Details

sample472.0ms

Algorithm

intervals

Results

114.0ms	50×	body	2560	valid
58.0ms	85×	body	1280	valid
19.0ms	53×	body	640	valid
8.0ms	37×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	12×	body	80	valid

simplify11.0ms

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: 34.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))

rewrite38.0ms

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))
6.0ms	(- x (sin x))

series173.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
56.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune242.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
12.0b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

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

series126.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
44.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify144.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117

prune71.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.0b	(- x (tan x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

3.0ms	(- x (tan x))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
4.0ms	(- x (sin x))

series145.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- x (tan x))
30.0ms	(- x (sin x))
30.0ms	(- x (sin x))
33.0ms	(- x (sin x))

simplify94.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	258	969
1	749	605
2	3295	569
3	5001	401

prune250.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 3)
2.0b	(- x (tan x))
2.0b	(- (pow x 3) (pow (sin x) 3))
16.8b	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (- x (tan x))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-sqr-sqrt`
153×	`prod-diff`
123×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
91×	`add-cube-cbrt`
50×	`sqr-pow`
49×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
16×	`distribute-lft-out--`
15×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-*r/` `div-exp` `associate-/r/` `associate-/l/`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 317

Calls

4 calls:

2.0ms	(pow (sin x) 3)
3.0ms	(- x (tan x))
21.0ms	(- (pow x 3) (pow (sin x) 3))
61.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (- x (tan x))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sin x) 3)
48.0ms	(- x (tan x))
98.0ms	(- (pow x 3) (pow (sin x) 3))
287.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (fma x x (fma (sin x) (sin x) (* x (sin x)))) (- x (tan x))))

simplify148.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	863	4164
1	3682	3059
2	5001	3050

prune495.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.6b

bsearch85.0ms

Steps

Iters	Range		Point
10	7.712829756242493e-08	8770343.893451896	0.028954196312268393
9	-1827977.1926269082	-0.00043085380315138777	-0.028975567409347768

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	1621×	body	2560	valid
1.9s	2664×	body	1280	valid
669.0ms	1932×	body	640	valid
221.0ms	938×	body	320	valid
79.0ms	472×	body	160	valid
36.0ms	373×	body	80	valid