Details

analyze543.0ms (19.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample23.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	17×	body	80	invalid

simplify198.0ms (7.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (196.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	15

prune10.0ms (0.4%)

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: 24.2b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.4b	(- (* b c) (* a d))
23.8b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

8.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
3.0ms	(- (* b c) (* a d))

series37.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
10.0ms	(- (* b c) (* a d))

simplify50.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5676	845

prune98.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 23.5b

Counts

50 → 7

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(- (* b c) (* a d))
14.6b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
27.9b	(sqrt (+ (* c c) (* d d)))
27.9b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

9.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(- (* b c) (* a d))

series58.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
10.0ms	(- (* b c) (* a d))
8.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify49.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5760	1553

prune143.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 21.2b

Counts

104 → 9

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(- (* b c) (* a d))
14.8b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
27.9b	(sqrt (+ (* c c) (* d d)))
27.9b	(sqrt (+ (* c c) (* d d)))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

15.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(- (* b c) (* a d))

series58.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
10.0ms	(- (* b c) (* a d))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify46.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5135	1499

prune151.0ms (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Merged error: 21.2b

Counts

115 → 9

localize17.0ms (0.6%)

Local error

Found 4 expressions with local error:

14.6b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
27.9b	(sqrt (+ (* c c) (* d d)))
27.9b	(sqrt (+ (* c c) (* d d)))
27.9b	(sqrt (+ (* c c) (* d d)))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

9.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series52.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify48.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5388	1572

prune118.0ms (4.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	100	10	110

Merged error: 21.2b

Counts

110 → 10

regimes321.0ms (11.6%)

Accuracy

Total 2.7b remaining (10.4%)

Threshold costs 0b (0%)

bsearch20.0ms (0.7%)

Steps

Iters	Range		Point
9	2.9969177490975104e+118	9.486301160583267e+124	5.1795073910038136e+123

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	42
1	56	42

end0.0ms (0%)

sample599.0ms (21.7%)

Algorithm

1×

intervals

Results

362.0ms	8000×	body	80	valid
21.0ms	471×	body	80	invalid

Details

analyze543.0ms (19.7%)

sample23.0ms (0.8%)

simplify198.0ms (7.2%)

prune10.0ms (0.4%)

localize10.0ms (0.3%)

rewrite12.0ms (0.4%)

series37.0ms (1.4%)

simplify50.0ms (1.8%)

prune98.0ms (3.5%)

localize12.0ms (0.4%)

rewrite22.0ms (0.8%)

series58.0ms (2.1%)

simplify49.0ms (1.8%)

prune143.0ms (5.2%)

localize13.0ms (0.5%)

rewrite29.0ms (1%)

series58.0ms (2.1%)

simplify46.0ms (1.7%)

prune151.0ms (5.5%)

localize17.0ms (0.6%)

rewrite23.0ms (0.8%)

series52.0ms (1.9%)

simplify48.0ms (1.7%)

prune118.0ms (4.3%)

regimes321.0ms (11.6%)

bsearch20.0ms (0.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample599.0ms (21.7%)

Profiling