Details

analyze782.0ms

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

sample88.0ms

Algorithm

intervals

Results

44.0ms	115×	body	1280	valid
17.0ms	68×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	21×	body	320	valid
1.0ms	31×	body	80	valid
1.0ms	7×	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: 39.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
4.2b	(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))

series41.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune68.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	20	10	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	10	31

Merged error: 12.2b

Counts

31 → 10

localize12.0ms

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))
2.4b	(- (/ (+ (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 → 85

Calls

4 calls:

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

series203.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
102.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5109	1560

prune182.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	82	15	97
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	89	18	107

Merged error: 12.0b

Counts

107 → 18

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (* (tan eps) (tan eps)))
0.3b	(* (tan eps) (tan eps))
2.4b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`tan-quot`
18×	`pow1`
16×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`frac-times` `associate-r/` `associate-l*`
7×	`associate-r`
6×	`associate-*l/` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `frac-sub` `cbrt-unprod`
3×	`swap-sqr` `*-commutative` `unswap-sqr`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 93

Calls

4 calls:

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

series388.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (tan x) (tan eps))
27.0ms	(* (tan x) (* (tan eps) (tan eps)))
9.0ms	(* (tan eps) (tan eps))
329.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4983	1620
1	4983	1620

prune380.0ms

Filtered

72 candidates to 105 candidates (-45.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	104	19	123

Merged error: 12.0b

Counts

123 → 19

localize20.0ms

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)
2.4b	(- (* (/ (+ (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))

rewrite48.0ms

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 → 113

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
7.0ms	(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))

series676.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (tan x) (tan eps))
32.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
36.0ms	(pow (* (tan x) (tan eps)) 3)
586.0ms	(- (* (/ (+ (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))

simplify42.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5033	2257

prune173.0ms

Filtered

78 candidates to 125 candidates (-60.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	9	9	18
Picked	1	0	1
Done	0	0	0
Total	131	13	144

Merged error: 10.5b

Counts

144 → 13

regimes203.0ms

Accuracy

63% (2.6b remaining)

Error of 15.1b against oracle of 12.5b and baseline of 19.6b

bsearch72.0ms

Steps

Iters	Range		Point
7	1.3583413253800626e-78	1.4284492369682818e-76	5.817203080719242e-77
6	-1.8181891631897414e-61	-1.6988373604368242e-62	-1.7248288871182305e-62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	175
1	94	175

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3323×	body	1280	valid
541.0ms	619×	body	2560	valid
417.0ms	1867×	body	640	valid
114.0ms	760×	body	320	valid
50.0ms	1102×	body	80	valid
32.0ms	329×	body	160	valid

Details

analyze782.0ms

sample88.0ms

simplify5.0ms

prune3.0ms

localize9.0ms

rewrite11.0ms

series41.0ms

simplify50.0ms

prune68.0ms

localize12.0ms

rewrite32.0ms

series203.0ms

simplify51.0ms

prune182.0ms

localize17.0ms

rewrite32.0ms

series388.0ms

simplify44.0ms

prune380.0ms

localize20.0ms

rewrite48.0ms

series676.0ms

simplify42.0ms

prune173.0ms

regimes203.0ms

bsearch72.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling