Details

analyze77.0ms (2.7%)

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

sample20.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	186×	body	80	valid
3.0ms	24×	body	640	valid
2.0ms	15×	body	1280	valid
2.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify300.0ms (10.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (298.0ms)

Iter	Nodes	Cost
0	5206	11

prune5.0ms (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: 23.5b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.5b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.1b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1` `associate-l` `add-log-exp`
4×	`times-frac` `associate-l/` `associate-/r`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 62

Calls

3 calls:

12.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
7.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.0ms	(* (- 1.0 x) y)

series24.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

12.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
5.0ms	(* (- 1.0 x) y)

simplify42.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5369	732

prune131.0ms (4.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.3b

Counts

72 → 4

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ 1.0 y))
0.0b	(* (- 1.0 x) (/ y (+ 1.0 y)))
3.5b	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 87

Calls

3 calls:

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

series21.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

12.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))
7.0ms	(* (- 1.0 x) (/ y (+ 1.0 y)))
3.0ms	(/ y (+ 1.0 y))

simplify45.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5083	1043

prune139.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Merged error: 0.3b

Counts

100 → 4

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 x) (sqrt (+ 1.0 y)))
0.1b	(* (/ (- 1.0 x) (sqrt (+ 1.0 y))) (/ y (sqrt (+ 1.0 y))))
0.1b	(/ y (sqrt (+ 1.0 y)))
4.7b	(- 1.0 (* (/ (- 1.0 x) (sqrt (+ 1.0 y))) (/ y (sqrt (+ 1.0 y)))))

rewrite63.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`*-un-lft-identity`
132×	`add-sqr-sqrt`
124×	`times-frac`
78×	`sqrt-prod`
72×	`add-cube-cbrt`
41×	`associate-l`
27×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
18×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r*`
9×	`unswap-sqr`
8×	`sqrt-div` `associate-/r/` `associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `div-inv`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 217

Calls

4 calls:

35.0ms	(* (/ (- 1.0 x) (sqrt (+ 1.0 y))) (/ y (sqrt (+ 1.0 y))))
9.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 y)))
6.0ms	(/ y (sqrt (+ 1.0 y)))
3.0ms	(- 1.0 (* (/ (- 1.0 x) (sqrt (+ 1.0 y))) (/ y (sqrt (+ 1.0 y)))))

series35.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(- 1.0 (* (/ (- 1.0 x) (sqrt (+ 1.0 y))) (/ y (sqrt (+ 1.0 y)))))
9.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 y)))
8.0ms	(/ y (sqrt (+ 1.0 y)))
7.0ms	(* (/ (- 1.0 x) (sqrt (+ 1.0 y))) (/ y (sqrt (+ 1.0 y))))

simplify77.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4963	3359
1	4963	3359

prune547.0ms (19.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	229	4	233

Merged error: 0.3b

Counts

233 → 4

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

7.1b	(/ (* (- 1.0 x) y) (+ 1.0 y))
7.1b	(/ (* (- 1.0 x) y) (+ 1.0 y))
7.1b	(/ (* (- 1.0 x) y) (+ 1.0 y))
8.1b	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ 1.0 y)) (/ (* (- 1.0 x) y) (+ 1.0 y)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ 1.0 y))))

rewrite43.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`times-frac`
21×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/r*`
11×	`distribute-lft-out`
8×	`associate-/r/` `associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`associate-*l/`
5×	`difference-of-squares`
4×	`pow1` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`div-sub`

Counts

4 → 122

Calls

4 calls:

13.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ 1.0 y)) (/ (* (- 1.0 x) y) (+ 1.0 y)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
9.0ms	(/ (* (- 1.0 x) y) (+ 1.0 y))
9.0ms	(/ (* (- 1.0 x) y) (+ 1.0 y))
9.0ms	(/ (* (- 1.0 x) y) (+ 1.0 y))

series102.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ 1.0 y)) (/ (* (- 1.0 x) y) (+ 1.0 y)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
7.0ms	(/ (* (- 1.0 x) y) (+ 1.0 y))
7.0ms	(/ (* (- 1.0 x) y) (+ 1.0 y))
7.0ms	(/ (* (- 1.0 x) y) (+ 1.0 y))

simplify68.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4966	2310
1	4966	2310

prune294.0ms (10.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	134	4	138

Merged error: 0.3b

Counts

138 → 4

regimes183.0ms (6.4%)

Accuracy

Total 0.0b remaining (5%)

Threshold costs 0.0b (5%)

bsearch30.0ms (1%)

Steps

Iters	Range		Point
9	8198245.812992215	662569279520.1381	168484587.68162763
8	-8260501411.424482	-11912045.116125666	-121916909.90807547

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	331	31
1	331	31

end0.0ms (0%)

sample508.0ms (17.8%)

Algorithm

1×

intervals

Results

187.0ms	6130×	body	80	valid
83.0ms	727×	body	640	valid
51.0ms	361×	body	1280	valid
42.0ms	479×	body	320	valid
17.0ms	303×	body	160	valid

Details

analyze77.0ms (2.7%)

sample20.0ms (0.7%)

simplify300.0ms (10.5%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite27.0ms (0.9%)

series24.0ms (0.8%)

simplify42.0ms (1.5%)

prune131.0ms (4.6%)

localize7.0ms (0.2%)

rewrite24.0ms (0.8%)

series21.0ms (0.7%)

simplify45.0ms (1.6%)

prune139.0ms (4.9%)

localize9.0ms (0.3%)

rewrite63.0ms (2.2%)

series35.0ms (1.2%)

simplify77.0ms (2.7%)

prune547.0ms (19.2%)

localize12.0ms (0.4%)

rewrite43.0ms (1.5%)

series102.0ms (3.6%)

simplify68.0ms (2.4%)

prune294.0ms (10.3%)

regimes183.0ms (6.4%)

bsearch30.0ms (1%)

simplify8.0ms (0.3%)

end0.0ms (0%)

sample508.0ms (17.8%)

Profiling