Details

sample348.0ms

Algorithm

intervals

Results

105.0ms	258×	body	80	valid
57.0ms	47×	body	1280	valid
35.0ms	39×	body	640	valid
11.0ms	17×	body	320	valid
4.0ms	10×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

localize65.0ms

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))
0.7b	(* (atan2 x.im x.re) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
32.3b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

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×	`cos-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))
7.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(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)
27.0ms	(* (atan2 x.im x.re) y.im)
250.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (360.0ms)

Iter	Nodes	Cost
0	101	729
1	177	720
2	412	634
3	803	630
4	1494	630
5	4360	630
done	5000	630

prune560.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
0.7b	(* (atan2 x.im x.re) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
32.3b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `cos-sum` `pow-pow` `unpow3` `pow-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

7.0ms	(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
15.0ms	(* (atan2 x.im x.re) y.re)
14.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
33.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(* (atan2 x.im x.re) y.im)
312.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts

87 → 87

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	117	1100
1	241	1018
2	624	910
3	2587	902
done	5000	902

prune637.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
0.7b	(* (atan2 x.im x.re) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
32.3b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 68

Calls

4 calls:

5.0ms	(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
14.0ms	(* (atan2 x.im x.re) y.re)
21.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
21.0ms	(* (atan2 x.im x.re) y.re)
39.0ms	(* (atan2 x.im x.re) y.im)
263.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.3s

Counts

80 → 80

Iterations

Useful iterations: 3 (382.0ms)

Iter	Nodes	Cost
0	116	936
1	195	889
2	430	788
3	743	784
4	1081	784
5	2032	784
6	4780	784
done	5000	784

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
0.7b	(* (atan2 x.im x.re) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
32.3b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 68

Calls

4 calls:

11.0ms	(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
7.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
37.0ms	(* (atan2 x.im x.re) y.re)
23.0ms	(* (atan2 x.im x.re) y.im)
238.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.6s

Counts

80 → 80

Iterations

Useful iterations: 3 (357.0ms)

Iter	Nodes	Cost
0	116	936
1	195	889
2	430	788
3	743	784
4	1081	784
5	2032	784
6	4780	784
done	5000	784

prune524.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

regimes568.0ms

Accuracy

84.9% (0.5b remaining)

Error of 6.1b against oracle of 5.6b and baseline of 8.7b

bsearch7.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	129
1	42	129
done	42	129

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.3s	1936×	body	1280	valid
1.8s	7997×	body	80	valid
1.2s	1402×	body	640	valid
415.0ms	663×	body	320	valid
98.0ms	305×	body	160	valid