Details

sample948.0ms

Algorithm

intervals

Results

290.0ms	54×	body	2560	valid
177.0ms	81×	body	1280	valid
122.0ms	47×	body	640	valid
36.0ms	40×	body	320	valid
10.0ms	18×	body	160	valid
6.0ms	16×	body	80	valid

simplify78.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite31.0ms

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:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series268.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (- x (sin x)) (- x (tan x)))
83.0ms	(- x (tan x))
58.0ms	(- x (sin x))

simplify1.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5017
3	3306
2	964
1	375
0	160

prune386.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x 9/40)
0.2b	(* (* x x) (* x x))
0.2b	(* x (* x 9/40))
13.1b	(+ (* -27/2800 (* (* x x) (* x x))) (+ -1/2 (* x (* x 9/40))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
36×	`pow-prod-up`
27×	`pow-prod-down`
23×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
12×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
2×	`unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 116

Calls

4 calls:

5.0ms	(* x 9/40)
42.0ms	(* (* x x) (* x x))
26.0ms	(* x (* x 9/40))
118.0ms	(+ (* -27/2800 (* (* x x) (* x x))) (+ -1/2 (* x (* x 9/40))))

series204.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* x 9/40)
68.0ms	(* (* x x) (* x x))
53.0ms	(* x (* x 9/40))
63.0ms	(+ (* -27/2800 (* (* x x) (* x x))) (+ -1/2 (* x (* x 9/40))))

simplify1.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1618
1	389
0	124

prune282.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
1.9b	(- x (/ (sin x) (cos x)))
1.9b	(- x (sin x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
46×	`times-frac`
25×	`add-cube-cbrt`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3--` `insert-posit16` `flip--`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `associate-/r/` `div-inv` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 119

Calls

4 calls:

24.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
16.0ms	(/ (sin x) (cos x))
12.0ms	(- x (/ (sin x) (cos x)))
5.0ms	(- x (sin x))

series255.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
20.0ms	(/ (sin x) (cos x))
89.0ms	(- x (/ (sin x) (cos x)))
40.0ms	(- x (sin x))

simplify2.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	5006
3	4149
2	1342
1	483
0	210

prune568.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- x (/ (sin x) (cos x))) (- x (sin x))))
0.2b	(/ (sin x) (cos x))
1.9b	(- x (/ (sin x) (cos x)))
1.9b	(- x (sin x))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
252×	`add-sqr-sqrt`
189×	`*-un-lft-identity`
97×	`add-cube-cbrt`
67×	`difference-of-squares`
46×	`distribute-lft-out--`
39×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `sub-neg` `frac-2neg` `diff-log` `1-exp`
1×	`quot-tan` `pow-flip` `inv-pow`

Counts

4 → 229

Calls

4 calls:

50.0ms	(/ 1 (/ (- x (/ (sin x) (cos x))) (- x (sin x))))
16.0ms	(/ (sin x) (cos x))
15.0ms	(- x (/ (sin x) (cos x)))
10.0ms	(- x (sin x))

series256.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ 1 (/ (- x (/ (sin x) (cos x))) (- x (sin x))))
26.0ms	(/ (sin x) (cos x))
70.0ms	(- x (/ (sin x) (cos x)))
38.0ms	(- x (sin x))

simplify2.1s

Counts

241 → 241

Iterations

Iter	Nodes
done	5003
2	2415
1	915
0	370

prune731.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes92.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch140.0ms

Steps

Iters	Range		Point
8	0.006928851504795399	68.55102067575892	0.029335377355220408
9	-17438.246738609338	-0.0018335887134067947	-0.03333148510890561

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample16.8s

Algorithm

intervals

Results

7.8s	1613×	body	2560	valid
5.4s	2707×	body	1280	valid
2.0s	1838×	body	640	valid
1.1s	946×	body	320	valid
231.0ms	502×	body	160	valid
99.0ms	394×	body	80	valid