Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

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 (+ (* x x) 1.0))

rewrite20.0ms

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`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

15.0ms

(/ x (+ (* x x) 1.0))

series98.0ms

Counts

1 → 3

Calls

1 calls:

98.0ms

(/ x (+ (* x x) 1.0))

simplify2.8s

Counts

32 → 32

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	74	428
1	167	413
2	438	373
3	1017	373
4	2805	373
done	5000	373

prune115.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
13.1b	(sqrt (+ (* x x) 1.0))
13.1b	(sqrt (+ (* x x) 1.0))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 158

Calls

4 calls:

29.0ms	(/ x (sqrt (+ (* x x) 1.0)))
111.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
11.0ms	(sqrt (+ (* x x) 1.0))
16.0ms	(sqrt (+ (* x x) 1.0))

series395.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ x (sqrt (+ (* x x) 1.0)))
75.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
83.0ms	(sqrt (+ (* x x) 1.0))
75.0ms	(sqrt (+ (* x x) 1.0))

simplify2.3s

Counts

170 → 170

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	228	3302
1	589	2939
2	1745	2433
done	5000	2426

prune427.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

8.5b	(* (/ (/ 1 (sqrt (+ (* x x) 1.0))) (sqrt (sqrt (+ (* x x) 1.0)))) (/ x (sqrt (sqrt (+ (* x x) 1.0)))))
13.1b	(sqrt (+ (* x x) 1.0))
13.1b	(sqrt (+ (* x x) 1.0))
13.1b	(sqrt (+ (* x x) 1.0))

rewrite414.0ms

Algorithm

rewrite-expression-head

Rules

561×	`times-frac`
479×	`add-sqr-sqrt`
465×	`sqrt-prod`
240×	`*-un-lft-identity`
222×	`associate-l`
216×	`add-cube-cbrt`
64×	`unswap-sqr`
39×	`add-exp-log`
33×	`associate-r`
32×	`sqrt-div`
25×	`add-cbrt-cube`
22×	`associate-/r/`
17×	`div-exp`
14×	`flip3-+` `flip-+`
11×	`div-inv`
10×	`prod-exp`
9×	`pow1` `cbrt-undiv`
6×	`cbrt-unprod`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`rec-exp` `1-exp`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 392

Calls

4 calls:

323.0ms	(* (/ (/ 1 (sqrt (+ (* x x) 1.0))) (sqrt (sqrt (+ (* x x) 1.0)))) (/ x (sqrt (sqrt (+ (* x x) 1.0)))))
17.0ms	(sqrt (+ (* x x) 1.0))
10.0ms	(sqrt (+ (* x x) 1.0))
10.0ms	(sqrt (+ (* x x) 1.0))

series295.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (/ (/ 1 (sqrt (+ (* x x) 1.0))) (sqrt (sqrt (+ (* x x) 1.0)))) (/ x (sqrt (sqrt (+ (* x x) 1.0)))))
66.0ms	(sqrt (+ (* x x) 1.0))
72.0ms	(sqrt (+ (* x x) 1.0))
75.0ms	(sqrt (+ (* x x) 1.0))

simplify2.1s

Counts

404 → 404

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	384	12839
1	1157	12154
2	2897	10065
done	5000	9407

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
97×	`times-frac`
69×	`*-un-lft-identity`
47×	`add-cube-cbrt`
33×	`unpow-prod-down`
20×	`difference-of-squares`
19×	`associate-/r*`
17×	`sqr-pow`
16×	`cube-prod`
14×	`add-exp-log`
11×	`add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out--`
6×	`div-exp` `div-inv` `associate-/l*`
5×	`distribute-lft-out`
4×	`pow1` `cube-mult` `unpow3`
3×	`frac-add`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 171

Calls

4 calls:

338.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
10.0ms	(/ 1.0 (pow x 3))
12.0ms	(/ 1.0 (pow x 5))
93.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
65.0ms	(/ 1.0 (pow x 3))
100.0ms	(/ 1.0 (pow x 5))
207.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify1.2s

Counts

183 → 183

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	257	2827
1	552	2514
2	1508	2422
done	5001	2416

prune579.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

Details

sample21.0ms

simplify4.0ms

prune3.0ms

localize5.0ms

rewrite20.0ms

series98.0ms

simplify2.8s

prune115.0ms

localize23.0ms

rewrite179.0ms

series395.0ms

simplify2.3s

prune427.0ms

localize31.0ms

rewrite414.0ms

series295.0ms

simplify2.1s

prune1.4s

localize14.0ms

rewrite470.0ms

series442.0ms

simplify1.2s

prune579.0ms

regimes1.0ms