Details

analyze452.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample40.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
3.0ms	35×	body	80	nan

simplify166.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4829	28
1	4829	28

prune5.0ms

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: 32.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

9.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (atan2 im re) (log base))
7.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (atan2 im re) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4942	1828
1	4942	1828

prune231.0ms

Filtered

80 candidates to 120 candidates (-50.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	109	11	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 0.1b

Counts

121 → 11

localize6.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (log base))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

3.0ms

(/ (atan2 im re) (log base))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(/ (atan2 im re) (log base))

simplify56.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4938	330
1	4938	330

prune87.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	25	9	34
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	30	15	45

Merged error: 0.0b

Counts

45 → 15

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 74

Calls

2 calls:

3.0ms	(/ 1 (log base))
8.0ms	(* (atan2 im re) (/ 1 (log base)))

series27.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(/ 1 (log base))
10.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify57.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5190	556

prune105.0ms

Filtered

37 candidates to 80 candidates (-116.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	81	14	95

Merged error: 0.0b

Counts

95 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (pow (log base) 3))
0.3b	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
0.6b	(cbrt (/ 1 (pow (log base) 3)))
0.7b	(pow (log base) 3)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
106×	`add-sqr-sqrt`
101×	`cbrt-prod`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
49×	`associate-r`
46×	`unpow-prod-down` `cube-prod`
29×	`pow1`
22×	`log-pow`
16×	`add-exp-log`
14×	`associate-/r*`
13×	`sqr-pow`
11×	`cube-mult` `unpow3`
10×	`unswap-sqr`
8×	`add-cbrt-cube`
6×	`div-exp`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`rec-exp` `pow-unpow` `1-exp` `associate-l` `div-inv` `associate-/l*`
2×	`cbrt-div`
1×	`cbrt-undiv` `pow-flip` `pow-pow` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `inv-pow` `rem-cube-cbrt`

Counts

4 → 235

Calls

4 calls:

6.0ms	(/ 1 (pow (log base) 3))
15.0ms	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
5.0ms	(cbrt (/ 1 (pow (log base) 3)))
2.0ms	(pow (log base) 3)

series73.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1 (pow (log base) 3))
11.0ms	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
16.0ms	(cbrt (/ 1 (pow (log base) 3)))
21.0ms	(pow (log base) 3)

simplify68.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4975	2477
1	4975	2477

prune214.0ms

Filtered

106 candidates to 247 candidates (-133.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	247	14	261

Merged error: 0.0b

Counts

261 → 14

regimes386.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

end0.0ms

sample1.1s

Algorithm

intervals

Results

791.0ms	8000×	body	80	valid
91.0ms	1005×	body	80	nan

Details

analyze452.0ms

sample40.0ms

simplify166.0ms

prune5.0ms

localize19.0ms

rewrite28.0ms

series40.0ms

simplify45.0ms

prune231.0ms

localize6.0ms

rewrite4.0ms

series11.0ms

simplify56.0ms

prune87.0ms

localize7.0ms

rewrite15.0ms

series27.0ms

simplify57.0ms

prune105.0ms

localize11.0ms

rewrite40.0ms

series73.0ms

simplify68.0ms

prune214.0ms

regimes386.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling