Details

sample323.0ms

Algorithm

intervals

Results

218.0ms	259×	body	80	valid
45.0ms	63×	body	1280	valid
21.0ms	43×	body	640	valid
4.0ms	11×	body	320	valid
3.0ms	15×	body	160	valid

simplify38.0ms

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

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 32.7b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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

series94.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
74.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

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

prune125.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 19.6b

Counts

70 → 6

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)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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:

5.0ms	(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)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
26.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	299	557
1	864	497
2	2274	481
3	5002	479

prune143.0ms

Filtered

81 candidates to 60 candidates (25.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	76	11	87

Merged error: 3.8b

Counts

87 → 11

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
0.0b	(exp (* (atan2 x.im x.re) y.im))
1.2b	(* (atan2 x.im x.re) y.im)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`unpow-prod-down`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `add-log-exp`
4×	`sqr-pow`
3×	`div-exp` `associate-r` `associate-l` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

5.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
2.0ms	(exp (* (atan2 x.im x.re) y.im))
3.0ms	(* (atan2 x.im x.re) y.im)

series44.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
9.0ms	(exp (* (atan2 x.im x.re) y.im))
7.0ms	(* (atan2 x.im x.re) y.im)

simplify35.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	266	599
1	1004	563
2	5001	558

prune130.0ms

Filtered

82 candidates to 58 candidates (29.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 3.8b

Counts

93 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y.im)
0.5b	(cbrt y.im)
0.6b	(* (cbrt y.im) (cbrt y.im))
1.2b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

1.0ms	(cbrt y.im)
1.0ms	(cbrt y.im)
6.0ms	(* (cbrt y.im) (cbrt y.im))
7.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt y.im)
25.0ms	(cbrt y.im)
26.0ms	(* (cbrt y.im) (cbrt y.im))
26.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))

simplify126.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	214	461
1	737	412
2	3890	352
3	5002	333

prune95.0ms

Filtered

93 candidates to 61 candidates (34.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 3.8b

Counts

105 → 13

regimes637.0ms

Accuracy

81.8% (5.2b remaining)

Error of 8.9b against oracle of 3.7b and baseline of 32.4b

bsearch260.0ms

Steps

Iters	Range		Point
7	4.104989284195868e-12	3.525489735606849e-10	3.235096469728847e-10
8	2.3370961207514916e-213	5.506218586352494e-209	2.764877752207601e-209
11	-6.7935373210721584e-298	1.3740349501288148e-299	7.2216902337184e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	39
1	63	39
2	63	39

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	2109×	body	1280	valid
834.0ms	7977×	body	80	valid
696.0ms	1466×	body	640	valid
226.0ms	679×	body	320	valid
74.0ms	338×	body	160	valid

Details

sample323.0ms

simplify38.0ms

prune20.0ms

localize32.0ms

rewrite22.0ms

series94.0ms

simplify81.0ms

prune125.0ms

localize16.0ms

rewrite19.0ms

series80.0ms

simplify59.0ms

prune143.0ms

localize12.0ms

rewrite13.0ms

series44.0ms

simplify35.0ms

prune130.0ms

localize17.0ms

rewrite17.0ms

series100.0ms

simplify126.0ms

prune95.0ms

regimes637.0ms

bsearch260.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling