Details

sample82.0ms

Algorithm

intervals

Results

35.0ms	100×	body	1280	valid
19.0ms	22×	body	2560	valid
12.0ms	58×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	38×	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: 35.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (tan (+ x eps)) (tan x))
3.1b	(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:

9.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series150.0ms

Counts

2 → 6

Calls

2 calls:

102.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(tan (+ x eps))

simplify101.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (36.0ms)

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

prune81.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 14.3b

Counts

32 → 8

localize15.0ms

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))))
0.2b	(* (tan x) (tan eps))
1.5b	(- (/ (+ (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:

5.0ms	(+ (tan x) (tan eps))
9.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series970.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (tan x) (tan eps))
217.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
107.0ms	(* (tan x) (tan eps))
555.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

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

prune273.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	89	17	106

Merged error: 14.2b

Counts

106 → 17

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
6.4b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite29.0ms

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)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (+ (tan x) (tan eps)) (cos x))
89.0ms	(* (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
206.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (14.0ms)

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

prune343.0ms

Filtered

94 candidates to 72 candidates (76.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	13	3	16
Picked	1	0	1
Done	0	0	0
Total	100	11	111

Merged error: 0.1b

Counts

111 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

6.0ms	(* (pow (sin x) 2) (sin eps))
11.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
5.0ms	(* (tan x) (tan eps))
3.0ms	(pow (sin x) 2)

series259.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (pow (sin x) 2) (sin eps))
99.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
90.0ms	(* (tan x) (tan eps))
18.0ms	(pow (sin x) 2)

simplify57.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	443	718
1	2027	593
2	5001	593

prune372.0ms

Filtered

104 candidates to 66 candidates (63.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 0.0b

Counts

115 → 11

regimes131.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	21
1	28	21

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3280×	body	1280	valid
563.0ms	641×	body	2560	valid
408.0ms	1830×	body	640	valid
121.0ms	803×	body	320	valid
51.0ms	1110×	body	80	valid
34.0ms	336×	body	160	valid