Details

sample645.0ms

Algorithm

intervals

Results

291.0ms	71×	body	2560	valid
161.0ms	78×	body	1280	valid
53.0ms	55×	body	640	valid
19.0ms	29×	body	320	valid
5.0ms	11×	body	160	valid
3.0ms	12×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

17.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series269.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (- x (sin x)) (- x (tan x)))
93.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
3	3119
2	973
1	373
0	160

prune724.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* 27/2800 (* x x)))
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.2b	(* 27/2800 (* x x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`sub-neg` `insert-posit16`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 59

Calls

3 calls:

5.0ms	(- 9/40 (* 27/2800 (* x x)))
23.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
16.0ms	(* 27/2800 (* x x))

series270.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(- 9/40 (* 27/2800 (* x x)))
135.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
49.0ms	(* 27/2800 (* x x))

simplify1.1s

Counts

68 → 68

Iterations

Iter	Nodes
3	2326
2	747
1	263
0	89

prune346.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
1.7b	(- 1 (/ (sin x) x))
18.4b	(/ (sin x) (* x x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
64×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
56×	`add-cube-cbrt`
19×	`associate-/l*`
16×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `div-inv`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`pow1` `insert-posit16` `difference-of-squares`
3×	`clear-num` `frac-2neg`
1×	`quot-tan` `sub-neg` `flip3--` `diff-log` `prod-exp` `cbrt-unprod` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 140

Calls

4 calls:

10.0ms	(/ (sin x) (cos x))
20.0ms	(/ (/ (sin x) x) (cos x))
16.0ms	(- 1 (/ (sin x) x))
25.0ms	(/ (sin x) (* x x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (sin x) (cos x))
66.0ms	(/ (/ (sin x) x) (cos x))
77.0ms	(- 1 (/ (sin x) x))
55.0ms	(/ (sin x) (* x x))

simplify3.8s

Counts

152 → 152

Iterations

Iter	Nodes
3	8150
2	1768
1	590
0	263

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch134.0ms

Steps

Iters	Range		Point
10	0.002603609100038161	6235082944194588.0	0.02658761844916455
8	-145.89507053458865	-0.006947246361207331	-0.0328281005146998

simplify7.0ms

Iterations

Iter	Nodes
2	25
1	25
0	20

end1.0ms

sample16.9s

Algorithm

intervals

Results

7.3s	1657×	body	2560	valid
5.8s	2758×	body	1280	valid
2.2s	1857×	body	640	valid
1.1s	921×	body	320	valid
277.0ms	441×	body	160	valid
88.0ms	366×	body	80	valid