Details

sample447.0ms

Algorithm

intervals

Results

266.0ms	92×	body	1280	valid
130.0ms	56×	body	2560	valid
25.0ms	55×	body	640	valid
9.0ms	27×	body	320	valid
3.0ms	12×	body	160	valid
2.0ms	14×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

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:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series41.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
27.0ms	(- x (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune553.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.1b	(- x (sin x))
2.0b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
28.3b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-prod` `fma-neg` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/3` `diff-log` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

0.0ms	(cbrt x)
3.0ms	(- x (sin x))
9.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt x)
3.0ms	(- x (sin x))
57.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
31.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	342	1106
1	1185	942
2	5001	904

prune636.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (tan x) (- x (sin x)))
1.1b	(- x (sin x))
1.1b	(- x (sin x))
1.1b	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))

rewrite138.0ms

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:

6.0ms	(/ (tan x) (- x (sin x)))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
72.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (tan x) (- x (sin x)))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
14.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))

simplify203.0ms

Algorithm

egg-herbie

Counts

601 → 601

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1342	22028
1	3814	15786
2	5001	15718

prune3.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
17.1b	(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)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(fma 27/2800 (pow x 4) 1/2)
6.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify141.0ms

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

prune152.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.4b

bsearch52.0ms

Steps

Iters	Range		Point
9	0.006665254470786589	7065.8830381017015	0.027484538016213013
9	-14674.600957416102	-0.00012459925560949148	-0.026260449326479987

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.6s	1548×	body	2560	valid
2.2s	2797×	body	1280	valid
850.0ms	1881×	body	640	valid
296.0ms	929×	body	320	valid
99.0ms	473×	body	160	valid
44.0ms	372×	body	80	valid