Details

analyze50.0ms (2.4%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

sample22.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan
0.0ms	3×	body	80	invalid

simplify151.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	4819	14
1	4819	14

prune9.0ms (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: 0.3b

Counts

2 → 2

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+ y (- (/ 1.0 (* x 9.0)) 1.0))
0.3b	(* (sqrt x) (+ y (- (/ 1.0 (* x 9.0)) 1.0)))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (* (sqrt x) (+ y (- (/ 1.0 (* x 9.0)) 1.0))))

rewrite38.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-l` `add-log-exp`
6×	`associate-r/` `associate-r*`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
4×	`pow-prod-down` `sqrt-prod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `sum-log` `*-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 89

Calls

4 calls:

12.0ms	(* 3.0 (* (sqrt x) (+ y (- (/ 1.0 (* x 9.0)) 1.0))))
12.0ms	(* (sqrt x) (+ y (- (/ 1.0 (* x 9.0)) 1.0)))
8.0ms	(+ y (- (/ 1.0 (* x 9.0)) 1.0))
4.0ms	(/ 1.0 (* x 9.0))

series29.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (sqrt x) (+ y (- (/ 1.0 (* x 9.0)) 1.0)))
12.0ms	(* 3.0 (* (sqrt x) (+ y (- (/ 1.0 (* x 9.0)) 1.0))))
4.0ms	(+ y (- (/ 1.0 (* x 9.0)) 1.0))
2.0ms	(/ 1.0 (* x 9.0))

simplify27.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5778	1241

prune202.0ms (9.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	89	12	101
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	90	13	103

Merged error: 0.0b

Counts

103 → 13

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt x) (- (/ 1.0 (* x 9.0)) 1.0))
0.2b	(* (sqrt x) y)
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (+ (* (sqrt x) y) (* (sqrt x) (- (/ 1.0 (* x 9.0)) 1.0))))

rewrite27.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

10.0ms	(* (sqrt x) (- (/ 1.0 (* x 9.0)) 1.0))
7.0ms	(* 3.0 (+ (* (sqrt x) y) (* (sqrt x) (- (/ 1.0 (* x 9.0)) 1.0))))
4.0ms	(* (sqrt x) y)
4.0ms	(/ 1.0 (* x 9.0))

series32.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(* 3.0 (+ (* (sqrt x) y) (* (sqrt x) (- (/ 1.0 (* x 9.0)) 1.0))))
8.0ms	(* (sqrt x) y)
6.0ms	(* (sqrt x) (- (/ 1.0 (* x 9.0)) 1.0))
2.0ms	(/ 1.0 (* x 9.0))

simplify42.0ms (2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4995	1191
1	4995	1191

prune199.0ms (9.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	106	13	119

Merged error: 0.0b

Counts

119 → 13

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(* 3.0 (sqrt x))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(/ 1.0 (* x 9.0))

rewrite28.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

13.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
5.0ms	(+ y (/ 1.0 (* x 9.0)))
4.0ms	(* 3.0 (sqrt x))
4.0ms	(/ 1.0 (* x 9.0))

series21.0ms (1%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(+ y (/ 1.0 (* x 9.0)))
4.0ms	(* 3.0 (sqrt x))
2.0ms	(/ 1.0 (* x 9.0))

simplify25.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5384	938

prune180.0ms (8.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	95	12	107

Merged error: 0b

Counts

107 → 12

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ (/ 1.0 x) 9.0))
0.2b	(* 3.0 (sqrt x))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
0.3b	(/ (/ 1.0 x) 9.0)

rewrite44.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac`
57×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`associate-r`
11×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
4×	`associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
3×	`cbrt-undiv` `div-exp` `associate-/r*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r/` `associate--l+` `-commutative` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip--` `flip-+` `associate-/l/` `difference-of-squares`

Counts

4 → 131

Calls

4 calls:

18.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
11.0ms	(+ y (/ (/ 1.0 x) 9.0))
6.0ms	(/ (/ 1.0 x) 9.0)
4.0ms	(* 3.0 (sqrt x))

series23.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
4.0ms	(+ y (/ (/ 1.0 x) 9.0))
4.0ms	(* 3.0 (sqrt x))
2.0ms	(/ (/ 1.0 x) 9.0)

simplify32.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5548	1567

prune231.0ms (11.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	144	11	155

Merged error: 0b

Counts

155 → 11

regimes132.0ms (6.4%)

Accuracy

Total 0.4b remaining (93.8%)

Threshold costs 0.4b (93.8%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms (0%)

sample492.0ms (23.7%)

Algorithm

1×

intervals

Results

352.0ms	8000×	body	80	valid
6.0ms	141×	body	80	nan
3.0ms	74×	body	80	invalid

Details

analyze50.0ms (2.4%)

sample22.0ms (1.1%)

simplify151.0ms (7.3%)

prune9.0ms (0.4%)

localize10.0ms (0.5%)

rewrite38.0ms (1.8%)

series29.0ms (1.4%)

simplify27.0ms (1.3%)

prune202.0ms (9.8%)

localize11.0ms (0.5%)

rewrite27.0ms (1.3%)

series32.0ms (1.5%)

simplify42.0ms (2%)

prune199.0ms (9.6%)

localize9.0ms (0.4%)

rewrite28.0ms (1.4%)

series21.0ms (1%)

simplify25.0ms (1.2%)

prune180.0ms (8.7%)

localize9.0ms (0.4%)

rewrite44.0ms (2.1%)

series23.0ms (1.1%)

simplify32.0ms (1.5%)

prune231.0ms (11.1%)

regimes132.0ms (6.4%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample492.0ms (23.7%)

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