Details

sample452.0ms

Algorithm

intervals

Results

117.0ms	59×	body	2560	valid
42.0ms	68×	body	1280	valid
21.0ms	61×	body	640	valid
11.0ms	42×	body	320	valid
3.0ms	16×	body	160	valid
1.0ms	10×	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: 32.2b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

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 (sin x))
5.0ms	(- x (tan x))

series170.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- x (sin x)) (- x (tan x)))
35.0ms	(- x (sin x))
60.0ms	(- x (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune235.0ms

Pruning

3 alts after pruning (2 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)
14.6b	(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)))

series127.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 27/2800 (pow x 4) 1/2)
45.0ms	(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

prune72.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
14.6b	(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)))

series123.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(fma 27/2800 (pow x 4) 1/2)
42.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify143.0ms

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

prune85.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (fma (sqrt x) (sqrt x) (- (tan x))))
2.3b	(- x (sin x))
14.8b	(fma (sqrt x) (sqrt x) (- (tan x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

9.0ms	(/ (- x (sin x)) (fma (sqrt x) (sqrt x) (- (tan x))))
4.0ms	(- x (sin x))
0.0ms	(fma (sqrt x) (sqrt x) (- (tan x)))

series296.0ms

Counts

3 → 9

Calls

3 calls:

160.0ms	(/ (- x (sin x)) (fma (sqrt x) (sqrt x) (- (tan x))))
34.0ms	(- x (sin x))
102.0ms	(fma (sqrt x) (sqrt x) (- (tan x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	415	1008
1	1630	865
2	5001	837

prune206.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch77.0ms

Steps

Iters	Range		Point
7	0.003064448021395057	0.16998237910242062	0.028890275250899152
10	-4.508778152722845	-1.8057709034692785e-13	-0.030137210439935006

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1609×	body	2560	valid
1.9s	2735×	body	1280	valid
629.0ms	1888×	body	640	valid
220.0ms	933×	body	320	valid
76.0ms	448×	body	160	valid
37.0ms	387×	body	80	valid