- (* x.im y.re) (* x.re y.im))
25.3b	(/ (cbrt (pow (- (* x.im y.re) (* x.re y.im)) 3)) (+ (* y.re y.re) (* y.im y.im)))
26.0b	(cbrt (pow (- (* x.im y.re) (* x.re y.im)) 3))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-prod`
45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
15×	`associate-/l*`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3--` `flip--`
3×	`pow-unpow` `associate-/r*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

20.0ms	(pow (- (* x.im y.re) (* x.re y.im)) 3)
14.0ms	(- (* x.im y.re) (* x.re y.im))
77.0ms	(/ (cbrt (pow (- (* x.im y.re) (* x.re y.im)) 3)) (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(cbrt (pow (- (* x.im y.re) (* x.re y.im)) 3))

series564.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(pow (- (* x.im y.re) (* x.re y.im)) 3)
69.0ms	(- (* x.im y.re) (* x.re y.im))
157.0ms	(/ (cbrt (pow (- (* x.im y.re) (* x.re y.im)) 3)) (+ (* y.re y.re) (* y.im y.im)))
72.0ms	(cbrt (pow (- (* x.im y.re) (* x.re y.im)) 3))

simplify2.7s

Counts

151 → 151

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	196	3678
1	511	3149
2	2987	2881
done	5000	2879

prune935.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 22.5b

localize50.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (* y.re y.re) (* y.im y.im))
10.7b	(- (pow y.re 4) (pow y.im 4))
25.3b	(/ (- (* x.im y.re) (* x.re y.im)) (/ (- (pow y.re 4) (pow y.im 4)) (- (* y.re y.re) (* y.im y.im))))
38.4b	(/ (- (pow y.re 4) (pow y.im 4)) (- (* y.re y.re) (* y.im y.im)))

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

466×	`times-frac`
427×	`add-sqr-sqrt`
270×	`difference-of-squares`
251×	`*-un-lft-identity`
176×	`unpow-prod-down`
163×	`add-cube-cbrt`
132×	`sqr-pow`
66×	`associate-/r*`
44×	`distribute-lft-out--`
17×	`associate-/l*`
11×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
9×	`flip3--` `flip--`
8×	`add-log-exp`
6×	`div-inv`
4×	`pow1` `cbrt-undiv` `div-exp` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 396

Calls

4 calls:

16.0ms	(- (* y.re y.re) (* y.im y.im))
41.0ms	(- (pow y.re 4) (pow y.im 4))
134.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (/ (- (pow y.re 4) (pow y.im 4)) (- (* y.re y.re) (* y.im y.im))))
111.0ms	(/ (- (pow y.re 4) (pow y.im 4)) (- (* y.re y.re) (* y.im y.im)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* y.re y.re) (* y.im y.im))
95.0ms	(- (pow y.re 4) (pow y.im 4))
315.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (/ (- (pow y.re 4) (pow y.im 4)) (- (* y.re y.re) (* y.im y.im))))
138.0ms	(/ (- (pow y.re 4) (pow y.im 4)) (- (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts

408 → 408

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	646	14788
1	2212	13956
done	5001	13678

prune4.3s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 22.5b

regimes711.0ms

Accuracy

37.3% (1.9b remaining)

Error of 25.1b against oracle of 23.2b and baseline of 26.3b

bsearch8.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	82
1	28	82
done	28	82

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s

8499×

body

valid