Details

sample529.0ms

Algorithm

intervals

Results

100.0ms	47×	body	2560	valid
55.0ms	86×	body	1280	valid
46.0ms	74×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	15×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (sin x))
1.4b	(- x (tan x))

rewrite57.0ms

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:

35.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (sin x))
9.0ms	(- x (tan x))

series179.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
64.0ms	(- x (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune232.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))))
1.1b	(- x (sin x))
1.4b	(- x (tan x))

rewrite86.0ms

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:

28.0ms	(/ (- x (tan x)) (- x (sin x)))
27.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
8.0ms	(- x (sin x))
8.0ms	(- x (tan x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- x (tan x)) (- x (sin x)))
76.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
32.0ms	(- x (sin x))
51.0ms	(- x (tan x))

simplify102.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	856	3002
1	3993	2620
2	5001	2457

prune405.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan x) (- x (sin x)))
1.1b	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
1.1b	(- x (sin x))
1.1b	(- x (sin x))

rewrite207.0ms

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×	`tan-quot` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `associate-/l/` `sub-div`

Counts

4 → 589

Calls

4 calls:

15.0ms	(/ (tan x) (- x (sin x)))
119.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
8.0ms	(- x (sin x))
8.0ms	(- x (sin x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (tan x) (- x (sin x)))
129.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
37.0ms	(- x (sin x))
31.0ms	(- x (sin x))

simplify203.0ms

Algorithm

egg-herbie

Counts

601 → 601

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1342	22028
1	3815	15786
2	5001	15720

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (* 9/10 (pow x 2))) (fma 513/1400 (pow x 4) 2))
0.0b	(fma 513/1400 (pow x 4) 2)
0.0b	(/ 1 (- (- (* 9/10 (pow x 2))) (fma 513/1400 (pow x 4) 2)))
0.1b	(* 9/10 (pow x 2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
15×	`times-frac`
13×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
5×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `neg-mul-1` `unpow-prod-down` `distribute-rgt-neg-in` `log1p-expm1-u` `unswap-sqr`
3×	`associate-l` `prod-exp` `associate-/l*`
2×	`flip3--` `diff-log` `div-exp` `associate-/r/` `flip--` `fma-udef` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `sub-neg` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `neg-log` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `associate--r+` `inv-pow`

Counts

4 → 125

Calls

4 calls:

17.0ms	(- (- (* 9/10 (pow x 2))) (fma 513/1400 (pow x 4) 2))
0.0ms	(fma 513/1400 (pow x 4) 2)
23.0ms	(/ 1 (- (- (* 9/10 (pow x 2))) (fma 513/1400 (pow x 4) 2)))
13.0ms	(* 9/10 (pow x 2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (- (* 9/10 (pow x 2))) (fma 513/1400 (pow x 4) 2))
83.0ms	(fma 513/1400 (pow x 4) 2)
60.0ms	(/ 1 (- (- (* 9/10 (pow x 2))) (fma 513/1400 (pow x 4) 2)))
25.0ms	(* 9/10 (pow x 2))

simplify63.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	421	1324
1	1774	989
2	5001	946

prune255.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch68.0ms

Steps

Iters	Range		Point
8	0.002806896206153352	41.96612619086958	0.015291166436094373
7	-0.5149414008252181	-0.002950799818357885	-0.01665811831216181

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	24
1	40	24
2	40	24

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	1653×	body	2560	valid
1.8s	2759×	body	1280	valid
613.0ms	1836×	body	640	valid
203.0ms	916×	body	320	valid
72.0ms	478×	body	160	valid
32.0ms	358×	body	80	valid