Details

analyze79.0ms (3.1%)

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

sample19.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	201×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	4×	body	1280	valid

simplify255.0ms (10%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (250.0ms)

Iter	Nodes	Cost
0	5206	11

prune8.0ms (0.3%)

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: 12.6b

Counts

2 → 2

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/ (- x 1.0) (+ 1.0 y))
0.1b	(* y (/ (- x 1.0) (+ 1.0 y)))
4.5b	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite27.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 102

Calls

3 calls:

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

series21.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))
5.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
5.0ms	(/ (- x 1.0) (+ 1.0 y))

simplify62.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	6163	1269

prune230.0ms (9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	12	111
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 7.2b

Counts

113 → 13

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
0.5b	(cbrt y)
9.8b	(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 44

Calls

4 calls:

4.0ms	(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series82.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt y)
22.0ms	(cbrt y)
22.0ms	(cbrt y)
15.0ms	(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify57.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4943	365
1	4943	365

prune110.0ms (4.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	56	13	69

Merged error: 7.2b

Counts

69 → 13

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.5b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.5b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
8.3b	(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity`
78×	`cbrt-prod`
60×	`times-frac`
58×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 116

Calls

4 calls:

7.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
7.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
7.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
4.0ms	(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

series62.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
16.0ms	(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))
14.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))

simplify75.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4947	2010
1	4947	2010

prune425.0ms (16.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	128	13	141

Merged error: 7.2b

Counts

141 → 13

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.8b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite26.0ms (1%)

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:

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

series23.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(- 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 (1.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5369	732

prune108.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	11	0	11
Picked	0	1	1
Done	0	1	1
Total	81	3	84

Merged error: 0.2b

Counts

84 → 3

regimes212.0ms (8.3%)

Accuracy

Total 0.0b remaining (20.7%)

Threshold costs 0.0b (20.7%)

bsearch24.0ms (1%)

Steps

Iters	Range		Point
9	45.443605402652814	2584089009.7401896	29063706.880189914
6	-4687726544009.001	-1071378915657.1898	-1080471527719.7518

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	331	31
1	331	31

end0.0ms (0%)

sample533.0ms (20.8%)

Algorithm

1×

intervals

Results

191.0ms	6110×	body	80	valid
93.0ms	747×	body	640	valid
49.0ms	340×	body	1280	valid
44.0ms	510×	body	320	valid
17.0ms	293×	body	160	valid

Details

analyze79.0ms (3.1%)

sample19.0ms (0.7%)

simplify255.0ms (10%)

prune8.0ms (0.3%)

localize7.0ms (0.3%)

rewrite27.0ms (1.1%)

series21.0ms (0.8%)

simplify62.0ms (2.4%)

prune230.0ms (9%)

localize11.0ms (0.4%)

rewrite8.0ms (0.3%)

series82.0ms (3.2%)

simplify57.0ms (2.2%)

prune110.0ms (4.3%)

localize12.0ms (0.4%)

rewrite29.0ms (1.1%)

series62.0ms (2.4%)

simplify75.0ms (2.9%)

prune425.0ms (16.6%)

localize7.0ms (0.3%)

rewrite26.0ms (1%)

series23.0ms (0.9%)

simplify42.0ms (1.6%)

prune108.0ms (4.2%)

regimes212.0ms (8.3%)

bsearch24.0ms (1%)

simplify9.0ms (0.3%)

end0.0ms (0%)

sample533.0ms (20.8%)

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