Details

analyze2.4s

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 24.993896%

sample87.0ms

Algorithm

intervals

Results

42.0ms	111×	body	1280	valid
16.0ms	19×	body	2560	valid
13.0ms	61×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	31×	body	80	valid
1.0ms	14×	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

prune6.0ms

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: 37.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
3.9b	(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))

series43.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- (tan (+ x eps)) (tan x))
18.0ms	(tan (+ x eps))

simplify83.0ms

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	2482	199
4	5001	199

prune77.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	22	9	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	9	32

Merged error: 15.5b

Counts

32 → 9

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))
3.2b	(- (/ (+ (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:

7.0ms	(/ (+ (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))

series202.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(+ (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
101.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

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

prune176.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	83	15	98
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	88	19	107

Merged error: 15.4b

Counts

107 → 19

localize17.0ms

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)))
3.2b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite35.0ms

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

series403.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
34.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
324.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify80.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune183.0ms

Filtered

76 candidates to 122 candidates (-60.5%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	3	15	18
Picked	0	1	1
Done	0	0	0
Total	121	20	141

Merged error: 15.4b

Counts

141 → 20

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
8.1b	(- (* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x)) (* (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (sin x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

87×	`pow1`
86×	`associate-*l/`
82×	`tan-quot`
52×	`frac-times`
37×	`pow-prod-down`
33×	`add-exp-log` `add-cbrt-cube`
28×	`associate-*r/`
22×	`frac-sub`
21×	`flip3-+` `flip-+`
19×	`prod-exp` `cbrt-unprod`
12×	`flip3--` `flip--`
9×	`frac-add`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
4×	`pow-plus`
3×	`associate-l` `*-commutative`
2×	`pow2` `swap-sqr`
1×	`sub-neg` `diff-log`

Counts

4 → 161

Calls

4 calls:

11.0ms	(* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x))
10.0ms	(* (* (tan x) (tan eps)) (* (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)))) (cos x)) (* (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (sin x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x))
30.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
31.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
126.0ms	(- (* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x)) (* (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (sin x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1332	3359
1	5001	3192

prune231.0ms

Filtered

102 candidates to 173 candidates (-69.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	168	5	173
Fresh	15	3	18
Picked	1	0	1
Done	0	1	1
Total	184	9	193

Merged error: 0.2b

Counts

193 → 9

regimes165.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	45
1	47	45

end0.0ms

analyze2.4s

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 24.993896%

sample2.6s

Algorithm

intervals

Results

1.3s	3241×	body	1280	valid
564.0ms	659×	body	2560	valid
400.0ms	1840×	body	640	valid
106.0ms	768×	body	320	valid
50.0ms	1150×	body	80	valid
32.0ms	342×	body	160	valid

Details

analyze2.4s

sample87.0ms

simplify4.0ms

prune6.0ms

localize8.0ms

rewrite10.0ms

series43.0ms

simplify83.0ms

prune77.0ms

localize11.0ms

rewrite33.0ms

series202.0ms

simplify46.0ms

prune176.0ms

localize17.0ms

rewrite35.0ms

series403.0ms

simplify80.0ms

prune183.0ms

localize25.0ms

rewrite53.0ms

series243.0ms

simplify55.0ms

prune231.0ms

regimes165.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze2.4s

sample2.6s

Profiling