Details

analyze43.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

sample22.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true
0.0ms	4×	pre	80	false

simplify68.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5165	11

prune7.0ms (0.3%)

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: 12.6b

Counts

2 → 1

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
12.2b	(/ (- (* a a) (* b b)) (* a a))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`sqrt-prod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 51

Calls

3 calls:

7.0ms	(/ (- (* a a) (* b b)) (* a a))
4.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

series26.0ms (1%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
9.0ms	(/ (- (* a a) (* b b)) (* a a))
6.0ms	(- (* a a) (* b b))

simplify74.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4948	663
1	4948	663

prune106.0ms (4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	2	61

Merged error: 0.0b

Counts

61 → 2

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (/ (+ a b) (/ a (/ (- a b) a)))))
0.0b	(/ (+ a b) (/ a (/ (- a b) a)))
0.0b	(/ a (/ (- a b) a))
0.0b	(/ (- a b) a)

rewrite79.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

890×	`times-frac`
617×	`*-un-lft-identity`
492×	`add-sqr-sqrt`
369×	`add-cube-cbrt`
84×	`associate-/r*`
63×	`distribute-lft-out`
61×	`distribute-lft-out--` `difference-of-squares`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/l*`
10×	`cbrt-undiv` `div-exp`
7×	`associate-/r/`
5×	`pow1`
4×	`associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `sqrt-prod`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `flip--` `flip-+`

Counts

4 → 478

Calls

4 calls:

21.0ms	(/ (+ a b) (/ a (/ (- a b) a)))
8.0ms	(/ a (/ (- a b) a))
8.0ms	(/ (- a b) a)
1.0ms	(sqrt (fabs (/ (+ a b) (/ a (/ (- a b) a)))))

series29.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (+ a b) (/ a (/ (- a b) a)))
9.0ms	(sqrt (fabs (/ (+ a b) (/ a (/ (- a b) a)))))
6.0ms	(/ a (/ (- a b) a))
5.0ms	(/ (- a b) a)

simplify108.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

490 → 490

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5010	9101

prune625.0ms (23.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	489	3	492

Merged error: 0b

Counts

492 → 3

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(- 1 (* (/ b a) (/ b a)))
0.0b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity`
32×	`add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`difference-of-squares`
1×	`pow2` `frac-times` `sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow-plus` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

3 → 93

Calls

3 calls:

10.0ms	(* (/ b a) (/ b a))
3.0ms	(- 1 (* (/ b a) (/ b a)))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series20.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
6.0ms	(- 1 (* (/ b a) (/ b a)))
5.0ms	(* (/ b a) (/ b a))

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5046	860

prune184.0ms (7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	102	3	105

Merged error: 0b

Counts

105 → 3

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ a (- a (/ (* b b) a)))
0.0b	(sqrt (fabs (/ 1 (/ a (- a (/ (* b b) a))))))
0.0b	(/ 1 (/ a (- a (/ (* b b) a))))
15.5b	(/ (* b b) a)

rewrite33.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`times-frac`
148×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
83×	`add-cube-cbrt`
33×	`associate-/r*`
32×	`difference-of-squares`
22×	`add-exp-log`
16×	`add-cbrt-cube` `distribute-lft-out--`
11×	`associate-/r/`
10×	`div-exp`
7×	`div-inv` `associate-/l*`
6×	`pow1` `cbrt-undiv`
5×	`flip3--` `flip--`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `sqrt-prod`
2×	`rec-exp` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `inv-pow`

Counts

4 → 195

Calls

4 calls:

11.0ms	(/ 1 (/ a (- a (/ (* b b) a))))
7.0ms	(/ a (- a (/ (* b b) a)))
5.0ms	(/ (* b b) a)
1.0ms	(sqrt (fabs (/ 1 (/ a (- a (/ (* b b) a))))))

series29.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1 (/ a (- a (/ (* b b) a))))
8.0ms	(sqrt (fabs (/ 1 (/ a (- a (/ (* b b) a))))))
8.0ms	(/ a (- a (/ (* b b) a)))
4.0ms	(/ (* b b) a)

simplify65.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4961	3099
1	4961	3099

prune304.0ms (11.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	207	3	210

Merged error: 0b

Counts

210 → 3

regimes107.0ms (4.1%)

Accuracy

Total 0.0b remaining (59.1%)

Threshold costs 0.0b (59.1%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	11
1	33	11

end0.0ms (0%)

sample578.0ms (22.1%)

Algorithm

1×

intervals

Results

278.0ms	8000×	body	80	valid
152.0ms	8000×	pre	80	true
2.0ms	126×	pre	80	false

Details

analyze43.0ms (1.6%)

sample22.0ms (0.8%)

simplify68.0ms (2.6%)

prune7.0ms (0.3%)

localize8.0ms (0.3%)

rewrite14.0ms (0.5%)

series26.0ms (1%)

simplify74.0ms (2.8%)

prune106.0ms (4%)

localize9.0ms (0.3%)

rewrite79.0ms (3%)

series29.0ms (1.1%)

simplify108.0ms (4.1%)

prune625.0ms (23.8%)

localize7.0ms (0.3%)

rewrite18.0ms (0.7%)

series20.0ms (0.8%)

simplify47.0ms (1.8%)

prune184.0ms (7%)

localize9.0ms (0.3%)

rewrite33.0ms (1.3%)

series29.0ms (1.1%)

simplify65.0ms (2.5%)

prune304.0ms (11.6%)

regimes107.0ms (4.1%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample578.0ms (22.1%)

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