Details

sample163.0ms

Algorithm

intervals

Results

85.0ms	118×	body	1280	valid
38.0ms	20×	body	2560	valid
18.0ms	44×	body	640	valid
7.0ms	25×	body	320	valid
3.0ms	16×	body	160	valid
3.0ms	33×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
1.9b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series136.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify79.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune85.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
41.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series721.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (tan x) (tan eps))
203.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
88.0ms	(* (tan x) (tan eps))
341.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune284.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
10.5b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

12.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (+ (tan x) (tan eps)) (cos x))
88.0ms	(* (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
200.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	527	955
1	2405	907
2	5002	907

prune352.0ms

Filtered

94 candidates to 72 candidates (76.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (/ (* (sin eps) (cos x)) (cos eps)) (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
0.2b	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
0.2b	(pow (sin x) 2)
0.2b	(* (tan x) (tan eps))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
23×	`add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
10×	`add-cube-cbrt` `div-exp`
7×	`pow1`
6×	`cbrt-undiv` `cbrt-unprod`
5×	`times-frac` `associate-/l*`
4×	`tan-quot` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `pow-unpow` `associate-r` `associate-l` `associate-*l/` `pow-exp` `associate-/r/` `associate-/l/`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`
1×	`frac-times` `flip3--` `pow-pow` `flip3-+` `associate-r/` `pow-prod-down` `frac-add` `cos-mult` `-commutative` `flip--` `flip-+` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

36.0ms	(/ (+ (/ (* (sin eps) (cos x)) (cos eps)) (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
6.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
1.0ms	(pow (sin x) 2)
5.0ms	(* (tan x) (tan eps))

series517.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(/ (+ (/ (* (sin eps) (cos x)) (cos eps)) (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
98.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
18.0ms	(pow (sin x) 2)
89.0ms	(* (tan x) (tan eps))

simplify70.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	612	1386
1	2904	1160
2	5001	1160

prune363.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	35
1	46	35
2	46	35

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.5s	3273×	body	1280	valid
1.2s	693×	body	2560	valid
774.0ms	1793×	body	640	valid
223.0ms	742×	body	320	valid
103.0ms	1130×	body	80	valid
70.0ms	369×	body	160	valid