Details

analyze432.0ms (10.2%)

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

sample40.0ms (0.9%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	80	valid
3.0ms	34×	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

prune8.0ms (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: 33.4b

Counts

2 → 1

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
31.0b	(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)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series66.0ms (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))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5011	2020

prune299.0ms (7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 7.9b

Counts

123 → 15

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
0.5b	(pow (log base) 2)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-r`
16×	`add-exp-log`
14×	`pow1`
11×	`times-frac` `add-cbrt-cube`
9×	`associate-l`
6×	`log-prod`
5×	`prod-exp` `log-pow`
4×	`unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

13.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(pow (log base) 2)

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)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4960	2097
1	4960	2097

prune280.0ms (6.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	115	16	131

Merged error: 7.8b

Counts

131 → 16

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4))) (- (pow (log base) 2) (* 0.0 0.0)))
0.5b	(pow (log base) 2)
0.9b	(pow (log base) 4)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
51×	`associate-l`
46×	`times-frac`
44×	`*-un-lft-identity`
39×	`unpow-prod-down`
31×	`difference-of-squares`
29×	`add-cube-cbrt`
21×	`sqr-pow`
14×	`pow1`
11×	`add-exp-log`
9×	`add-cbrt-cube` `distribute-lft-out--`
7×	`associate-r`
6×	`pow-unpow`
5×	`log-pow`
4×	`add-log-exp`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`frac-times` `pow-to-exp` `sub-neg` `pow-pow` `sqrt-div` `associate-*r/` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unpow2` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 132

Calls

4 calls:

25.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4))) (- (pow (log base) 2) (* 0.0 0.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(pow (log base) 4)
2.0ms	(pow (log base) 2)

series61.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (pow 0.0 4))) (- (pow (log base) 2) (* 0.0 0.0)))
17.0ms	(pow (log base) 4)
14.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5327	3054

prune470.0ms (11.1%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	2	12	14
Picked	0	1	1
Done	0	1	1
Total	142	18	160

Merged error: 7.8b

Counts

160 → 18

localize21.0ms (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)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`pow1` `cbrt-prod` `unpow-prod-down`
7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-div` `associate-/r/` `log-pow` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))
2.0ms	(pow (log base) 6)
2.0ms	(cbrt (pow (log base) 6))

series66.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
22.0ms	(pow (log base) 6)
14.0ms	(cbrt (pow (log base) 6))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4995	1566
1	4995	1566

prune179.0ms (4.2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	15	15
Picked	1	0	1
Done	0	2	2
Total	91	19	110

Merged error: 7.8b

Counts

110 → 19

regimes631.0ms (14.9%)

Accuracy

Total 11.2b remaining (60.3%)

Threshold costs 0b (0%)

bsearch177.0ms (4.2%)

Steps

Iters	Range		Point
10	1.7732951930628207e+43	3.2619386735714566e+53	1.702622659109618e+52
8	-1.2917131679977722e-74	-8.286737828436817e-79	-1.267660774867362e-74
9	-3.0820256303824825e-44	-6.169081402694406e-50	-6.248145331558188e-50
9	-2.16952560437672e+123	-4.0088116396452295e+117	-1.506084148724459e+120

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	111
1	87	111

end0.0ms (0%)

sample1.0s (24.8%)

Algorithm

1×

intervals

Results

748.0ms	8000×	body	80	valid
98.0ms	1068×	body	80	nan

Details

analyze432.0ms (10.2%)

sample40.0ms (0.9%)

simplify3.0ms (0.1%)

prune8.0ms (0.2%)

localize18.0ms (0.4%)

rewrite26.0ms (0.6%)

series66.0ms (1.6%)

simplify69.0ms (1.6%)

prune299.0ms (7%)

localize21.0ms (0.5%)

rewrite27.0ms (0.6%)

series67.0ms (1.6%)

simplify43.0ms (1%)

prune280.0ms (6.6%)

localize25.0ms (0.6%)

rewrite40.0ms (1%)

series61.0ms (1.4%)

simplify37.0ms (0.9%)

prune470.0ms (11.1%)

localize21.0ms (0.5%)

rewrite20.0ms (0.5%)

series66.0ms (1.5%)

simplify62.0ms (1.5%)

prune179.0ms (4.2%)

regimes631.0ms (14.9%)

bsearch177.0ms (4.2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (24.8%)

Profiling