Details

sample88.0ms

Algorithm

intervals

Results

36.0ms	101×	body	1280	valid
24.0ms	29×	body	2560	valid
10.0ms	52×	body	640	valid
4.0ms	15×	body	160	valid
3.0ms	23×	body	320	valid
2.0ms	36×	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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
2.9b	(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:

6.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series134.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(tan (+ x eps))

simplify82.0ms

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

prune86.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	22	9	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	9	32

Merged error: 17.4b

Counts

32 → 9

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))))
0.3b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

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:

4.0ms	(+ (tan x) (tan eps))
8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series726.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (tan x) (tan eps))
205.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
87.0ms	(* (tan x) (tan eps))
347.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

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

prune238.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	93	14	107

Merged error: 17.3b

Counts

107 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
7.1b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

8.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
8.0ms	(* (tan x) (tan eps))
11.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
25.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series884.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
86.0ms	(* (tan x) (tan eps))
201.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
342.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify85.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	703	2793
1	3290	2509
2	5001	2506

prune334.0ms

Filtered

190 candidates to 105 candidates (55.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	181	9	190
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	190	14	204

Merged error: 17.3b

Counts

204 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
10.4b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite28.0ms

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:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
9.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (+ (tan x) (tan eps)) (cos x))
91.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
204.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (14.0ms)

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

prune291.0ms

Filtered

94 candidates to 72 candidates (76.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	102	6	108

Merged error: 0.2b

Counts

108 → 6

regimes97.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	21
1	29	21

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	3239×	body	1280	valid
554.0ms	654×	body	2560	valid
402.0ms	1857×	body	640	valid
109.0ms	787×	body	320	valid
47.0ms	1114×	body	80	valid
34.0ms	349×	body	160	valid

Details

sample88.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite11.0ms

series134.0ms

simplify82.0ms

prune86.0ms

localize11.0ms

rewrite32.0ms

series726.0ms

simplify45.0ms

prune238.0ms

localize12.0ms

rewrite58.0ms

series884.0ms

simplify85.0ms

prune334.0ms

localize21.0ms

rewrite28.0ms

series499.0ms

simplify78.0ms

prune291.0ms

regimes97.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling