Details

sample41.0ms

Algorithm

intervals

Results

18.0ms

262×

body

valid

simplify226.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize42.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
25.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

49.0ms	(- (* x.im y.re) (* x.re y.im))
270.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series359.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (* x.im y.re) (* x.re y.im))
288.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify5.7s

Counts

50 → 50

Iterations

Iter	Nodes
done	5001
3	3106
2	935
1	259
0	89

prune816.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`flip3--` `flip--`

Counts

4 → 266

Calls

4 calls:

102.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
126.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series951.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
625.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
76.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
67.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify6.1s

Counts

278 → 278

Iterations

Iter	Nodes
done	5003
2	2090
1	741
0	307

prune4.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
16.5b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp`
7×	`pow1`
6×	`sqrt-div` `div-inv`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 193

Calls

4 calls:

62.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
53.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
27.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series974.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
336.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
145.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
253.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify11.9s

Counts

205 → 205

Iterations

Iter	Nodes
done	5001
2	1779
1	633
0	243

prune3.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
25.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.im y.im) (* y.re y.re)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

17.0ms	(- (* x.im y.re) (* x.re y.im))
60.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.im y.im) (* y.re y.re)))

series275.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (* x.im y.re) (* x.re y.im))
203.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.im y.im) (* y.re y.re)))

simplify7.6s

Counts

50 → 50

Iterations

Iter	Nodes
done	5002
3	3115
2	935
1	259
0	89

prune533.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.4b

regimes763.0ms

Accuracy

0% (2.9b remaining)

Error of 25.9b against oracle of 23.0b and baseline of 25.9b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	15

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.6s

8466×

body

valid