Details

sample246.0ms

Algorithm

intervals

Results

84.0ms	63×	body	1280	valid
28.0ms	253×	body	80	valid
26.0ms	49×	body	640	valid
9.0ms	26×	body	320	valid
5.0ms	11×	body	160	valid
2.0ms	1×	body	2560	valid

simplify29.0ms

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize56.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
28.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
180.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify68.0ms

Counts: 68 → 68

prune382.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.6b

localize49.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify136.0ms

Counts: 72 → 72

prune523.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.6b

localize56.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.8b	(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
15×	`add-sqr-sqrt` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cube-div` `cbrt-div`
1×	`cube-mult` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series174.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify52.0ms

Counts: 86 → 86

prune601.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.6b

localize41.0ms

Local error

Found 4 expressions with local error:

15.0b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
28.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

12.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
176.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify148.0ms

Counts: 71 → 71

prune362.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 20.6b

regimes519.0ms

Accuracy

78.2% (3.1b remaining)

Error of 22.4b against oracle of 19.3b and baseline of 33.6b

bsearch160.0ms

Steps

Iters	Range		Point
9	-9.205433752799553e-305	1.5534809022725981e-305	-5.57158609869316e-309

simplify1.0ms

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.6s	2171×	body	1280	valid
1.6s	7991×	body	80	valid
1.3s	1450×	body	640	valid
213.0ms	586×	body	320	valid
94.0ms	52×	body	2560	valid
55.0ms	235×	body	160	valid