Details

sample606.0ms

Algorithm

intervals

Results

227.0ms	50×	body	2560	valid
193.0ms	80×	body	1280	valid
64.0ms	69×	body	640	valid
18.0ms	33×	body	320	valid
6.0ms	15×	body	160	valid
2.0ms	9×	body	80	valid

simplify31.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.6b	(- x (sin x))
0.6b	(- x (tan x))

rewrite133.0ms

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:

49.0ms	(/ (- x (sin x)) (- x (tan x)))
18.0ms	(- x (sin x))
58.0ms	(- x (tan x))

series336.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(/ (- x (sin x)) (- x (tan x)))
55.0ms	(- x (sin x))
136.0ms	(- x (tan x))

simplify1.1s

Counts

89 → 89

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	157	1237
1	371	1200
2	1360	1149
done	5000	1147

prune530.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.6b	(- x (tan x))
0.6b	(- x (tan x))

rewrite232.0ms

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:

32.0ms	(/ (sin x) (- x (tan x)))
171.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

series726.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (sin x) (- x (tan x)))
372.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
112.0ms	(- x (tan x))
109.0ms	(- x (tan x))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	177	1565
1	388	1511
2	1424	1450
done	5000	1449

prune658.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
16.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite96.0ms

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:

23.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series217.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* 27/2800 (pow x 4))
50.0ms	(* 9/40 (pow x 2))
96.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify1.3s

Counts

75 → 75

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	121	788
1	291	703
2	1116	645
done	5000	643

prune398.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes152.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch197.0ms

Steps

Iters	Range		Point
10	2.8868360106527892e-08	453261925.93168354	0.035008502692176
9	-4.26929226401081	-3.26160511802404e-08	-0.02767094041582889

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	44
1	29	44
done	29	44

end0.0ms

sample17.4s

Algorithm

intervals

Results

7.7s	1572×	body	2560	valid
5.7s	2765×	body	1280	valid
2.3s	1944×	body	640	valid
863.0ms	927×	body	320	valid
177.0ms	446×	body	160	valid
81.0ms	346×	body	80	valid