Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample15.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

valid

simplify69.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4970	14
1	4970	14

prune5.0ms (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

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.1b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

10.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))
5.0ms	(* 6.0 (- x 1.0))
5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))

series15.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))
4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
3.0ms	(* 6.0 (- x 1.0))

simplify43.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4992	903
1	4992	903

prune121.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0b

Counts

72 → 4

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.0b	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite32.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*`
4×	`associate-/r/`
3×	`flip3-+` `associate-l` `associate-/r*` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 93

Calls

3 calls:

13.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
9.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))

series19.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
7.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))

simplify45.0ms (2%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4974	1828
1	4974	1828

prune182.0ms (7.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Merged error: 0b

Counts

106 → 4

localize11.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
0.0b	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

rewrite32.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `sum-log`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+`

Counts

3 → 154

Calls

3 calls:

10.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))
9.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
6.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))

series17.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))
6.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))

simplify56.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5079	3735

prune336.0ms (14.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	163	4	167

Merged error: 0b

Counts

167 → 4

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.1b	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.1b	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
0.2b	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

rewrite61.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt`
108×	`times-frac`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
60×	`sqrt-prod`
36×	`associate-r`
24×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
9×	`add-log-exp` `unswap-sqr`
8×	`sqrt-div` `associate-/r/` `associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`flip3-+` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv`
3×	`sum-log`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `frac-times` `associate-+l+` `flip3--` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 201

Calls

4 calls:

30.0ms	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
10.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
7.0ms	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
6.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))

series44.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
14.0ms	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
8.0ms	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))

simplify65.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5076	5069

prune666.0ms (28.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	213	4	217

Merged error: 0b

Counts

217 → 4

regimes34.0ms (1.5%)

Accuracy

Total 0.0b remaining (71.8%)

Threshold costs 0.0b (71.8%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms (0%)

sample389.0ms (16.8%)

Algorithm

1×

intervals

Results

303.0ms

8000×

body

valid

Details

analyze3.0ms (0.1%)

sample15.0ms (0.6%)

simplify69.0ms (3%)

prune5.0ms (0.2%)

localize8.0ms (0.4%)

rewrite22.0ms (0.9%)

series15.0ms (0.6%)

simplify43.0ms (1.9%)

prune121.0ms (5.2%)

localize9.0ms (0.4%)

rewrite32.0ms (1.4%)

series19.0ms (0.8%)

simplify45.0ms (2%)

prune182.0ms (7.9%)

localize11.0ms (0.5%)

rewrite32.0ms (1.4%)

series17.0ms (0.8%)

simplify56.0ms (2.4%)

prune336.0ms (14.6%)

localize13.0ms (0.6%)

rewrite61.0ms (2.7%)

series44.0ms (1.9%)

simplify65.0ms (2.8%)

prune666.0ms (28.8%)

regimes34.0ms (1.5%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample389.0ms (16.8%)

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