Details

sample384.0ms

Algorithm

intervals

Results

193.0ms	52×	body	2560	valid
81.0ms	91×	body	1280	valid
23.0ms	46×	body	640	valid
11.0ms	38×	body	320	valid
4.0ms	20×	body	160	valid
1.0ms	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite103.0ms

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:

43.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
45.0ms	(- x (sin x))

series223.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
56.0ms	(- x (sin x))

simplify1.2s

Counts

119 → 119

Iterations

Useful iterations: done (1.2s)

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

prune319.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.2b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite37.0ms

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)
21.0ms	(* 9/40 (pow x 2))
13.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series225.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(fma 27/2800 (pow x 4) 1/2)
33.0ms	(* 9/40 (pow x 2))
71.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify2.9s

Counts

67 → 67

Iterations

Useful iterations: done (2.9s)

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

prune194.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
14.1b	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

rewrite16.0ms

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:

14.0ms	(* (pow x 4) -27/2800)
1.0ms	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

series195.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* (pow x 4) -27/2800)
137.0ms	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

simplify2.3s

Counts

43 → 43

Iterations

Useful iterations: 3 (476.0ms)

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

prune170.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
214×	`add-sqr-sqrt` `*-un-lft-identity`
106×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
18×	`prod-diff`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`fma-neg` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 260

Calls

4 calls:

31.0ms	(/ (- x (tan x)) (- x (sin x)))
42.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
7.0ms	(- x (tan x))
14.0ms	(- x (sin x))

series402.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- x (tan x)) (- x (sin x)))
135.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
67.0ms	(- x (tan x))
58.0ms	(- x (sin x))

simplify1.9s

Counts

272 → 272

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	374	5190
1	843	4436
2	2155	4000
done	5000	3846

prune634.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch140.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.029468351736831863
8	-11.923248480236845	-0.0008047768791668974	-0.02915706671350092

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	24	42
1	30	32
done	30	32

end0.0ms

sample14.1s

Algorithm

intervals

Results

5.9s	1596×	body	2560	valid
4.0s	2769×	body	1280	valid
3.1s	1873×	body	640	valid
492.0ms	958×	body	320	valid
148.0ms	470×	body	160	valid
56.0ms	334×	body	80	valid