Details

sample384.0ms

Algorithm

intervals

Results

54.0ms	81×	body	1280	valid
23.0ms	50×	body	640	valid
22.0ms	256×	body	80	valid
6.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	98	25
4	215	25
5	859	25
done	5000	25

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (pow (hypot x.re x.im) y.re) (sin (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.re)
1.5b	(* (atan2 x.im x.re) y.im)
33.3b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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` `frac-2neg` `sin-sum` `pow-exp` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

6.0ms	(/ (* (pow (hypot x.re x.im) y.re) (sin (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.re)
3.0ms	(* (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)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

410.0ms	(/ (* (pow (hypot x.re x.im) y.re) (sin (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.re)
17.0ms	(* (atan2 x.im x.re) y.im)
180.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

87 → 87

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	153	1462
1	332	1430
2	1029	1222
3	4573	1213
done	5000	1213

prune422.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (pow (hypot x.re x.im) y.re) (expm1 (log1p (sin (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.re)
1.5b	(* (atan2 x.im x.re) y.im)
33.3b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

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` `frac-2neg` `sin-sum` `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) (expm1 (log1p (sin (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.re)
3.0ms	(* (atan2 x.im x.re) y.im)
1.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

448.0ms	(/ (* (pow (hypot x.re x.im) y.re) (expm1 (log1p (sin (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.re)
16.0ms	(* (atan2 x.im x.re) y.im)
160.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

87 → 87

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	157	1524
1	337	1430
2	1037	1222
3	4589	1213
done	5000	1213

prune454.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
1.5b	(* (atan2 x.im x.re) y.im)
1.5b	(* (atan2 x.im x.re) y.im)
33.3b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(* (atan2 x.im x.re) y.im)
1.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(* (atan2 x.im x.re) y.im)
161.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts

82 → 82

Iterations

Useful iterations: 3 (211.0ms)

Iter	Nodes	Cost
0	92	721
1	167	710
2	384	626
3	732	624
4	1035	624
5	1803	624
6	3626	624
done	5000	624

prune607.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (exp (* (atan2 x.im x.re) y.im)) (* (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (pow (hypot x.re x.im) y.re)))
1.1b	(* (atan2 x.im x.re) y.re)
1.5b	(* (atan2 x.im x.re) y.im)
33.3b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

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` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `frac-2neg` `sin-sum` `pow-exp` `clear-num` `associate-/r*` `fma-udef` `div-inv`

Counts

4 → 75

Calls

4 calls:

5.0ms	(/ (exp (* (atan2 x.im x.re) y.im)) (* (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (pow (hypot x.re x.im) y.re)))
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
1.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(/ (exp (* (atan2 x.im x.re) y.im)) (* (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (pow (hypot x.re x.im) y.re)))
16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
157.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

87 → 87

Iterations

Useful iterations: 3 (966.0ms)

Iter	Nodes	Cost
0	180	1499
1	398	1464
2	1174	1266
3	4704	1257
done	5000	1257

prune376.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

regimes553.0ms

Accuracy

46.9% (3.0b remaining)

Error of 6.1b against oracle of 3.1b and baseline of 8.8b

bsearch379.0ms

Steps

Iters	Range		Point
8	2.3802294644426713e+157	2.123380866877602e+160	1.482437347436964e+158
7	5.139006765554396e-07	6.004887560100131e-05	5.9227529112519065e-05
7	-2.3364961565347435e+85	-9.850700213237158e+83	-5.095162325548454e+84

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	134
1	56	134
done	56	134

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2246×	body	1280	valid
710.0ms	7988×	body	80	valid
575.0ms	1395×	body	640	valid
168.0ms	587×	body	320	valid
68.0ms	43×	body	2560	valid
47.0ms	243×	body	160	valid