Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

sample13.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

simplify88.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4772	8
1	4772	8

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: 0.0b

Counts

2 → 1

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ (exp x) (exp (neg x)))
0.0b	(/ 2.0 (+ (exp x) (exp (neg x))))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity`
15×	`times-frac`
12×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`cosh-undef` `associate-/r*` `distribute-lft-out`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 50

Calls

2 calls:

6.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
5.0ms	(+ (exp x) (exp (neg x)))

series13.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

9.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
4.0ms	(+ (exp x) (exp (neg x)))

simplify96.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5322	597

prune88.0ms (3.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	3	57

Merged error: 0b

Counts

57 → 3

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (neg x)))
0.0b	(* (sqrt (/ 2.0 (+ (exp x) (exp (neg x))))) (sqrt (/ 2.0 (+ (exp x) (exp (neg x))))))
0.0b	(/ 2.0 (+ (exp x) (exp (neg x))))
0.0b	(/ 2.0 (+ (exp x) (exp (neg x))))

rewrite57.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`*-un-lft-identity`
110×	`sqrt-prod`
108×	`times-frac`
96×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
32×	`swap-sqr`
27×	`distribute-lft-out`
24×	`associate-r` `associate-l`
21×	`cosh-undef`
19×	`pow1`
12×	`associate-/r/`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`sqrt-pow1` `pow1/2`
7×	`flip3-+` `flip-+`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`pow-prod-up`
4×	`sqrt-div`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 204

Calls

4 calls:

29.0ms	(* (sqrt (/ 2.0 (+ (exp x) (exp (neg x))))) (sqrt (/ 2.0 (+ (exp x) (exp (neg x))))))
7.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
7.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
5.0ms	(+ (exp x) (exp (neg x)))

series35.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sqrt (/ 2.0 (+ (exp x) (exp (neg x))))) (sqrt (/ 2.0 (+ (exp x) (exp (neg x))))))
9.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
9.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
4.0ms	(+ (exp x) (exp (neg x)))

simplify73.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4916	2762
1	4916	2762

prune397.0ms (15.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	216	3	219

Merged error: 0b

Counts

219 → 3

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (/ 2.0 (+ (exp x) (exp (neg x))))) (cbrt (/ 2.0 (+ (exp x) (exp (neg x))))))
0.0b	(/ 2.0 (+ (exp x) (exp (neg x))))
0.0b	(/ 2.0 (+ (exp x) (exp (neg x))))
0.0b	(/ 2.0 (+ (exp x) (exp (neg x))))

rewrite56.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`*-un-lft-identity`
123×	`times-frac`
108×	`cbrt-prod`
102×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
30×	`swap-sqr` `distribute-lft-out`
24×	`cosh-undef` `associate-r` `associate-l`
15×	`associate-/r*`
14×	`associate-/r/`
12×	`add-exp-log`
11×	`pow1`
10×	`add-cbrt-cube`
9×	`associate-/l*` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`pow1/3`
4×	`cbrt-div` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 219

Calls

4 calls:

25.0ms	(* (cbrt (/ 2.0 (+ (exp x) (exp (neg x))))) (cbrt (/ 2.0 (+ (exp x) (exp (neg x))))))
7.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
7.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
7.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))

series76.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cbrt (/ 2.0 (+ (exp x) (exp (neg x))))) (cbrt (/ 2.0 (+ (exp x) (exp (neg x))))))
13.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
9.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))
9.0ms	(/ 2.0 (+ (exp x) (exp (neg x))))

simplify91.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4931	3749
1	4931	3749

prune672.0ms (25.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	231	3	234

Merged error: 0b

Counts

234 → 3

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(/ (sqrt 2.0) (cosh x))
0.5b	(* (/ (sqrt 2.0) 2) (/ (sqrt 2.0) (cosh x)))

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
66×	`times-frac`
43×	`add-cube-cbrt` `*-un-lft-identity`
36×	`sqrt-prod`
23×	`associate-r`
22×	`associate-l`
16×	`add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
6×	`associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `prod-exp` `cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`cosh-def` `associate-/r/` `add-log-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

2 → 114

Calls

2 calls:

20.0ms	(* (/ (sqrt 2.0) 2) (/ (sqrt 2.0) (cosh x)))
4.0ms	(/ (sqrt 2.0) (cosh x))

series34.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

20.0ms	(* (/ (sqrt 2.0) 2) (/ (sqrt 2.0) (cosh x)))
14.0ms	(/ (sqrt 2.0) (cosh x))

simplify77.0ms (3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4948	1204
1	4948	1204

prune232.0ms (8.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	120	3	123

Merged error: 0b

Counts

123 → 3

regimes95.0ms (3.6%)

Accuracy

Total 0.0b remaining (41%)

Threshold costs 0.0b (41%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	19
1	17	19

end0.0ms (0%)

sample323.0ms (12.4%)

Algorithm

1×

intervals

Results

232.0ms

8000×

body

valid

Details

analyze2.0ms (0.1%)

sample13.0ms (0.5%)

simplify88.0ms (3.4%)

prune5.0ms (0.2%)

localize7.0ms (0.3%)

rewrite13.0ms (0.5%)

series13.0ms (0.5%)

simplify96.0ms (3.7%)

prune88.0ms (3.4%)

localize9.0ms (0.4%)

rewrite57.0ms (2.2%)

series35.0ms (1.4%)

simplify73.0ms (2.8%)

prune397.0ms (15.3%)

localize13.0ms (0.5%)

rewrite56.0ms (2.1%)

series76.0ms (2.9%)

simplify91.0ms (3.5%)

prune672.0ms (25.8%)

localize7.0ms (0.3%)

rewrite29.0ms (1.1%)

series34.0ms (1.3%)

simplify77.0ms (3%)

prune232.0ms (8.9%)

regimes95.0ms (3.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample323.0ms (12.4%)

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