Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

sample11.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

valid

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

prune4.0ms (0.2%)

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: 0.1b

Counts

2 → 1

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))
0.1b	(* (/ 841.0 108.0) x)

rewrite13.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `div-exp` `pow-prod-down` `frac-add` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

7.0ms	(+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))
5.0ms	(* (/ 841.0 108.0) x)

series5.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))
2.0ms	(* (/ 841.0 108.0) x)

simplify53.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4950	401
1	4950	401

prune87.0ms (5.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	4	51

Merged error: 0b

Counts

51 → 4

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* 841.0 (/ x 108.0)) (/ 4.0 29.0))
0.3b	(* 841.0 (/ x 108.0))

rewrite17.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `div-exp` `pow-prod-down` `frac-add` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

9.0ms	(+ (* 841.0 (/ x 108.0)) (/ 4.0 29.0))
7.0ms	(* 841.0 (/ x 108.0))

series5.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ (* 841.0 (/ x 108.0)) (/ 4.0 29.0))
2.0ms	(* 841.0 (/ x 108.0))

simplify52.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4983	407
1	4983	407

prune78.0ms (5.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	50	4	54

Merged error: 0b

Counts

54 → 4

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* (sqrt (/ 841.0 108.0)) (* x (sqrt (/ 841.0 108.0)))) (/ 4.0 29.0))
0.2b	(* x (sqrt (/ 841.0 108.0)))
0.3b	(* (sqrt (/ 841.0 108.0)) (* x (sqrt (/ 841.0 108.0))))

rewrite34.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`sqrt-prod`
27×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac` `associate-l`
17×	`associate-r`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`sqrt-div`
7×	`associate-*r/`
5×	`add-log-exp`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`frac-add` `unswap-sqr`
2×	`frac-times` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 82

Calls

3 calls:

14.0ms	(+ (* (sqrt (/ 841.0 108.0)) (* x (sqrt (/ 841.0 108.0)))) (/ 4.0 29.0))
10.0ms	(* (sqrt (/ 841.0 108.0)) (* x (sqrt (/ 841.0 108.0))))
7.0ms	(* x (sqrt (/ 841.0 108.0)))

series18.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (* (sqrt (/ 841.0 108.0)) (* x (sqrt (/ 841.0 108.0)))) (/ 4.0 29.0))
7.0ms	(* (sqrt (/ 841.0 108.0)) (* x (sqrt (/ 841.0 108.0))))
4.0ms	(* x (sqrt (/ 841.0 108.0)))

simplify56.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4943	791
1	4943	791

prune183.0ms (12%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	91	4	95

Merged error: 0b

Counts

95 → 4

localize9.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))
0.1b	(* (/ 841.0 108.0) x)
0.1b	(* (/ 841.0 108.0) x)
0.1b	(* (sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))) (sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))))

rewrite44.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
32×	`associate-l`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`sqrt-div`
24×	`pow1`
21×	`sqrt-prod`
20×	`times-frac`
16×	`add-exp-log` `add-cbrt-cube`
14×	`associate-*l/`
12×	`associate-r`
9×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `frac-add` `flip-+`
8×	`swap-sqr` `unswap-sqr`
5×	`pow-prod-down` `prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`add-log-exp`
3×	`associate-r/` `pow-sqr` `-commutative`
2×	`cbrt-undiv` `div-exp` `div-inv`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 144

Calls

4 calls:

18.0ms	(* (sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))) (sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))))
8.0ms	(* (/ 841.0 108.0) x)
7.0ms	(sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))
6.0ms	(* (/ 841.0 108.0) x)

series12.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))
4.0ms	(* (sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))) (sqrt (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0))))
2.0ms	(* (/ 841.0 108.0) x)
2.0ms	(* (/ 841.0 108.0) x)

simplify64.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4958	1859
1	4958	1859

prune378.0ms (24.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	156	4	160

Merged error: 0b

Counts

160 → 4

regimes90.0ms (5.9%)

Accuracy

Total 0.1b remaining (88.1%)

Threshold costs 0.1b (88.1%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms (0%)

sample292.0ms (19.1%)

Algorithm

1×

intervals

Results

205.0ms	7997×	body	80	valid
0.0ms	2×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	80	invalid

Details

analyze3.0ms (0.2%)

sample11.0ms (0.7%)

simplify3.0ms (0.2%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

rewrite13.0ms (0.9%)

series5.0ms (0.3%)

simplify53.0ms (3.5%)

prune87.0ms (5.7%)

localize6.0ms (0.4%)

rewrite17.0ms (1.1%)

series5.0ms (0.3%)

simplify52.0ms (3.4%)

prune78.0ms (5.1%)

localize8.0ms (0.5%)

rewrite34.0ms (2.2%)

series18.0ms (1.2%)

simplify56.0ms (3.7%)

prune183.0ms (12%)

localize9.0ms (0.6%)

rewrite44.0ms (2.9%)

series12.0ms (0.8%)

simplify64.0ms (4.2%)

prune378.0ms (24.7%)

regimes90.0ms (5.9%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample292.0ms (19.1%)

Profiling