Details

sample629.0ms

Algorithm

intervals

Results

242.0ms	50×	body	2560	valid
130.0ms	69×	body	640	valid
127.0ms	80×	body	1280	valid
20.0ms	33×	body	320	valid
7.0ms	15×	body	160	valid
2.0ms	9×	body	80	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize80.0ms

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))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

54.0ms	(/ (- x (sin x)) (- x (tan x)))
15.0ms	(- x (sin x))
22.0ms	(- x (tan x))

series334.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(/ (- x (sin x)) (- x (tan x)))
62.0ms	(- x (sin x))
128.0ms	(- x (tan x))

simplify2.5s

Counts

119 → 119

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	209	1823
1	501	1569
2	2264	1386
done	5002	1362

prune653.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

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))

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

34.0ms	(/ (sin x) (- x (tan x)))
226.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
13.0ms	(- x (tan x))
14.0ms	(- x (tan x))

series711.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (sin x) (- x (tan x)))
375.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
102.0ms	(- x (tan x))
118.0ms	(- x (tan x))

simplify3.9s

Counts

600 → 600

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	617	35000
1	1404	31493
2	4797	24519
done	5000	24519

prune3.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 3 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
22.0ms	(* 9/40 (pow x 2))
21.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series295.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(fma 27/2800 (pow x 4) 1/2)
48.0ms	(* 9/40 (pow x 2))
88.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.9s

Counts

67 → 67

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	106	845
1	250	714
2	1251	624
done	5001	581

prune386.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes130.0ms

Accuracy

100% (0.0b remaining)

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

bsearch200.0ms

Steps

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	43
1	26	43
done	26	43

end0.0ms

sample17.8s

Algorithm

intervals

Results

7.8s	1572×	body	2560	valid
5.4s	2765×	body	1280	valid
2.1s	1944×	body	640	valid
1.7s	927×	body	320	valid
182.0ms	446×	body	160	valid
78.0ms	346×	body	80	valid