Details

sample51.0ms

Algorithm

intervals

Results

34.0ms

275×

body

valid

simplify55.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	70
5	70
4	66
3	48
2	36
1	19
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize27.0ms

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))
24.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

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×	`pow1` `associate-/r` `associate-/l`
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 → 55

Calls

3 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(- (* x.im y.re) (* x.re y.im))
32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* y.re y.re) (* y.im y.im))
52.0ms	(- (* x.im y.re) (* x.re y.im))
107.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

64 → 64

Iterations

Iter	Nodes
3	4321
2	1173
1	303
0	101

prune606.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
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 → 86

Calls

4 calls:

6.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(/ (- (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
129.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify786.0ms

Counts

98 → 98

Iterations

Iter	Nodes
3	2538
2	899
1	312
0	121

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.2b

localize62.0ms

Local error

Found 4 expressions with local error:

10.4b	(/ (- (* x.im y.re) (* x.re y.im)) (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))
27.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

14.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
120.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
113.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

83 → 83

Iterations

Iter	Nodes
3	3500
2	1034
1	322
0	136

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.2b

localize65.0ms

Local error

Found 4 expressions with local error:

10.4b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))))
27.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`cbrt-prod`
4×	`cbrt-div` `prod-exp` `add-log-exp`
3×	`flip3-+` `associate-l` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `pow1/3` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod` `flip--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 81

Calls

4 calls:

35.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
130.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
121.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.7s

Counts

93 → 93

Iterations

Iter	Nodes
3	4971
2	1461
1	411
0	163

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.2b

regimes500.0ms

Accuracy

0% (2.4b remaining)

Error of 25.3b against oracle of 22.8b and baseline of 25.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	16
1	16
0	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8454×

body

valid