Details

analyze806.0ms

Algorithm: search

sample86.0ms

Algorithm

intervals

Results

36.0ms	92×	body	1280	valid
18.0ms	20×	body	2560	valid
16.0ms	70×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	11×	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

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: 35.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
2.9b	(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))
3.0ms	(tan (+ x eps))

series44.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify76.0ms

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

prune65.0ms

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: 14.4b

Counts

32 → 9

localize12.0ms

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))))
0.3b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite29.0ms

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:

4.0ms	(+ (tan x) (tan eps))
7.0ms	(/ (+ (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))

series193.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
24.0ms	(* (tan x) (tan eps))
96.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

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

prune158.0ms

Filtered

74 candidates to 98 candidates (-32.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	93	14	107

Merged error: 14.3b

Counts

107 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
8.5b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
9.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ (tan x) (tan eps)) (cos x))
20.0ms	(* (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
52.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	527	955
1	2405	907
2	5002	907

prune149.0ms

Filtered

72 candidates to 94 candidates (-30.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	101	7	108

Merged error: 0.1b

Counts

108 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
23×	`add-cbrt-cube`
12×	`add-sqr-sqrt` `prod-exp`
10×	`add-cube-cbrt` `*-un-lft-identity` `div-exp`
7×	`pow1`
6×	`cbrt-undiv` `cbrt-unprod`
4×	`tan-quot` `times-frac` `associate-/r*` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `pow-unpow` `associate-r` `associate-l` `pow-exp`
2×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`
1×	`frac-times` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `cos-mult` `*-commutative` `sin-cos-mult` `associate-/l/` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

5.0ms	(/ (* (sin eps) (cos x)) (cos eps))
8.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
5.0ms	(* (tan x) (tan eps))
3.0ms	(pow (sin x) 2)

series62.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (* (sin eps) (cos x)) (cos eps))
24.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
21.0ms	(* (tan x) (tan eps))
4.0ms	(pow (sin x) 2)

simplify62.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	499	716
1	2434	579
2	5001	579

prune127.0ms

Filtered

64 candidates to 99 candidates (-54.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	89	10	99
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	91	15	106

Merged error: 0.0b

Counts

106 → 15

regimes209.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	23
1	29	23

end0.0ms

analyze799.0ms

Algorithm: search

sample2.7s

Algorithm

intervals

Results

1.3s	3217×	body	1280	valid
575.0ms	648×	body	2560	valid
415.0ms	1834×	body	640	valid
115.0ms	774×	body	320	valid
59.0ms	1168×	body	80	valid
38.0ms	359×	body	160	valid

Details

analyze806.0ms

sample86.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series44.0ms

simplify76.0ms

prune65.0ms

localize12.0ms

rewrite29.0ms

series193.0ms

simplify47.0ms

prune158.0ms

localize23.0ms

rewrite28.0ms

series118.0ms

simplify69.0ms

prune149.0ms

localize31.0ms

rewrite23.0ms

series62.0ms

simplify62.0ms

prune127.0ms

regimes209.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze799.0ms

sample2.7s

Profiling