Details

sample111.0ms

Algorithm

intervals

Results

53.0ms	100×	body	1280	valid
25.0ms	23×	body	2560	valid
15.0ms	58×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	21×	body	160	valid
2.0ms	30×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 40.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (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))

series142.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
52.0ms	(tan (+ x eps))

simplify87.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune87.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 16.7b

Counts

32 → 7

localize19.0ms

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))
4.1b	(- (/ (+ (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 → 86

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))

series726.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
88.0ms	(+ (tan x) (tan eps))
87.0ms	(* (tan x) (tan eps))
343.0ms	(- (/ (+ (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	995

prune254.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	93	12	105

Merged error: 16.6b

Counts

105 → 12

localize24.0ms

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))
10.6b	(- (* (+ (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)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (+ (tan x) (tan eps)) (cos x))
91.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
204.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (15.0ms)

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

prune354.0ms

Filtered

94 candidates to 72 candidates (76.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 0.1b

Counts

106 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
23×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`prod-exp`
11×	`add-cube-cbrt`
10×	`div-exp`
8×	`associate-l`
7×	`unpow-prod-down`
6×	`cbrt-undiv` `cbrt-unprod`
5×	`pow1` `times-frac` `associate-/l*`
4×	`pow-to-exp` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `associate-r` `associate-/r/` `associate-/l/` `unpow2` `sqr-pow`
2×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `div-inv` `distribute-lft-out`
1×	`flip3--` `pow-pow` `flip3-+` `frac-add` `cos-mult` `*-commutative` `flip--` `flip-+`

Counts

4 → 99

Calls

4 calls:

6.0ms	(* (pow (sin x) 2) (sin eps))
15.0ms	(/ (+ (/ (* (sin eps) (cos x)) (cos eps)) (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
8.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
3.0ms	(pow (sin x) 2)

series495.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (pow (sin x) 2) (sin eps))
325.0ms	(/ (+ (/ (* (sin eps) (cos x)) (cos eps)) (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
102.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
19.0ms	(pow (sin x) 2)

simplify85.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	583	1451
1	2845	1211
2	5001	1211

prune392.0ms

Filtered

111 candidates to 71 candidates (64.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	103	17	120

Merged error: 0.0b

Counts

120 → 17

regimes209.0ms

Accuracy

0% (0.4b 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	31	22
1	31	22

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3331×	body	1280	valid
530.0ms	608×	body	2560	valid
417.0ms	1878×	body	640	valid
109.0ms	738×	body	320	valid
50.0ms	1100×	body	80	valid
34.0ms	345×	body	160	valid