Details

sample589.0ms

Algorithm

intervals

Results

360.0ms	117×	body	2560	valid
121.0ms	70×	body	1280	valid
63.0ms	39×	body	640	valid
14.0ms	23×	body	320	valid
12.0ms	256×	pre	80	true
3.0ms	6×	body	160	valid
0.0ms	1×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	8
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize22.0ms

Local error

Found 1 expressions with local error:

2.8b	(- (/ 1 x) (/ 1 (tan x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`times-frac`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
4×	`div-inv`
3×	`add-cube-cbrt` `add-log-exp`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `frac-sub` `insert-posit16` `flip--`

Counts

1 → 30

Calls

1 calls:

16.0ms

(- (/ 1 x) (/ 1 (tan x)))

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

(- (/ 1 x) (/ 1 (tan x)))

simplify2.1s

Counts

33 → 33

Iterations

Iter	Nodes
4	2078
3	989
2	435
1	171
0	82

prune211.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (pow x 5) 2/945)
0.1b	(* 1/45 (* x x))
0.4b	(* x (+ 1/3 (* 1/45 (* x x))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-exp-log`
13×	`associate-l`
12×	`add-cbrt-cube`
10×	`pow1`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down`
3×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `flip3-+` `pow-exp` `flip-+`

Counts

3 → 69

Calls

3 calls:

21.0ms	(* (pow x 5) 2/945)
17.0ms	(* 1/45 (* x x))
11.0ms	(* x (+ 1/3 (* 1/45 (* x x))))

series250.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(* (pow x 5) 2/945)
39.0ms	(* 1/45 (* x x))
124.0ms	(* x (+ 1/3 (* 1/45 (* x x))))

simplify3.2s

Counts

78 → 78

Iterations

Iter	Nodes
3	5809
2	1146
1	334
0	121

prune524.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/45 (* x x))
0.1b	(* 1/45 (* x x))
0.3b	(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
0.4b	(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
16×	`pow1`
14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
8×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-r`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`associate-/r` `times-frac` `flip3--` `-commutative` `flip--` `unswap-sqr`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `associate-/r/` `associate-/l/`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

26.0ms	(* 1/45 (* x x))
15.0ms	(* 1/45 (* x x))
26.0ms	(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
31.0ms	(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 1/45 (* x x))
38.0ms	(* 1/45 (* x x))
270.0ms	(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
235.0ms	(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))

simplify5.7s

Counts

104 → 104

Iterations

Iter	Nodes
3	10524
2	1572
1	395
0	136

prune566.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 5) 2/945)
0.1b	(* 1/45 (* x x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-exp-log`
10×	`associate-l`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
4×	`unpow-prod-down` `associate-r` `cbrt-unprod` `unswap-sqr`
3×	`pow-prod-down`
2×	`*-commutative` `insert-posit16` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

2 → 46

Calls

2 calls:

8.0ms	(* (pow x 5) 2/945)
13.0ms	(* 1/45 (* x x))

series85.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(* (pow x 5) 2/945)
28.0ms	(* 1/45 (* x x))

simplify574.0ms

Counts

52 → 52

Iterations

Iter	Nodes
3	2057
2	544
1	188
0	81

prune331.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample14.2s

Algorithm

intervals

Results

8.3s	3219×	body	2560	valid
3.4s	2495×	body	1280	valid
1.7s	1261×	body	640	valid
339.0ms	661×	body	320	valid
282.0ms	8000×	pre	80	true
107.0ms	322×	body	160	valid
7.0ms	42×	body	80	valid