Details

sample407.0ms

Algorithm

intervals

Results

195.0ms	67×	body	1280	valid
72.0ms	259×	body	80	valid
30.0ms	41×	body	640	valid
9.0ms	22×	body	320	valid
5.0ms	13×	body	160	valid
2.0ms	1×	body	2560	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	96	25
4	215	25
5	843	25
done	5000	25

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
1.4b	(* (atan2 x.im x.re) y.re)
2.3b	(* (atan2 x.im x.re) y.im)
34.7b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`sin-sum`

Counts

4 → 60

Calls

4 calls:

0.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
8.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
26.0ms	(* (atan2 x.im x.re) y.re)
21.0ms	(* (atan2 x.im x.re) y.im)
245.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (369.0ms)

Iter	Nodes	Cost
0	101	738
1	177	728
2	412	642
3	803	638
4	1496	638
5	4355	638
done	5000	638

prune523.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(log1p (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
1.4b	(* (atan2 x.im x.re) y.re)
2.3b	(* (atan2 x.im x.re) y.im)
34.7b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`log1p-udef` `sin-sum` `log1p-expm1` `fma-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(log1p (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
8.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series701.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(log1p (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
20.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
313.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts

73 → 73

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	113	789
1	206	777
2	479	682
3	937	677
4	1873	677
done	5001	676

prune612.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize80.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (atan2 x.im x.re) y.re))
7.7b	(cbrt (* (atan2 x.im x.re) y.re))
7.7b	(cbrt (* (atan2 x.im x.re) y.re))
34.3b	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

7.0ms	(cbrt (* (atan2 x.im x.re) y.re))
7.0ms	(cbrt (* (atan2 x.im x.re) y.re))
7.0ms	(cbrt (* (atan2 x.im x.re) y.re))
5.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (* (atan2 x.im x.re) y.re))
87.0ms	(cbrt (* (atan2 x.im x.re) y.re))
97.0ms	(cbrt (* (atan2 x.im x.re) y.re))
268.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify1.8s

Counts

55 → 55

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	71	811
1	119	806
2	182	569
3	313	513
4	618	486
5	1466	486
done	5000	483

prune458.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.5b

localize81.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (atan2 x.im x.re) y.re))
7.7b	(cbrt (* (atan2 x.im x.re) y.re))
7.7b	(cbrt (* (atan2 x.im x.re) y.re))
34.7b	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (* (* (cbrt (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (cbrt (* (atan2 x.im x.re) y.re)))) (cbrt (cbrt (* (atan2 x.im x.re) y.re)))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

4.0ms	(cbrt (* (atan2 x.im x.re) y.re))
11.0ms	(cbrt (* (atan2 x.im x.re) y.re))
4.0ms	(cbrt (* (atan2 x.im x.re) y.re))
3.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (* (* (cbrt (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (cbrt (* (atan2 x.im x.re) y.re)))) (cbrt (cbrt (* (atan2 x.im x.re) y.re)))))))

series957.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (* (atan2 x.im x.re) y.re))
90.0ms	(cbrt (* (atan2 x.im x.re) y.re))
90.0ms	(cbrt (* (atan2 x.im x.re) y.re))
695.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (* (* (cbrt (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (cbrt (* (atan2 x.im x.re) y.re)))) (cbrt (cbrt (* (atan2 x.im x.re) y.re)))))))

simplify2.3s

Counts

55 → 55

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	73	1049
1	127	1044
2	208	749
3	374	513
4	769	486
5	2090	486
done	5001	465

prune448.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.5b

regimes641.0ms

Accuracy

87.9% (0.4b remaining)

Error of 6.0b against oracle of 5.7b and baseline of 8.7b

bsearch5.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	119
1	44	119
done	44	119

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.0s	2175×	body	1280	valid
2.1s	7945×	body	80	valid
1.4s	1425×	body	640	valid
317.0ms	576×	body	320	valid
168.0ms	50×	body	2560	valid
137.0ms	249×	body	160	valid