Details

sample461.0ms

Algorithm

intervals

Results

108.0ms	49×	body	2560	valid
60.0ms	83×	body	1280	valid
22.0ms	58×	body	640	valid
13.0ms	37×	body	320	valid
3.0ms	16×	body	160	valid
2.0ms	13×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (tan x))
2.3b	(- x (sin x))

rewrite27.0ms

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))

series185.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- x (sin x)) (- x (tan x)))
61.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune268.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
13.8b	(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)))

series140.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(fma 27/2800 (pow x 4) 1/2)
52.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify147.0ms

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

prune79.0ms

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 (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
2.3b	(- x (/ (sin x) (cos x)))
2.3b	(- x (sin x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 177

Calls

4 calls:

24.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
3.0ms	(/ (sin x) (cos x))
9.0ms	(- x (/ (sin x) (cos x)))
4.0ms	(- x (sin x))

series190.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
19.0ms	(/ (sin x) (cos x))
56.0ms	(- x (/ (sin x) (cos x)))
33.0ms	(- x (sin x))

simplify94.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	759	2708
1	2962	1984
2	5001	1876

prune366.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.1b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
2.3b	(- x (tan x))
2.3b	(- x (sin x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
64×	`add-cube-cbrt`
62×	`unpow-prod-down` `cube-prod`
42×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `fma-neg` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 220

Calls

4 calls:

13.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
15.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series270.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
82.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
57.0ms	(- x (tan x))
33.0ms	(- x (sin x))

simplify100.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	853	2547
1	3624	2257
2	5001	2239

prune388.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch110.0ms

Steps

Iters	Range		Point
9	0.00035723662727133143	33.11368705657117	0.0259592753200958
10	-29.541817090935037	-6.322351620237733e-11	-0.02689094511669957

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	24

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.7s	1625×	body	2560	valid
2.0s	2731×	body	1280	valid
752.0ms	1872×	body	640	valid
269.0ms	956×	body	320	valid
92.0ms	465×	body	160	valid
52.0ms	351×	body	80	valid