Details

analyze547.0ms (15.7%)

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
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

sample43.0ms (1.2%)

Algorithm

1×

intervals

Results

9.0ms	189×	body	80	valid
6.0ms	25×	body	1280	valid
5.0ms	27×	body	640	valid
4.0ms	20×	body	1280	nan
3.0ms	4×	body	160	valid
3.0ms	18×	body	640	nan
2.0ms	18×	body	320	nan
1.0ms	11×	body	320	valid
0.0ms	7×	body	160	nan
0.0ms	12×	body	80	nan

simplify112.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5039	12

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 16.9b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
1.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.5b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite55.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 106

Calls

4 calls:

19.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
13.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
7.0ms	(/ (- x y) (- 1.0 y))

series42.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
12.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
9.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
6.0ms	(/ (- x y) (- 1.0 y))

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5428	1660

prune240.0ms (6.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	3	119

Merged error: 0.1b

Counts

119 → 3

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (+ 1.0 (/ (- y x) (- 1.0 y)))))
0.0b	(/ (- y x) (- 1.0 y))
0.2b	(/ (exp 1.0) (+ 1.0 (/ (- y x) (- 1.0 y))))
1.1b	(+ 1.0 (/ (- y x) (- 1.0 y)))

rewrite56.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
49×	`times-frac`
33×	`add-cube-cbrt`
18×	`log-prod`
12×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `associate-/r*`
8×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1`
3×	`flip3-+` `div-exp` `flip-+` `div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `flip--` `associate-/l/`
1×	`+-commutative` `associate-+r-` `log-div` `sum-log` `log-pow`

Counts

4 → 127

Calls

4 calls:

16.0ms	(log (/ (exp 1.0) (+ 1.0 (/ (- y x) (- 1.0 y)))))
15.0ms	(/ (exp 1.0) (+ 1.0 (/ (- y x) (- 1.0 y))))
13.0ms	(+ 1.0 (/ (- y x) (- 1.0 y)))
8.0ms	(/ (- y x) (- 1.0 y))

series40.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(log (/ (exp 1.0) (+ 1.0 (/ (- y x) (- 1.0 y)))))
12.0ms	(/ (exp 1.0) (+ 1.0 (/ (- y x) (- 1.0 y))))
7.0ms	(+ 1.0 (/ (- y x) (- 1.0 y)))
5.0ms	(/ (- y x) (- 1.0 y))

simplify50.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5611	2124

prune276.0ms (7.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	139	3	142

Merged error: 0b

Counts

142 → 3

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(log (* 1.0 (* (exp 1.0) (- (+ x 1) y))))
0.2b	(* (exp 1.0) (- (+ x 1) y))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1`
9×	`*-un-lft-identity`
8×	`add-exp-log` `add-sqr-sqrt`
6×	`associate-r/` `associate-r*`
4×	`add-cube-cbrt` `pow-prod-down` `prod-exp` `add-cbrt-cube`
3×	`rem-log-exp` `associate-l` `log-pow`
2×	`distribute-rgt-in` `sub-neg` `log-div` `flip3--` `distribute-lft-in` `associate--l+` `flip--` `distribute-lft-out--` `add-log-exp`
1×	`log-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `difference-of-squares` `unswap-sqr`

Counts

2 → 43

Calls

2 calls:

10.0ms	(log (* 1.0 (* (exp 1.0) (- (+ x 1) y))))
10.0ms	(* (exp 1.0) (- (+ x 1) y))

series20.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(log (* 1.0 (* (exp 1.0) (- (+ x 1) y))))
5.0ms	(* (exp 1.0) (- (+ x 1) y))

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4967	503
1	4967	503

prune89.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	49	3	52

Merged error: 0b

Counts

52 → 3

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x y) -1)
0.1b	(* (/ 1.0 y) (+ (/ x y) -1))
2.3b	(+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))
2.9b	(log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1))))

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt` `associate-l`
12×	`times-frac`
10×	`add-exp-log` `frac-add`
9×	`flip3-+` `add-cbrt-cube` `flip-+`
8×	`add-log-exp`
7×	`pow1` `log-div`
6×	`frac-times` `associate-r/` `associate-r*`
4×	`difference-of-sqr--1`
3×	`log-prod` `associate-*l/`
2×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `rem-log-exp` `pow-prod-down` `log-pow` `*-commutative` `div-inv`

Counts

4 → 92

Calls

4 calls:

14.0ms	(* (/ 1.0 y) (+ (/ x y) -1))
8.0ms	(+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))
7.0ms	(log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1))))
6.0ms	(+ (/ x y) -1)

series29.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1))))
8.0ms	(+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))
6.0ms	(* (/ 1.0 y) (+ (/ x y) -1))
3.0ms	(+ (/ x y) -1)

simplify62.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4978	1539
1	4978	1539

prune166.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	104	3	107

Merged error: 0b

Counts

107 → 3

regimes92.0ms (2.6%)

Accuracy

Total 0.1b remaining (87.6%)

Threshold costs 0.1b (87.6%)

bsearch121.0ms (3.5%)

Steps

Iters	Range		Point
11	0.0002891255061297509	2.700062056251984e+32	720987198.4659485
8	-1.203634389960884e+18	-81408879237946.69	-83317507269799.2

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	38
1	56	38

end0.0ms (0%)

sample1.2s (35.8%)

Algorithm

1×

intervals

Results

290.0ms	5668×	body	80	valid
203.0ms	825×	body	1280	valid
142.0ms	795×	body	640	valid
137.0ms	715×	body	1280	nan
104.0ms	709×	body	640	nan
60.0ms	451×	body	320	valid
48.0ms	425×	body	320	nan
23.0ms	261×	body	160	valid
19.0ms	262×	body	160	nan
13.0ms	358×	body	80	nan

Details

analyze547.0ms (15.7%)

sample43.0ms (1.2%)

simplify112.0ms (3.2%)

prune6.0ms (0.2%)

localize9.0ms (0.2%)

rewrite55.0ms (1.6%)

series42.0ms (1.2%)

simplify43.0ms (1.2%)

prune240.0ms (6.9%)

localize11.0ms (0.3%)

rewrite56.0ms (1.6%)

series40.0ms (1.1%)

simplify50.0ms (1.4%)

prune276.0ms (7.9%)

localize9.0ms (0.3%)

rewrite21.0ms (0.6%)

series20.0ms (0.6%)

simplify43.0ms (1.2%)

prune89.0ms (2.5%)

localize10.0ms (0.3%)

rewrite38.0ms (1.1%)

series29.0ms (0.8%)

simplify62.0ms (1.8%)

prune166.0ms (4.8%)

regimes92.0ms (2.6%)

bsearch121.0ms (3.5%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.2s (35.8%)

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