Details

sample84.0ms

Algorithm

intervals

Results

34.0ms	95×	body	1280	valid
16.0ms	19×	body	2560	valid
13.0ms	61×	body	640	valid
5.0ms	39×	body	80	valid
4.0ms	30×	body	320	valid
1.0ms	12×	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 36.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.3b	(- (tan (+ x eps)) (tan x))
4.1b	(tan (+ x eps))

rewrite10.0ms

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))

series42.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

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

prune57.0ms

Filtered

31 candidates to 25 candidates (19.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 12.9b

Counts

32 → 7

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))
4.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite31.0ms

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

series196.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (33.0ms)

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

prune161.0ms

Filtered

98 candidates to 74 candidates (24.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	12	98
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Merged error: 12.8b

Counts

105 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
4.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
6.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan x) (sin eps))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
22.0ms	(/ (* (tan x) (sin eps)) (cos eps))
16.0ms	(* (tan x) (sin eps))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	385	785
1	1424	711
2	5001	699

prune118.0ms

Filtered

82 candidates to 60 candidates (26.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	82	14	96

Merged error: 12.8b

Counts

96 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(pow (* (tan x) (tan eps)) 3)
4.2b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
45×	`tan-quot`
21×	`add-exp-log` `frac-times` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
10×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up`
3×	`cube-div` `pow-unpow`
2×	`pow-pow` `flip3-+` `pow-plus` `pow-exp` `associate--l+` `*-commutative` `flip-+` `rem-cube-cbrt`
1×	`pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `distribute-lft-in` `diff-log` `unpow3` `cube-prod` `swap-sqr` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 114

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
5.0ms	(pow (* (tan x) (tan eps)) 3)
21.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series664.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (tan x) (tan eps))
32.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
40.0ms	(pow (* (tan x) (tan eps)) 3)
570.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify132.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	848	1703
1	4786	1486
2	5001	1486

prune173.0ms

Filtered

126 candidates to 77 candidates (38.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	130	10	140

Merged error: 0.3b

Counts

140 → 10

regimes172.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	114
1	63	114

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3370×	body	1280	valid
502.0ms	594×	body	2560	valid
392.0ms	1875×	body	640	valid
106.0ms	784×	body	320	valid
42.0ms	1035×	body	80	valid
33.0ms	342×	body	160	valid

Details

sample84.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series42.0ms

simplify74.0ms

prune57.0ms

localize11.0ms

rewrite31.0ms

series196.0ms

simplify42.0ms

prune161.0ms

localize16.0ms

rewrite34.0ms

series158.0ms

simplify40.0ms

prune118.0ms

localize19.0ms

rewrite45.0ms

series664.0ms

simplify132.0ms

prune173.0ms

regimes172.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

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