Details

sample541.0ms

Algorithm

intervals

Results

131.0ms	52×	body	2560	valid
56.0ms	85×	body	1280	valid
23.0ms	68×	body	640	valid
5.0ms	22×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	9×	body	80	valid

simplify16.0ms

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: 32.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (sin x))
0.9b	(- x (tan x))

rewrite55.0ms

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:

33.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (sin x))
9.0ms	(- x (tan x))

series183.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
65.0ms	(- x (tan x))

simplify806.0ms

Counts

119 → 119

Iterations

Useful iterations: done (801.0ms)

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

prune241.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
0.2b	(* 9/40 (pow x 2))
16.1b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite25.0ms

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

series164.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(fma 27/2800 (pow x 4) 1/2)
27.0ms	(* 9/40 (pow x 2))
50.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.8s

Counts

67 → 67

Iterations

Useful iterations: done (1.8s)

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

prune151.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
16.2b	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`associate-r` `prod-exp` `unswap-sqr`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 37

Calls

2 calls:

11.0ms	(* (pow x 4) -27/2800)
0.0ms	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

series132.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(* (pow x 4) -27/2800)
95.0ms	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

simplify1.6s

Counts

43 → 43

Iterations

Useful iterations: 3 (330.0ms)

Iter	Nodes	Cost
0	66	400
1	126	375
2	345	346
3	1266	343
done	5000	343

prune106.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.9b	(- x (tan x))
0.9b	(- x (tan x))

rewrite190.0ms

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:

16.0ms	(/ (sin x) (- x (tan x)))
108.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (sin x) (- x (tan x)))
188.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
52.0ms	(- x (tan x))
61.0ms	(- x (tan x))

simplify1.5s

Counts

600 → 600

Iterations

Useful iterations: done (1.5s)

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

prune731.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch77.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.026533802681284316
9	-76786.820650899	-0.0002772006047103471	-0.028801687005274378

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	48
1	27	35
done	27	35

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.8s	1719×	body	2560	valid
1.9s	2751×	body	1280	valid
605.0ms	1804×	body	640	valid
204.0ms	911×	body	320	valid
78.0ms	468×	body	160	valid
31.0ms	347×	body	80	valid