Details

sample340.0ms

Algorithm

intervals

Results

223.0ms	250×	body	80	valid
49.0ms	69×	body	1280	valid
20.0ms	40×	body	640	valid
7.0ms	22×	body	320	valid
1.0ms	5×	body	160	valid

simplify290.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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: 34.3b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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)))
25.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series83.0ms

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)))
65.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify87.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	199	428
1	523	391
2	1179	387
3	2665	387
4	5002	387

prune106.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Merged error: 20.2b

Counts

69 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (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)
1.8b	(* (atan2 x.im x.re) y.im)
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(exp (- (* (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)
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (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)))

simplify63.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	299	556
1	864	496
2	2274	481
3	5002	479

prune114.0ms

Filtered

81 candidates to 60 candidates (25.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	78	7	85

Merged error: 4.4b

Counts

85 → 7

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (* -1 x.re)) y.re)
1.8b	(* (atan2 x.im x.re) y.im)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`exp-prod` `pow-prod-down`
2×	`exp-sum` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `exp-diff` `diff-log`

Counts

3 → 53

Calls

3 calls:

5.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (* -1 x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series38.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
10.0ms	(* (log (* -1 x.re)) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

simplify64.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	224	328
1	723	286
2	3027	278
3	5002	278

prune102.0ms

Filtered

62 candidates to 41 candidates (33.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	62	7	69

Merged error: 4.4b

Counts

69 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
6.0b	(cbrt (atan2 x.im x.re))
6.0b	(cbrt (atan2 x.im x.re))
6.0b	(cbrt (atan2 x.im x.re))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(cbrt (atan2 x.im x.re))

series49.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
13.0ms	(cbrt (atan2 x.im x.re))
10.0ms	(cbrt (atan2 x.im x.re))
11.0ms	(cbrt (atan2 x.im x.re))

simplify83.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	84	426
1	350	374
2	2569	342
3	5002	335

prune102.0ms

Filtered

85 candidates to 56 candidates (34.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	85	7	92

Merged error: 4.4b

Counts

92 → 7

regimes464.0ms

Accuracy

56.3% (6.8b remaining)

Error of 9.6b against oracle of 2.8b and baseline of 18.3b

bsearch283.0ms

Steps

Iters	Range		Point
8	3.065218416585725e-49	2.85474721885261e-46	2.7537773299991192e-46
8	-3.98517332061362e-215	-1.1131410174225641e-218	-5.360679538500438e-216
8	-1.7162390217926309e-121	-2.569617010254377e-125	-3.363631805911557e-124
5	-7.709446683712433e-75	-2.2305918671351703e-75	-4.713360258067728e-75

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	64
1	66	64
2	66	64

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1792×	body	1280	valid
897.0ms	8030×	body	80	valid
628.0ms	1290×	body	640	valid
192.0ms	559×	body	320	valid
61.0ms	267×	body	160	valid

Details

sample340.0ms

simplify290.0ms

prune15.0ms

localize26.0ms

rewrite39.0ms

series83.0ms

simplify87.0ms

prune106.0ms

localize16.0ms

rewrite20.0ms

series73.0ms

simplify63.0ms

prune114.0ms

localize15.0ms

rewrite14.0ms

series38.0ms

simplify64.0ms

prune102.0ms

localize16.0ms

rewrite11.0ms

series49.0ms

simplify83.0ms

prune102.0ms

regimes464.0ms

bsearch283.0ms

simplify3.0ms

end0.0ms

sample3.6s

Profiling