Details

sample529.0ms

Algorithm

intervals

Results

186.0ms	56×	body	2560	valid
61.0ms	90×	body	1280	valid
13.0ms	51×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	10×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.2b	(- x (sin x))

rewrite24.0ms

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:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series182.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune239.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt x) (cbrt x))
1.2b	(- x (sin x))
2.2b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
26.8b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
29×	`add-cube-cbrt`
16×	`cbrt-prod`
15×	`times-frac`
11×	`pow1`
9×	`prod-diff`
8×	`add-exp-log`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `associate-/r*`
2×	`flip3--` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--` `associate-/l/`
1×	`cbrt-undiv` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 120

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
4.0ms	(- x (sin x))
6.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (cbrt x) (cbrt x))
30.0ms	(- x (sin x))
521.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
324.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	396	1252
1	1470	1067
2	5001	1017

prune310.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (tan x) (- x (sin x)))
1.2b	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
1.2b	(- x (sin x))
1.2b	(- x (sin x))

rewrite113.0ms

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)))
41.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
4.0ms	(- x (sin x))
5.0ms	(- x (sin x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (tan x) (- x (sin x)))
138.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
30.0ms	(- x (sin x))
31.0ms	(- x (sin x))

simplify206.0ms

Algorithm

egg-herbie

Counts

601 → 601

Iterations

Useful iterations: 2 (82.0ms)

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

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma 27/2800 (pow x 4) 1/2)
14.3b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

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:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series132.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
48.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify145.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

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

prune64.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch82.0ms

Steps

Iters	Range		Point
10	1.4316099847845607e-10	21.660028671588154	0.028138209226020946
9	-8.718619127186496	-1.4100946153605287e-08	-0.027117839518358274

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.8s	1584×	body	2560	valid
1.5s	2769×	body	1280	valid
459.0ms	1889×	body	640	valid
153.0ms	913×	body	320	valid
60.0ms	487×	body	160	valid
25.0ms	358×	body	80	valid