Details

sample46.0ms

Algorithm

intervals

Results

31.0ms

272×

body

valid

simplify59.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize36.0ms

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))
22.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

260×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
92×	`associate-l`
88×	`times-frac`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
26×	`swap-sqr`
24×	`add-cube-cbrt`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `insert-posit16`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 163

Calls

3 calls:

46.0ms	(+ (* y.re y.re) (* y.im y.im))
41.0ms	(- (* x.im y.re) (* x.re y.im))
183.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
51.0ms	(- (* x.im y.re) (* x.re y.im))
118.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.4s

Counts

172 → 172

Iterations

Iter	Nodes
done	5037
3	4717
2	1274
1	413
0	157

prune490.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
11.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite433.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 224

Calls

4 calls:

51.0ms	(- (* x.im y.re) (* x.re y.im))
205.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
99.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* x.im y.re) (* x.re y.im))
167.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

236 → 236

Iterations

Iter	Nodes
done	5035
3	2984
2	1103
1	436
0	190

prune926.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
12.0b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite896.0ms

Algorithm

rewrite-expression-head

Rules

149×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
66×	`sqrt-prod`
51×	`associate-l`
40×	`distribute-lft-out`
39×	`associate-r`
37×	`times-frac`
34×	`frac-times` `add-cube-cbrt`
33×	`associate-/r*`
19×	`flip3--` `flip--`
17×	`associate-*r/`
16×	`swap-sqr`
13×	`add-exp-log` `unswap-sqr`
10×	`associate-/l*`
9×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`sqrt-div` `add-log-exp`
4×	`clear-num` `prod-exp` `insert-posit16`
3×	`frac-2neg` `flip3-+` `un-div-inv` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 190

Calls

4 calls:

81.0ms	(- (* x.im y.re) (* x.re y.im))
616.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
83.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
102.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* x.im y.re) (* x.re y.im))
162.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
65.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
2	1541
1	591
0	218

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* y.re x.im) (* x.re y.im))
11.8b	(/ (- (* y.re x.im) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite549.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 224

Calls

4 calls:

80.0ms	(- (* y.re x.im) (* x.re y.im))
261.0ms	(/ (- (* y.re x.im) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
101.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
84.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* y.re x.im) (* x.re y.im))
134.0ms	(/ (- (* y.re x.im) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.8s

Counts

236 → 236

Iterations

Iter	Nodes
done	5001
3	2913
2	1104
1	436
0	189

prune844.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.8b

regimes515.0ms

Accuracy

0% (2.4b remaining)

Error of 25.0b against oracle of 22.6b and baseline of 25.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8445×

body

valid