Details

analyze308.0ms (14.9%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.6%	0.1%	6
15.6%	84.3%	0.1%	7
29.6%	70.2%	0.1%	8
33.5%	63.2%	3.3%	9
43.3%	49.5%	7.2%	10
52.1%	39.2%	8.7%	11
54.5%	34.2%	11.3%	12
60.6%	25.6%	13.8%	13
65.2%	20.4%	14.4%	14

sample17.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
1.0ms	18×	body	80	invalid

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	345	9
1	345	9

prune6.0ms (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: 0.0b

Counts

2 → 1

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* x y) (* (- x 1.0) z))
0.0b	(* (- x 1.0) z)

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity`
5×	`associate-l`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

6.0ms	(* (- x 1.0) z)
4.0ms	(+ (* x y) (* (- x 1.0) z))

series14.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(+ (* x y) (* (- x 1.0) z))
4.0ms	(* (- x 1.0) z)

simplify41.0ms (2%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5186	345

prune69.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Merged error: 0.0b

Counts

40 → 5

localize16.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
0.0b	(+ (* x y) (/ (* z (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
4.8b	(* z (- (pow x 3) (pow 1.0 3)))
13.0b	(/ (* z (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite61.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

20.0ms	(* z (- (pow x 3) (pow 1.0 3)))
20.0ms	(/ (* z (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
11.0ms	(+ (* x y) (/ (* z (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
6.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))

series66.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* z (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
23.0ms	(+ (* x y) (/ (* z (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
13.0ms	(* z (- (pow x 3) (pow 1.0 3)))
3.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))

simplify48.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4970	1574
1	4970	1574

prune246.0ms (11.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	105	5	110

Merged error: 0.0b

Counts

110 → 5

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (- x 1.0) z))
0.0b	(* (- x 1.0) z)
0.0b	(* (- x 1.0) z)
0.2b	(* (sqrt (* (- x 1.0) z)) (sqrt (* (- x 1.0) z)))

rewrite36.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`pow1`
30×	`sqrt-pow1`
23×	`pow-prod-down`
22×	`add-sqr-sqrt`
20×	`associate-*l/`
16×	`*-un-lft-identity`
14×	`sqrt-div` `associate-l`
12×	`add-cube-cbrt`
11×	`pow1/2`
10×	`add-exp-log` `associate-r` `pow-prod-up` `add-cbrt-cube`
9×	`flip3--` `flip--`
6×	`pow-sqr`
5×	`sqrt-prod`
4×	`frac-times` `swap-sqr` `add-log-exp`
3×	`prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 114

Calls

4 calls:

14.0ms	(* (sqrt (* (- x 1.0) z)) (sqrt (* (- x 1.0) z)))
6.0ms	(* (- x 1.0) z)
6.0ms	(* (- x 1.0) z)
5.0ms	(sqrt (* (- x 1.0) z))

series24.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (* (- x 1.0) z))
4.0ms	(* (sqrt (* (- x 1.0) z)) (sqrt (* (- x 1.0) z)))
4.0ms	(* (- x 1.0) z)
4.0ms	(* (- x 1.0) z)

simplify41.0ms (2%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5392	890

prune208.0ms (10.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	126	5	131

Merged error: 0.0b

Counts

131 → 5

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* x y) (* (* (- x 1.0) (sqrt z)) (sqrt z)))
0.0b	(* (- x 1.0) (sqrt z))
0.2b	(* (* (- x 1.0) (sqrt z)) (sqrt z))

rewrite22.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`associate-r`
10×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`associate-l` `associate-*l/`
5×	`add-log-exp`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 60

Calls

3 calls:

9.0ms	(* (* (- x 1.0) (sqrt z)) (sqrt z))
7.0ms	(* (- x 1.0) (sqrt z))
4.0ms	(+ (* x y) (* (* (- x 1.0) (sqrt z)) (sqrt z)))

series23.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ (* x y) (* (* (- x 1.0) (sqrt z)) (sqrt z)))
6.0ms	(* (- x 1.0) (sqrt z))
6.0ms	(* (* (- x 1.0) (sqrt z)) (sqrt z))

simplify43.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4992	619
1	4992	619

prune85.0ms (4.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	69	5	74

Merged error: 0.0b

Counts

74 → 5

regimes203.0ms (9.9%)

Accuracy

Total 0.0b remaining (52.1%)

Threshold costs 0.0b (52.1%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms (0%)

sample437.0ms (21.2%)

Algorithm

1×

intervals

Results

234.0ms	8000×	body	80	valid
19.0ms	691×	body	80	invalid

Details

analyze308.0ms (14.9%)

sample17.0ms (0.8%)

simplify13.0ms (0.6%)

prune6.0ms (0.3%)

localize6.0ms (0.3%)

rewrite11.0ms (0.5%)

series14.0ms (0.7%)

simplify41.0ms (2%)

prune69.0ms (3.4%)

localize16.0ms (0.8%)

rewrite61.0ms (3%)

series66.0ms (3.2%)

simplify48.0ms (2.3%)

prune246.0ms (11.9%)

localize8.0ms (0.4%)

rewrite36.0ms (1.8%)

series24.0ms (1.2%)

simplify41.0ms (2%)

prune208.0ms (10.1%)

localize8.0ms (0.4%)

rewrite22.0ms (1.1%)

series23.0ms (1.1%)

simplify43.0ms (2.1%)

prune85.0ms (4.1%)

regimes203.0ms (9.9%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample437.0ms (21.2%)

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