Details

sample3.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.993896%

Results

42.0ms	107×	body	1280	valid
18.0ms	20×	body	2560	valid
14.0ms	62×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 37.1b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

2.6b	(tan (+ x eps))
2.7b	(- (tan (+ x eps)) (tan x))

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:

3.0ms	(tan (+ x eps))
6.0ms	(- (tan (+ x eps)) (tan x))

series42.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(tan (+ x eps))
27.0ms	(- (tan (+ x eps)) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2481	199
4	5001	199

prune63.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	6	32

Merged error: 13.2b

Counts

32 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite33.0ms

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:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series198.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	994

prune161.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 13.1b

Counts

104 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.4b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
13.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series395.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
31.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
321.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	599	1358
1	3021	1222
2	5001	1222

prune169.0ms

Filtered

76 candidates to 122 candidates (-60.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	121	15	136

Merged error: 13.0b

Counts

136 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
9.3b	(- (* (+ (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)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ (tan x) (tan eps)) (cos x))
21.0ms	(* (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
50.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

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

prune115.0ms

Filtered

72 candidates to 94 candidates (-30.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 0.1b

Counts

109 → 10

regimes154.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	21
1	29	21

end0.0ms

sample5.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.993896%

Results

1.3s	3296×	body	1280	valid
562.0ms	649×	body	2560	valid
419.0ms	1891×	body	640	valid
104.0ms	713×	body	320	valid
49.0ms	1104×	body	80	valid
34.0ms	347×	body	160	valid

Details

sample3.2s

simplify4.0ms

prune3.0ms

localize11.0ms

rewrite11.0ms

series42.0ms

simplify77.0ms

prune63.0ms

localize11.0ms

rewrite33.0ms

series198.0ms

simplify44.0ms

prune161.0ms

localize14.0ms

rewrite37.0ms

series395.0ms

simplify77.0ms

prune169.0ms

localize20.0ms

rewrite28.0ms

series123.0ms

simplify69.0ms

prune115.0ms

regimes154.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.7s

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