Details

sample456.0ms

Algorithm

intervals

Results

113.0ms	50×	body	2560	valid
61.0ms	93×	body	1280	valid
19.0ms	57×	body	640	valid
6.0ms	24×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	12×	body	80	valid

simplify14.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
3.1b	(- x (tan x))
3.1b	(- x (sin x))

rewrite29.0ms

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:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series180.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify644.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (146.0ms)

Iter	Nodes	Cost
0	209	1823
1	489	1563
2	1680	1384
done	5001	1384

prune245.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

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))
15.8b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite15.0ms

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)
9.0ms	(* 9/40 (pow x 2))
5.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series162.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(fma 27/2800 (pow x 4) 1/2)
25.0ms	(* 9/40 (pow x 2))
46.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify4.1s

Counts

67 → 67

Iterations

Useful iterations: 3 (565.0ms)

Iter	Nodes	Cost
0	106	845
1	234	700
2	885	624
3	4737	573
done	5000	573

prune149.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

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))))
3.1b	(- x (tan x))
3.1b	(- x (sin x))

rewrite51.0ms

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:

13.0ms	(/ (- x (tan x)) (- x (sin x)))
16.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- x (tan x)) (- x (sin x)))
80.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
50.0ms	(- x (tan x))
37.0ms	(- x (sin x))

simplify1.6s

Counts

272 → 272

Iterations

Useful iterations: 2 (329.0ms)

Iter	Nodes	Cost
0	374	5190
1	883	4532
2	3388	4000
done	5001	4000

prune389.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.5b	(expm1 (/ (- x (sin x)) (- x (tan x))))
3.1b	(- x (tan x))
3.1b	(- x (sin x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
0.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series274.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
108.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
55.0ms	(- x (tan x))
32.0ms	(- x (sin x))

simplify754.0ms

Counts

133 → 133

Iterations

Useful iterations: 2 (186.0ms)

Iter	Nodes	Cost
0	246	2121
1	595	1852
2	2166	1650
done	5001	1650

prune309.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch82.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.029125046562482146
10	-155084744.97222546	-0.0009113054925467739	-0.02756549793614824

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.6s	1658×	body	2560	valid
2.0s	2659×	body	1280	valid
638.0ms	1836×	body	640	valid
218.0ms	945×	body	320	valid
86.0ms	508×	body	160	valid
38.0ms	394×	body	80	valid