Details

sample456.0ms

Algorithm

intervals

Results

161.0ms	82×	body	1280	valid
136.0ms	43×	body	2560	valid
49.0ms	66×	body	640	valid
23.0ms	37×	body	320	valid
6.0ms	17×	body	160	valid
2.0ms	11×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite111.0ms

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×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

50.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
47.0ms	(- x (sin x))

series236.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (- x (sin x)) (- x (tan x)))
70.0ms	(- x (tan x))
54.0ms	(- x (sin x))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	915	1147
3	2339	1147
done	5000	1133

prune349.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (* x (cos x)))
2.0b	(- (/ (sin x) (cos x)) (sin x))
13.7b	(/ (sin x) (* (pow x 2) (cos x)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt` `times-frac` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-exp`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/r*`
4×	`pow1` `prod-exp`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`cbrt-unprod` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `quot-tan` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

17.0ms	(/ (sin x) (cos x))
26.0ms	(/ (sin x) (* x (cos x)))
35.0ms	(- (/ (sin x) (cos x)) (sin x))
22.0ms	(/ (sin x) (* (pow x 2) (cos x)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (sin x) (cos x))
61.0ms	(/ (sin x) (* x (cos x)))
71.0ms	(- (/ (sin x) (cos x)) (sin x))
88.0ms	(/ (sin x) (* (pow x 2) (cos x)))

simplify3.7s

Counts

99 → 99

Iterations

Useful iterations: 3 (2.4s)

Iter	Nodes	Cost
0	167	1135
1	373	1072
2	1164	980
3	4961	977
done	5001	977

prune496.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
14.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

26.0ms	(* 27/2800 (pow x 4))
23.0ms	(* 9/40 (pow x 2))
23.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series163.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* 27/2800 (pow x 4))
31.0ms	(* 9/40 (pow x 2))
65.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify2.5s

Counts

75 → 75

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	121	788
1	277	703
2	674	643
3	2581	637
done	5000	634

prune200.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
14.3b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

12.0ms	(* 27/2800 (pow x 4))
30.0ms	(* 9/40 (pow x 2))
21.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* 27/2800 (pow x 4))
49.0ms	(* 9/40 (pow x 2))
138.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify2.1s

Counts

73 → 73

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	113	715
1	254	624
2	574	570
3	2285	560
done	5000	555

prune172.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes93.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.6b

bsearch165.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	2.401275434249347
9	-7465.585501010854	-0.008005822963963436	-0.030293763080502873

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	65
1	47	65
done	47	65

end0.0ms

sample13.5s

Algorithm

intervals

Results

6.1s	1659×	body	2560	valid
4.4s	2670×	body	1280	valid
2.0s	1927×	body	640	valid
509.0ms	942×	body	320	valid
168.0ms	380×	body	80	valid
122.0ms	422×	body	160	valid