Details

sample13.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify212.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	12	5
2	14	5
3	15	5
4	20	5
5	41	5
6	66	5
7	165	5
8	1123	5
9	5001	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 52

Calls

2 calls:

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

series63.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (exp x) (exp (- x)))
41.0ms	(/ 2.0 (+ (exp x) (exp (- x))))

simplify121.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	200	433
1	666	397
2	3139	394
3	5001	393

prune104.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	1	59

Merged error: 0b

Counts

59 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.0b	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
0.0b	(/ 2.0 (+ (exp (* -1 x)) (exp x)))
0.0b	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
60×	`times-frac`
48×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube`

Counts

4 → 164

Calls

4 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
9.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
6.0ms	(/ 2.0 (+ (exp (* -1 x)) (exp x)))
8.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)

series173.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (exp (* -1 x)) (exp x))
36.0ms	(cbrt (pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3))
41.0ms	(/ 2.0 (+ (exp (* -1 x)) (exp x)))
76.0ms	(pow (/ 2.0 (+ (exp (* -1 x)) (exp x))) 3)

simplify68.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	475	1670
1	2035	1557
2	5002	1539

prune243.0ms

Filtered

176 candidates to 94 candidates (53.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	176	1	177

Merged error: 0b

Counts

177 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample312.0ms

Algorithm

intervals

Results

222.0ms

8000×

body

valid

Details

sample13.0ms

simplify212.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series63.0ms

simplify121.0ms

prune104.0ms

localize9.0ms

rewrite34.0ms

series173.0ms

simplify68.0ms

prune243.0ms

simplify1.0ms

end0.0ms

sample312.0ms

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