Details

analyze443.0ms (10.6%)

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

sample38.0ms (0.9%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	80	valid
2.0ms	25×	body	80	nan

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

prune9.0ms (0.2%)

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: 31.9b

Counts

2 → 1

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series67.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5011	2020

prune322.0ms (7.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	104	18	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	18	123

Merged error: 8.2b

Counts

123 → 18

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
0.5b	(* (log base) (log base))
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`log-prod`
11×	`log-pow`
10×	`associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(pow (log base) 2)

series57.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(pow (log base) 2)
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4953	926
1	4953	926

prune337.0ms (8%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	110	18	128

Merged error: 8.2b

Counts

128 → 18

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (cbrt base)))
0.5b	(cbrt base)
0.5b	(cbrt base)
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod` `log-prod`
9×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
5×	`associate-r`
4×	`associate-l` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `log-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

7.0ms	(* (log base) (log (cbrt base)))
4.0ms	(sqrt (+ (* re re) (* im im)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series99.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (log base) (log (cbrt base)))
22.0ms	(cbrt base)
21.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5104	594

prune208.0ms (5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	4	12	16
Picked	1	0	1
Done	0	1	1
Total	83	17	100

Merged error: 8.2b

Counts

100 → 17

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
0.7b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `sqrt-div` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow1/3` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `flip-+` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

5.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))

series93.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
21.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
16.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4962	983
1	4962	983

prune193.0ms (4.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	98	21	119

Merged error: 8.2b

Counts

119 → 21

regimes692.0ms (16.5%)

Accuracy

Total 10.8b remaining (61.4%)

Threshold costs 0b (0%)

bsearch163.0ms (3.9%)

Steps

Iters	Range		Point
7	15004680.116774563	812719246.368939	800712819.842004
8	-1.3642355686218201e-260	-2.136588986775749e-264	-2.1434906871881392e-263
8	-7.266638217871674e-189	-4.1060637446278703e-193	-7.823143127285978e-193
10	-3.0758993662576154e+128	-6.421666187812336e+117	-1.5736914859440464e+121

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	117
1	64	117

end0.0ms (0%)

sample1.1s (25.5%)

Algorithm

1×

intervals

Results

770.0ms	8000×	body	80	valid
96.0ms	1063×	body	80	nan

Details

analyze443.0ms (10.6%)

sample38.0ms (0.9%)

simplify3.0ms (0.1%)

prune9.0ms (0.2%)

localize22.0ms (0.5%)

rewrite26.0ms (0.6%)

series67.0ms (1.6%)

simplify72.0ms (1.7%)

prune322.0ms (7.7%)

localize28.0ms (0.7%)

rewrite19.0ms (0.4%)

series57.0ms (1.4%)

simplify44.0ms (1%)

prune337.0ms (8%)

localize25.0ms (0.6%)

rewrite15.0ms (0.4%)

series99.0ms (2.4%)

simplify56.0ms (1.3%)

prune208.0ms (5%)

localize25.0ms (0.6%)

rewrite17.0ms (0.4%)

series93.0ms (2.2%)

simplify47.0ms (1.1%)

prune193.0ms (4.6%)

regimes692.0ms (16.5%)

bsearch163.0ms (3.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (25.5%)

Profiling