Details

sample44.0ms

Algorithm

intervals

Results

21.0ms

271×

body

valid

simplify100.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize18.0ms

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))
30.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

3 → 64

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* y.re y.re) (* y.im y.im))
64.0ms	(- (* x.im y.re) (* x.re y.im))
126.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1862
1	339
0	111

prune590.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
17.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 98

Calls

4 calls:

12.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
20.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* x.im y.re) (* x.re y.im))
160.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1259
1	337
0	131

prune763.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 28.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.5b	(- (* x.im y.re) (* x.re y.im))
0.7b	(/ 1 (fma y.im y.im (* y.re y.re)))
30.2b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma y.im y.im (* y.re y.re))
6.0ms	(- (* x.im y.re) (* x.re y.im))
4.0ms	(/ 1 (fma y.im y.im (* y.re y.re)))
27.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma y.im y.im (* y.re y.re))
42.0ms	(- (* x.im y.re) (* x.re y.im))
60.0ms	(/ 1 (fma y.im y.im (* y.re y.re)))
128.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))

simplify2.1s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	2001
1	315
0	135

prune742.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 28.4b

localize63.0ms

Local error

Found 4 expressions with local error:

33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
34.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
34.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 63

Calls

4 calls:

7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
124.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
160.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
161.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	3636
2	599
1	161
0	69

prune691.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 28.4b

regimes553.0ms

Accuracy

0% (3.2b remaining)

Error of 26.9b against oracle of 23.7b and baseline of 26.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

717.0ms

8480×

body

valid