Details

sample462.0ms

Algorithm

intervals

Results

137.0ms	15×	body	320	valid
112.0ms	55×	body	1280	valid
96.0ms	250×	body	80	valid
45.0ms	40×	body	640	valid
6.0ms	11×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1115
4	236
3	85
2	53
1	31
0	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize83.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

11.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
191.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	2751
2	552
1	202
0	99

prune670.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.8b	(* (atan2 x.im x.re) y.im)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
8×	`add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
6×	`associate-r`
4×	`insert-posit16`
3×	`exp-prod` `log-pow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 73

Calls

4 calls:

32.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
19.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
130.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
34.0ms	(* (atan2 x.im x.re) y.im)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	968
1	297
0	137

prune890.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re x.re) (* x.im x.im))
1.8b	(* (atan2 x.im x.re) y.im)
3.0b	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`log-pow`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `associate-r` `associate-l`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

15.0ms	(+ (* x.re x.re) (* x.im x.im))
11.0ms	(* (atan2 x.im x.re) y.im)
21.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re x.re) (* x.im x.im))
26.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1073
1	242
0	108

prune662.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize154.0ms

Local error

Found 4 expressions with local error:

31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cos-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 43

Calls

4 calls:

12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
241.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
206.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
180.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
4	1906
3	651
2	291
1	141
0	70

prune615.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

regimes612.0ms

Accuracy

79.9% (6.1b remaining)

Error of 9.7b against oracle of 3.6b and baseline of 34.1b

bsearch1.1s

Steps

Iters	Range		Point
9	3.0660807951351545e-33	4.403371930147517e-28	3.102132787630003e-33
7	1.4015695320788811e-64	1.0033532377411923e-62	9.798541471285326e-63
8	-6.28539424680076e-307	3.3383700148803893e-307	-1.91205330543206e-310
9	-1.0136022580229297e-153	-3.773586630999499e-162	-3.7737597763103814e-161
6	-1.790535254998819e-16	-1.1589515176165432e-17	-4.9835237568442066e-17

simplify22.0ms

Iterations

Iter	Nodes
done	78
2	78
1	75
0	56

end0.0ms

sample11.2s

Algorithm

intervals

Results

4.0s	1988×	body	1280	valid
3.4s	7962×	body	80	valid
2.5s	1502×	body	640	valid
648.0ms	609×	body	320	valid
231.0ms	333×	body	160	valid