Details

sample361.0ms

Algorithm

intervals

Results

43.0ms	71×	body	1280	valid
24.0ms	266×	body	80	valid
16.0ms	42×	body	640	valid
5.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid

simplify345.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	98	25
4	215	25
5	882	25
done	5000	25

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
1.1b	(* (atan2 x.im x.re) y.im)
1.2b	(* (atan2 x.im x.re) y.re)
32.1b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-sqr-sqrt`
13×	`add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `cos-sum` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

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

series517.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(* (atan2 x.im x.re) y.re)
165.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts

87 → 87

Iterations

Useful iterations: 3 (411.0ms)

Iter	Nodes	Cost
0	149	1444
1	326	1414
2	1056	1207
3	4706	1200
done	5000	1200

prune389.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
0.9b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
1.2b	(* (atan2 x.im x.re) y.re)
32.1b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `*-commutative`
2×	`unswap-sqr`
1×	`cos-sum` `fma-udef`

Counts

4 → 77

Calls

4 calls:

34.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
12.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms	(* (atan2 x.im x.re) y.re)
1.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
83.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
16.0ms	(* (atan2 x.im x.re) y.re)
147.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts

89 → 89

Iterations

Useful iterations: 3 (485.0ms)

Iter	Nodes	Cost
0	132	1085
1	290	1066
2	1009	839
3	4287	768
done	5001	768

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
0.9b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
1.2b	(* (atan2 x.im x.re) y.re)
32.1b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `*-commutative`
2×	`unswap-sqr`
1×	`cos-sum` `fma-udef`

Counts

4 → 77

Calls

4 calls:

37.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
10.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms	(* (atan2 x.im x.re) y.re)
1.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
82.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
16.0ms	(* (atan2 x.im x.re) y.re)
145.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.3s

Counts

89 → 89

Iterations

Useful iterations: 3 (489.0ms)

Iter	Nodes	Cost
0	132	1085
1	290	1066
2	1009	839
3	4287	768
done	5001	768

prune446.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
0.9b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
1.2b	(* (atan2 x.im x.re) y.re)
32.1b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `*-commutative`
2×	`unswap-sqr`
1×	`cos-sum` `fma-udef`

Counts

4 → 77

Calls

4 calls:

36.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
10.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms	(* (atan2 x.im x.re) y.re)
1.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
84.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
20.0ms	(* (atan2 x.im x.re) y.re)
147.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts

89 → 89

Iterations

Useful iterations: 3 (495.0ms)

Iter	Nodes	Cost
0	132	1085
1	290	1066
2	1009	839
3	4287	768
done	5001	768

prune449.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

regimes348.0ms

Accuracy

46.5% (2.6b remaining)

Error of 6.2b against oracle of 3.6b and baseline of 8.4b

bsearch6.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	100
1	46	100
done	46	100

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	2022×	body	1280	valid
655.0ms	7969×	body	80	valid
567.0ms	1479×	body	640	valid
169.0ms	628×	body	320	valid
59.0ms	309×	body	160	valid