Details

sample353.0ms

Algorithm

intervals

Results

253.0ms	75×	body	1280	valid
29.0ms	251×	body	80	valid
21.0ms	43×	body	640	valid
7.0ms	20×	body	320	valid
3.0ms	11×	body	160	valid

simplify417.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 28.8b

Counts

2 → 1

localize48.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im 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-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune125.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 16.0b

Counts

69 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.1b	(* (atan2 x.im x.re) y.im)
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
22.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	307	551
1	925	510
2	2748	491
3	5002	491

prune133.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Merged error: 3.3b

Counts

84 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) 3)
1.1b	(* (atan2 x.im x.re) y.im)
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.1b	(cbrt (pow (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) 3))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`cbrt-prod`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `sqrt-prod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `sqrt-div` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `*-commutative` `rem-cbrt-cube` `flip-+` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

5.0ms	(pow (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) 3)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
2.0ms	(cbrt (pow (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) 3))

series157.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(pow (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) 3)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms	(cbrt (pow (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) 3))

simplify154.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	290	560
1	1050	512
2	4854	507
3	5001	507

prune160.0ms

Filtered

60 candidates to 84 candidates (-40.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 3.3b

Counts

93 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune95.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Merged error: 3.3b

Counts

77 → 9

regimes429.0ms

Accuracy

68.1% (5.5b remaining)

Error of 9.1b against oracle of 3.6b and baseline of 20.9b

bsearch92.0ms

Steps

Iters	Range		Point
9	-4.701248319910525e-307	3.7613894419133676e-305	-9.0249257815008e-312

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	17
1	38	17
2	38	17

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	2053×	body	1280	valid
911.0ms	7992×	body	80	valid
695.0ms	1429×	body	640	valid
235.0ms	661×	body	320	valid
75.0ms	331×	body	160	valid

Details

sample353.0ms

simplify417.0ms

prune16.0ms

localize48.0ms

rewrite21.0ms

series85.0ms

simplify79.0ms

prune125.0ms

localize16.0ms

rewrite17.0ms

series72.0ms

simplify77.0ms

prune133.0ms

localize20.0ms

rewrite16.0ms

series157.0ms

simplify154.0ms

prune160.0ms

localize26.0ms

rewrite19.0ms

series70.0ms

simplify78.0ms

prune95.0ms

regimes429.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling