Details

sample460.0ms

Algorithm

intervals

Results

100.0ms	52×	body	2560	valid
69.0ms	104×	body	1280	valid
16.0ms	48×	body	640	valid
8.0ms	32×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	7×	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: 31.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.6b	(- x (tan x))
0.6b	(- x (sin x))

rewrite41.0ms

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))

series176.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
40.0ms	(- 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

prune244.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
18.3b	(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)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(fma 27/2800 (pow x 4) 1/2)
46.0ms	(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

prune69.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
0.1b	(fma 27/2800 (pow x 4) 1/2)
0.3b	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
18.3b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

1.0ms	(exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
0.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
85.0ms	(fma 27/2800 (pow x 4) 1/2)
49.0ms	(log (exp (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))))
44.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify49.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	119	426
1	328	378
2	1289	378
3	5001	376

prune184.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

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

bsearch71.0ms

Steps

Iters	Range		Point
8	0.003342748024832997	13.582308112339199	0.02851743899812111
9	-118.89002763209811	-0.00028315217264546786	-0.024514420160319003

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

3.5s	1593×	body	2560	valid
1.9s	2768×	body	1280	valid
654.0ms	1882×	body	640	valid
219.0ms	934×	body	320	valid
74.0ms	460×	body	160	valid
34.0ms	363×	body	80	valid