Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

sample20.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

valid

simplify229.0ms (9.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (227.0ms)

Iter	Nodes	Cost
0	1987	20
1	1987	20

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: 1.0b

Counts

2 → 1

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.2b	(* 6.0 (* v v))
1.0b	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite46.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

13.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
12.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
11.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
6.0ms	(* 6.0 (* v v))

series44.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
14.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
8.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
3.0ms	(* 6.0 (* v v))

simplify50.0ms (2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5626	2185

prune269.0ms (11%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	2	120

Merged error: 0b

Counts

120 → 2

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))
0.2b	(* (* v v) 6.0)
1.0b	(/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))
1.0b	(pow (/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))) 3)

rewrite57.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log` `add-cbrt-cube`
32×	`associate-*l/`
24×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
21×	`prod-exp` `cbrt-unprod`
19×	`pow1`
16×	`frac-times`
15×	`add-sqr-sqrt` `unpow-prod-down` `cube-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac` `pow-prod-down`
8×	`cbrt-undiv` `associate-*r/` `div-exp`
7×	`associate-l`
5×	`pow-exp` `rem-cube-cbrt`
4×	`associate-r` `add-log-exp`
3×	`pow-unpow` `sqrt-prod` `div-inv` `associate-/l*`
2×	`*-commutative`
1×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `clear-num` `associate-/r*` `unswap-sqr` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

16.0ms	(pow (/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))) 3)
14.0ms	(/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))
13.0ms	(* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))
6.0ms	(* (* v v) 6.0)

series77.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))) 3)
18.0ms	(/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))
17.0ms	(* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))
3.0ms	(* (* v v) 6.0)

simplify44.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5051	3828

prune487.0ms (19.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	152	2	154

Merged error: 0b

Counts

154 → 2

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))
0.2b	(* (* v v) 6.0)
1.0b	(/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))
1.0b	(log (exp (/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))))

rewrite46.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
24×	`associate-*l/`
19×	`pow1`
18×	`flip3--` `sqrt-div` `flip--`
16×	`associate-/r/` `log-pow`
15×	`exp-prod` `prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt`
12×	`frac-times` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-prod-down`
7×	`associate-l`
6×	`times-frac` `associate-*r/`
4×	`cbrt-undiv` `div-exp` `associate-r` `add-log-exp`
3×	`log-prod` `sqrt-prod` `associate-/l*`
2×	`*-commutative` `div-inv`
1×	`frac-2neg` `rem-log-exp` `clear-num` `associate-/r*` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

15.0ms	(/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))
12.0ms	(* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))
7.0ms	(log (exp (/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))))
6.0ms	(* (* v v) 6.0)

series57.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(log (exp (/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))))
18.0ms	(/ 4.0 (* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI))))
17.0ms	(* (sqrt (- 2.0 (* (* v v) 6.0))) (* (- 1.0 (* v v)) (* 3.0 PI)))
3.0ms	(* (* v v) 6.0)

simplify45.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5345	2723

prune342.0ms (13.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	123	2	125

Merged error: 0b

Counts

125 → 2

regimes53.0ms (2.2%)

Accuracy

Total 0.0b remaining (44.8%)

Threshold costs 0.0b (44.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	23
1	59	23

end0.0ms (0%)

sample529.0ms (21.6%)

Algorithm

1×

intervals

Results

426.0ms	8000×	body	80	valid
0.0ms	3×	body	80	nan

Details

analyze5.0ms (0.2%)

sample20.0ms (0.8%)

simplify229.0ms (9.3%)

prune6.0ms (0.2%)

localize13.0ms (0.5%)

rewrite46.0ms (1.9%)

series44.0ms (1.8%)

simplify50.0ms (2%)

prune269.0ms (11%)

localize15.0ms (0.6%)

rewrite57.0ms (2.3%)

series77.0ms (3.1%)

simplify44.0ms (1.8%)

prune487.0ms (19.9%)

localize16.0ms (0.7%)

rewrite46.0ms (1.9%)

series57.0ms (2.3%)

simplify45.0ms (1.8%)

prune342.0ms (13.9%)

regimes53.0ms (2.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample529.0ms (21.6%)

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