Details

sample476.0ms

Algorithm

intervals

Results

144.0ms	59×	body	2560	valid
48.0ms	91×	body	1280	valid
18.0ms	67×	body	640	valid
3.0ms	18×	body	320	valid
3.0ms	12×	body	160	valid
1.0ms	9×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- 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))

simplify59.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune237.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
16.8b	(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)))

series126.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 27/2800 (pow x 4) 1/2)
44.0ms	(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

prune74.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
16.8b	(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)))

series126.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 27/2800 (pow x 4) 1/2)
43.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify142.0ms

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

prune80.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.9b	(- x (sin x))
1.0b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
30.5b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite15.0ms

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:

1.0ms	(cbrt x)
4.0ms	(- x (sin x))
7.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt x)
30.0ms	(- x (sin x))
497.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
326.0ms	(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

prune251.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.3b

bsearch76.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	0.038683104185563734
8	-1.0806682141483241	-0.0004106978961831668	-0.03626982160086084

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	22
1	31	22

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.0s	1588×	body	2560	valid
1.6s	2763×	body	1280	valid
470.0ms	1925×	body	640	valid
148.0ms	903×	body	320	valid
57.0ms	461×	body	160	valid
31.0ms	360×	body	80	valid