Details

sample88.0ms

Algorithm

intervals

Results

39.0ms	106×	body	1280	valid
23.0ms	26×	body	2560	valid
11.0ms	50×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	34×	body	80	valid
1.0ms	13×	body	160	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: 36.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (tan (+ x eps)) (tan x))
4.6b	(tan (+ x eps))

rewrite13.0ms

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:

9.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series132.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(tan (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (21.0ms)

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

prune75.0ms

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: 14.6b

Counts

32 → 7

localize13.0ms

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))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite30.0ms

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

series716.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
87.0ms	(+ (tan x) (tan eps))
87.0ms	(* (tan x) (tan eps))
342.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune248.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 14.5b

Counts

105 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(* (sin x) (sin eps))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
17.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series543.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
48.0ms	(* (sin x) (sin eps))
95.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
361.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	406	926
1	1897	794
2	5001	794

prune285.0ms

Filtered

89 candidates to 61 candidates (68.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 14.5b

Counts

105 → 16

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.2b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
4.7b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
104×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
23×	`associate-/r*`
19×	`add-exp-log`
16×	`associate-/r/` `distribute-lft-out`
15×	`tan-quot`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `pow-flip` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 178

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
8.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
10.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
25.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series950.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan x) (tan eps))
271.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
226.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
360.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify86.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	703	2793
1	3294	2509
2	5001	2506

prune314.0ms

Filtered

190 candidates to 105 candidates (55.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	187	19	206

Merged error: 14.4b

Counts

206 → 19

regimes174.0ms

Accuracy

88.3% (0.8b remaining)

Error of 14.7b against oracle of 13.9b and baseline of 21.0b

bsearch125.0ms

Steps

Iters	Range		Point
7	6.36136280187789e-24	8.2289824352113225e-22	9.19032739794849e-24
10	-7.66540900750845e-16	-4.646653718895944e-33	-6.149362912317085e-28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	50
1	53	50

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3319×	body	1280	valid
531.0ms	603×	body	2560	valid
420.0ms	1839×	body	640	valid
114.0ms	771×	body	320	valid
56.0ms	1104×	body	80	valid
37.0ms	364×	body	160	valid