Details

analyze775.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample99.0ms

Algorithm

intervals

Results

49.0ms	113×	body	1280	valid
16.0ms	18×	body	2560	valid
14.0ms	59×	body	640	valid
6.0ms	31×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

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: 39.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
3.6b	(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 → 24

Calls

2 calls:

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

series39.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (tan (+ x eps)) (tan x))
15.0ms	(tan (+ x eps))

simplify49.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune65.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 14.5b

Counts

31 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (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 → 85

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

series193.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (+ (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))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5109	1560

prune176.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	81	16	97
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	88	18	106

Merged error: 14.3b

Counts

106 → 18

localize20.0ms

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))
9.1b	(+ (* (+ (tan x) (tan eps)) (cos x)) (* (sin x) (+ (* (tan x) (tan eps)) -1)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
11×	`associate-*l/`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r` `frac-add`
8×	`associate-*r/`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sum-log` `distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(+ (* (+ (tan x) (tan eps)) (cos x)) (* (sin x) (+ (* (tan x) (tan eps)) -1)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ (tan x) (tan eps)) (cos x))
21.0ms	(* (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
52.0ms	(+ (* (+ (tan x) (tan eps)) (cos x)) (* (sin x) (+ (* (tan x) (tan eps)) -1)))

simplify40.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5015	1412

prune167.0ms

Filtered

74 candidates to 95 candidates (-28.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	12	5	17
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 0.2b

Counts

113 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
0.2b	(* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x))))
0.2b	(* (tan x) (tan eps))
0.3b	(pow (sin x) 2)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
32×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt` `associate-l`
11×	`times-frac`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1` `cbrt-undiv` `div-exp`
7×	`associate-r`
5×	`frac-times` `associate-r/` `associate-l/` `associate-/l/`
4×	`tan-quot` `flip3-+` `flip-+` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `unswap-sqr`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `pow-exp` `clear-num` `associate-/r` `flip--` `distribute-lft-out` `associate-/l` `unpow2` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

20.0ms	(/ (* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
16.0ms	(* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x))))
5.0ms	(* (tan x) (tan eps))
3.0ms	(pow (sin x) 2)

series136.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
34.0ms	(* (/ (sin eps) (cos eps)) (+ (cos x) (/ (pow (sin x) 2) (cos x))))
21.0ms	(* (tan x) (tan eps))
4.0ms	(pow (sin x) 2)

simplify39.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5369	2052

prune164.0ms

Filtered

83 candidates to 122 candidates (-47.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	10	122
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 0.0b

Counts

132 → 13

regimes187.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	51	33
1	51	33

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3297×	body	1280	valid
550.0ms	647×	body	2560	valid
390.0ms	1828×	body	640	valid
105.0ms	749×	body	320	valid
51.0ms	1096×	body	80	valid
35.0ms	383×	body	160	valid

Details

analyze775.0ms

sample99.0ms

simplify5.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series39.0ms

simplify49.0ms

prune65.0ms

localize13.0ms

rewrite31.0ms

series193.0ms

simplify49.0ms

prune176.0ms

localize20.0ms

rewrite30.0ms

series120.0ms

simplify40.0ms

prune167.0ms

localize24.0ms

rewrite46.0ms

series136.0ms

simplify39.0ms

prune164.0ms

regimes187.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

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