Details

sample383.0ms

Algorithm

intervals

Results

122.0ms	45×	body	2560	valid
91.0ms	86×	body	1280	valid
71.0ms	56×	body	640	valid
13.0ms	34×	body	320	valid
6.0ms	20×	body	160	valid
2.0ms	15×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 31.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.1b	(- x (tan x))
2.1b	(- x (sin x))

rewrite84.0ms

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:

28.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
42.0ms	(- x (sin x))

series240.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (- x (sin x)) (- x (tan x)))
68.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify1.6s

Counts

89 → 89

Iterations

Useful iterations: done (1.6s)

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

prune329.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
2.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.1b	(- x (tan x))
2.1b	(- x (tan x))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

37.0ms	(/ (sin x) (- x (tan x)))
170.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series534.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (sin x) (- x (tan x)))
258.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
77.0ms	(- x (tan x))
73.0ms	(- x (tan x))

simplify1.8s

Counts

106 → 106

Iterations

Useful iterations: 3 (785.0ms)

Iter	Nodes	Cost
0	177	1565
1	377	1511
2	938	1449
3	2824	1445
done	5001	1445

prune418.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
13.0b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
13.0b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 136

Calls

4 calls:

7.0ms	(pow (sin x) 2)
8.0ms	(pow (sin x) 2)
38.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
17.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (sin x) 2)
45.0ms	(pow (sin x) 2)
107.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
89.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify907.0ms

Counts

148 → 148

Iterations

Useful iterations: done (900.0ms)

Iter	Nodes	Cost
0	161	1988
1	361	1788
2	1107	1628
done	5000	1566

prune523.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
13.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite92.0ms

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:

32.0ms	(* 27/2800 (pow x 4))
26.0ms	(* 9/40 (pow x 2))
31.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series170.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
83.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify2.1s

Counts

75 → 75

Iterations

Useful iterations: done (2.1s)

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

prune240.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch130.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.03007487465186483
9	-1501.2167507114543	-0.006495210018506858	-0.027057923325783554

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	49
1	30	36
done	30	36

end0.0ms

sample14.0s

Algorithm

intervals

Results

6.2s	1545×	body	2560	valid
4.1s	2810×	body	1280	valid
1.9s	1867×	body	640	valid
1.1s	952×	body	320	valid
220.0ms	363×	body	80	valid
137.0ms	463×	body	160	valid