Details

sample28.0ms

Algorithm

intervals

Results

13.0ms

276×

body

valid

simplify50.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
26.3b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series218.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* y.re y.re) (* y.im y.im))
61.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts

64 → 64

Iterations

Useful iterations: 2 (289.0ms)

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

prune315.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
16.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite80.0ms

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:

8.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* x.im y.re) (* x.re y.im))
221.0ms	(/ (- (* 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)))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

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

prune440.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* y.re x.im) (* y.im x.re))))
16.7b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* y.re x.im) (* y.im x.re)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite170.0ms

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:

68.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* y.re x.im) (* y.im x.re))))
48.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* y.re x.im) (* y.im x.re)))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* y.re x.im) (* y.im x.re))))
109.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* y.re x.im) (* y.im x.re)))
64.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
70.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

205 → 205

Iterations

Useful iterations: 2 (525.0ms)

Iter	Nodes	Cost
0	243	5682
1	642	5079
2	3392	4824
done	5000	4824

prune615.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 161

Calls

4 calls:

117.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
50.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
141.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.7s

Counts

173 → 173

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	196	4890
1	610	4531
2	3555	3877
done	5000	3823

prune727.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.4b

regimes303.0ms

Accuracy

0% (2.9b remaining)

Error of 25.4b against oracle of 22.5b and baseline of 25.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	27
1	20	27
done	20	27

end0.0ms

sample1.3s

Algorithm

intervals

Results

776.0ms

8396×

body

valid