Details

analyze806.0ms

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

sample86.0ms

Algorithm

intervals

Results

38.0ms	103×	body	1280	valid
21.0ms	24×	body	2560	valid
11.0ms	52×	body	640	valid
4.0ms	27×	body	320	valid
2.0ms	38×	body	80	valid
1.0ms	12×	body	160	valid

simplify4.0ms

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: 37.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite15.0ms

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:

11.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series41.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify46.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune65.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 15.3b

Counts

31 → 8

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))
2.6b	(- (/ (+ (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 → 85

Calls

4 calls:

6.0ms	(+ (tan x) (tan eps))
8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (tan x) (tan eps))
58.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(* (tan x) (tan eps))
102.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5109	1560

prune173.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	13	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 15.2b

Counts

105 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

12.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
5.0ms	(* (sin x) (sin eps))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
19.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
9.0ms	(* (sin x) (sin eps))
23.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
104.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4991	2589
1	4991	2589

prune146.0ms

Filtered

82 candidates to 120 candidates (-46.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 13.1b

Counts

136 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
3.8b	(+ (/ 1 (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) -1)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
55×	`times-frac`
44×	`*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`add-exp-log` `add-cbrt-cube`
26×	`associate-r` `associate-l`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`div-inv` `add-log-exp`
3×	`difference-of-sqr--1` `associate-/r` `associate-/l`
2×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `distribute-lft-out`
1×	`+-commutative` `quot-tan` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`

Counts

4 → 144

Calls

4 calls:

4.0ms	(/ (sin x) (cos x))
11.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
10.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
9.0ms	(+ (/ 1 (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) -1)

series88.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (sin x) (cos x))
24.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
22.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
36.0ms	(+ (/ 1 (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) -1)

simplify52.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5129	2115

prune166.0ms

Filtered

115 candidates to 156 candidates (-35.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	154	10	164

Merged error: 13.1b

Counts

164 → 10

regimes144.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	43
1	62	43

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3218×	body	1280	valid
578.0ms	663×	body	2560	valid
407.0ms	1841×	body	640	valid
114.0ms	771×	body	320	valid
52.0ms	1132×	body	80	valid
37.0ms	375×	body	160	valid

Details

analyze806.0ms

sample86.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite15.0ms

series41.0ms

simplify46.0ms

prune65.0ms

localize11.0ms

rewrite33.0ms

series203.0ms

simplify49.0ms

prune173.0ms

localize22.0ms

rewrite47.0ms

series197.0ms

simplify48.0ms

prune146.0ms

localize22.0ms

rewrite41.0ms

series88.0ms

simplify52.0ms

prune166.0ms

regimes144.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling