Details

sample560.0ms

Algorithm

intervals

Results

122.0ms	57×	body	2560	valid
86.0ms	104×	body	1280	valid
16.0ms	46×	body	640	valid
10.0ms	28×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	12×	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: 31.6b

localize11.0ms

Local error

Found 2 expressions with local error:

1.1b	(- x (tan x))
1.1b	(- x (sin x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff`
16×	`add-cube-cbrt`
6×	`fma-neg` `add-log-exp`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 56

Calls

2 calls:

6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series99.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- x (tan x))
48.0ms	(- x (sin x))

simplify93.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	258	487
1	749	305
2	3295	287
3	5001	203

prune119.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 30.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.1b	(- x (sin x))
2.0b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
28.6b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite32.0ms

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)
7.0ms	(- x (sin x))
21.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
28.0ms	(- x (sin x))
489.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
314.0ms	(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

prune286.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 28.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.5b	(/ (fma (sqrt x) (sqrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
14.8b	(fma (sqrt x) (sqrt x) (- (sin x)))
28.6b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `associate-/r` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `pow1/3` `div-exp` `clear-num` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
5.0ms	(/ (fma (sqrt x) (sqrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series774.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
187.0ms	(/ (fma (sqrt x) (sqrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
90.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
320.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	299	934
1	981	833
2	5002	764

prune314.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 27.9b

localize20.0ms

Local error

Found 4 expressions with local error:

14.8b	(fma (sqrt x) (sqrt x) (- (sin x)))
14.8b	(fma (sqrt x) (sqrt x) (- (sin x)))
14.8b	(fma (sqrt x) (sqrt x) (- (sin x)))
28.6b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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

4 → 40

Calls

4 calls:

0.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
0.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
0.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
85.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
88.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))
317.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	109	415
1	338	349
2	1526	329
3	5001	318

prune225.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 27.9b

regimes204.0ms

Accuracy

36.3% (2.1b remaining)

Error of 30.1b against oracle of 28.1b and baseline of 31.3b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	1604×	body	2560	valid
1.9s	2796×	body	1280	valid
648.0ms	1853×	body	640	valid
216.0ms	898×	body	320	valid
75.0ms	476×	body	160	valid
34.0ms	373×	body	80	valid