Details

analyze1.5s

Algorithm: search

sample134.0ms

Algorithm

intervals

Results

50.0ms	63×	body	1280	invalid
27.0ms	236×	body	80	valid
19.0ms	38×	body	640	invalid
5.0ms	10×	body	640	valid
4.0ms	12×	body	320	invalid
4.0ms	5×	body	1280	valid
2.0ms	5×	body	320	valid
1.0ms	11×	body	80	invalid
1.0ms	5×	body	160	invalid

simplify422.0ms

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

prune15.0ms

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: 32.3b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
28.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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:

4.0ms	(* (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)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

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

prune120.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 18.3b

Counts

69 → 5

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))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.3b	(* (atan2 x.im x.re) y.im)
28.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

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

series70.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* (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 (24.0ms)

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

prune120.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 5.0b

Counts

83 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
28.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

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

prune121.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 5.0b

Counts

75 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
28.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(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:

4.0ms	(* (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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(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

prune111.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	68	7	75

Merged error: 5.0b

Counts

75 → 7

regimes447.0ms

Accuracy

81.1% (5.6b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 33.4b

bsearch1.5s

Steps

Iters	Range		Point
9	-3.9727907335540565e-306	1.8035056180605266e-305	1.4146169321567e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

analyze1.3s

Algorithm: search

sample3.7s

Algorithm

intervals

Results

1.4s	1923×	body	1280	invalid
843.0ms	7530×	body	80	valid
636.0ms	1301×	body	640	invalid
187.0ms	547×	body	320	invalid
103.0ms	144×	body	1280	valid
80.0ms	165×	body	640	valid
52.0ms	232×	body	160	invalid
46.0ms	403×	body	80	invalid
41.0ms	111×	body	320	valid
12.0ms	50×	body	160	valid

Details

analyze1.5s

sample134.0ms

simplify422.0ms

prune15.0ms

localize25.0ms

rewrite23.0ms

series89.0ms

simplify80.0ms

prune120.0ms

localize16.0ms

rewrite20.0ms

series70.0ms

simplify77.0ms

prune120.0ms

localize28.0ms

rewrite18.0ms

series70.0ms

simplify80.0ms

prune121.0ms

localize25.0ms

rewrite19.0ms

series69.0ms

simplify79.0ms

prune111.0ms

regimes447.0ms

bsearch1.5s

simplify2.0ms

end0.0ms

analyze1.3s

sample3.7s

Profiling