Details

sample91.0ms

Algorithm

intervals

Results

50.0ms	119×	body	1280	valid
16.0ms	19×	body	2560	valid
12.0ms	59×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	32×	body	80	valid
1.0ms	6×	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: 39.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite14.0ms

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:

10.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series134.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(tan (+ x eps))

simplify75.0ms

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

prune78.0ms

Filtered

31 candidates to 25 candidates (80.6%)

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: 14.0b

Counts

32 → 9

localize15.0ms

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))
0.7b	(- (/ (+ (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))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series715.0ms

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))
340.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

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

prune450.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	91	16	107

Merged error: 13.8b

Counts

107 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite37.0ms

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)))
18.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series522.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
46.0ms	(* (sin x) (sin eps))
92.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
346.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (10.0ms)

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

prune262.0ms

Filtered

89 candidates to 61 candidates (68.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	88	17	105

Merged error: 13.8b

Counts

105 → 17

localize14.0ms

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)))
0.7b	(- (* (/ (+ (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))

series1.2s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
107.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
870.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify82.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (17.0ms)

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

prune248.0ms

Filtered

122 candidates to 75 candidates (61.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	122	17	139

Merged error: 13.8b

Counts

139 → 17

regimes188.0ms

Accuracy

88.8% (0.8b remaining)

Error of 15.3b against oracle of 14.5b and baseline of 22.1b

bsearch112.0ms

Steps

Iters	Range		Point
7	2.623101215263658e-80	1.9599541972758083e-78	1.9335546041671055e-78
9	-6.669138218872808e-16	-2.3250751478766463e-21	-9.854486921118871e-19

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	18
1	38	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3281×	body	1280	valid
548.0ms	631×	body	2560	valid
399.0ms	1888×	body	640	valid
107.0ms	785×	body	320	valid
46.0ms	1088×	body	80	valid
31.0ms	327×	body	160	valid