Details

sample566.0ms

Algorithm

intervals

Results

261.0ms	79×	body	1280	valid
190.0ms	53×	body	2560	valid
37.0ms	65×	body	640	valid
10.0ms	27×	body	320	valid
5.0ms	20×	body	160	valid
2.0ms	12×	body	80	valid

simplify23.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.7b	(- x (sin x))

rewrite80.0ms

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:

30.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
37.0ms	(- x (sin x))

series204.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify1.3s

Counts

119 → 119

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	209	1823
1	476	1563
2	1343	1384
done	5000	1306

prune381.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

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))
13.1b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite31.0ms

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:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
17.0ms	(* 9/40 (pow x 2))
12.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series225.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(fma 27/2800 (pow x 4) 1/2)
39.0ms	(* 9/40 (pow x 2))
51.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify3.1s

Counts

67 → 67

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	106	845
1	219	700
2	588	624
3	2787	573
done	5000	572

prune257.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.7b	(- x (sin x))
2.5b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
30.1b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
8.0ms	(- x (sin x))
26.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.7s

Counts

4 → 12

Calls

4 calls:

301.0ms	(cbrt x)
55.0ms	(- x (sin x))
829.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
518.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify2.8s

Counts

103 → 103

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	168	1778
1	346	1642
2	939	1193
3	3296	950
done	5000	950

prune395.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.5b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite292.0ms

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:

35.0ms	(/ (sin x) (- x (tan x)))
151.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
14.0ms	(- x (tan x))
14.0ms	(- x (tan x))

series589.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (sin x) (- x (tan x)))
288.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
92.0ms	(- x (tan x))
79.0ms	(- x (tan x))

simplify2.3s

Counts

600 → 600

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	617	35000
1	1353	31424
2	3023	23405
done	5001	20458

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes115.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch173.0ms

Steps

Iters	Range		Point
9	0.0030847216915828425	5729.342694487068	1.5862025016764627
11	-30636816361710.875	-9.292394687435822e-10	-0.02805121074086329

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	55
1	28	55
done	28	55

end0.0ms

sample13.1s

Algorithm

intervals

Results

6.3s	1582×	body	2560	valid
4.2s	2688×	body	1280	valid
1.5s	1934×	body	640	valid
488.0ms	944×	body	320	valid
188.0ms	480×	body	160	valid
60.0ms	372×	body	80	valid