Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	5	7
1	7	6
done	7	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize5.0ms

Local error

Found 1 expressions with local error:

13.2b

(/ x (fma x x 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/ x (fma x x 1.0))

series101.0ms

Counts

1 → 3

Calls

1 calls:

101.0ms

(/ x (fma x x 1.0))

simplify2.4s

Counts

32 → 32

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	68	377
1	132	362
2	327	332
3	764	332
4	2008	332
done	5000	332

prune95.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
0.0b	(/ x (sqrt (fma x x 1.0)))
13.1b	(sqrt (fma x x 1.0))
13.1b	(sqrt (fma x x 1.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`add-cube-cbrt` `*-un-lft-identity`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 248

Calls

4 calls:

18.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
16.0ms	(/ x (sqrt (fma x x 1.0)))
3.0ms	(sqrt (fma x x 1.0))
2.0ms	(sqrt (fma x x 1.0))

series449.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (fma x x 1.0)))
178.0ms	(/ x (sqrt (fma x x 1.0)))
56.0ms	(sqrt (fma x x 1.0))
83.0ms	(sqrt (fma x x 1.0))

simplify2.7s

Counts

260 → 260

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	304	5985
1	687	5190
2	1471	4798
3	4056	4610
done	5000	4517

prune665.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (sqrt (fma x x 1.0))))
13.1b	(sqrt (fma x x 1.0))
13.1b	(sqrt (fma x x 1.0))
13.1b	(sqrt (fma x x 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 98

Calls

4 calls:

15.0ms	(/ x (sqrt (sqrt (fma x x 1.0))))
3.0ms	(sqrt (fma x x 1.0))
3.0ms	(sqrt (fma x x 1.0))
3.0ms	(sqrt (fma x x 1.0))

series678.0ms

Counts

4 → 12

Calls

4 calls:

435.0ms	(/ x (sqrt (sqrt (fma x x 1.0))))
78.0ms	(sqrt (fma x x 1.0))
83.0ms	(sqrt (fma x x 1.0))
80.0ms	(sqrt (fma x x 1.0))

simplify1.6s

Counts

110 → 110

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	159	1417
1	303	1267
2	771	1205
3	2080	1193
done	5000	1190

prune439.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 x) (/ 1.0 (pow x 5)))
0.3b	(/ 1.0 (pow x 3))
0.5b	(/ 1.0 (pow x 5))
21.0b	(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

rewrite609.0ms

Algorithm

rewrite-expression-head

Rules

532×	`*-un-lft-identity`
373×	`times-frac`
240×	`prod-diff`
238×	`add-sqr-sqrt`
225×	`add-cube-cbrt`
129×	`distribute-lft-out`
79×	`unpow-prod-down`
67×	`cube-prod`
52×	`div-inv`
27×	`sqr-pow`
22×	`cube-mult` `unpow3`
19×	`associate-/r*`
14×	`add-exp-log`
13×	`fma-def`
11×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`fma-neg` `div-exp` `associate-/l*`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`frac-sub`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `sum-log` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 418

Calls

4 calls:

40.0ms	(+ (/ 1 x) (/ 1.0 (pow x 5)))
8.0ms	(/ 1.0 (pow x 3))
7.0ms	(/ 1.0 (pow x 5))
522.0ms	(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (/ 1 x) (/ 1.0 (pow x 5)))
67.0ms	(/ 1.0 (pow x 3))
86.0ms	(/ 1.0 (pow x 5))
91.0ms	(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

simplify3.0s

Counts

430 → 430

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	480	17448
1	1062	14593
2	2924	9875
done	5000	8463

prune685.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

Details

sample21.0ms

simplify5.0ms

prune6.0ms

localize5.0ms

rewrite6.0ms

series101.0ms

simplify2.4s

prune95.0ms

localize8.0ms

rewrite57.0ms

series449.0ms

simplify2.7s

prune665.0ms

localize28.0ms

rewrite28.0ms

series678.0ms

simplify1.6s

prune439.0ms

localize13.0ms

rewrite609.0ms

series398.0ms

simplify3.0s

prune685.0ms

regimes52.0ms

bsearch2.0ms