Details

analyze440.0ms (13.5%)

Algorithm

1×

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

sample42.0ms (1.3%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	80	valid
3.0ms	34×	body	80	nan

simplify195.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (193.0ms)

Iter	Nodes	Cost
0	4829	28
1	4829	28

prune9.0ms (0.3%)

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: 33.1b

Counts

2 → 1

localize19.0ms (0.6%)

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))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms (0.7%)

Algorithm

1×	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	(* (log base) (log base))
4.0ms	(* (atan2 im re) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series42.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (log base) (log base))
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))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4942	1828
1	4942	1828

prune280.0ms (8.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 0.1b

Counts

121 → 12

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite4.0ms (0.1%)

Algorithm

1×	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))

series10.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify60.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4938	330
1	4938	330

prune105.0ms (3.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	27	7	34
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	30	16	46

Merged error: 0b

Counts

46 → 16

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite12.0ms (0.4%)

Algorithm

1×	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:

7.0ms	(* (atan2 im re) (/ 1 (log base)))
3.0ms	(/ 1 (log base))

series29.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(/ 1 (log base))
10.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify58.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5190	556

prune148.0ms (4.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	80	16	96

Merged error: 0b

Counts

96 → 16

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(/ (log base) (atan2 im re))
0.4b	(/ 1 (/ (log base) (atan2 im re)))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `associate-/r*`
16×	`log-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 119

Calls

2 calls:

6.0ms	(/ 1 (/ (log base) (atan2 im re)))
3.0ms	(/ (log base) (atan2 im re))

series26.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

13.0ms	(/ (log base) (atan2 im re))
12.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify59.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5227	1473

prune133.0ms (4.1%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	2	11	13
Picked	0	1	1
Done	0	2	2
Total	126	15	141

Merged error: 0b

Counts

141 → 15

regimes401.0ms (12.3%)

Accuracy

Total 0.3b remaining (86.9%)

Threshold costs 0.3b (86.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

end0.0ms (0%)

sample1.1s (33.5%)

Algorithm

1×

intervals

Results

787.0ms	8000×	body	80	valid
98.0ms	1068×	body	80	nan

Details

analyze440.0ms (13.5%)

sample42.0ms (1.3%)

simplify195.0ms (6%)

prune9.0ms (0.3%)

localize19.0ms (0.6%)

rewrite24.0ms (0.7%)

series42.0ms (1.3%)

simplify39.0ms (1.2%)

prune280.0ms (8.6%)

localize6.0ms (0.2%)

rewrite4.0ms (0.1%)

series10.0ms (0.3%)

simplify60.0ms (1.9%)

prune105.0ms (3.2%)

localize8.0ms (0.2%)

rewrite12.0ms (0.4%)

series29.0ms (0.9%)

simplify58.0ms (1.8%)

prune148.0ms (4.5%)

localize8.0ms (0.2%)

rewrite14.0ms (0.4%)

series26.0ms (0.8%)

simplify59.0ms (1.8%)

prune133.0ms (4.1%)

regimes401.0ms (12.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.1s (33.5%)

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