Details

sample41.0ms

Algorithm

intervals

Results

11.0ms	43×	body	1280	valid
8.0ms	43×	body	640	valid
8.0ms	141×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune203.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series71.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
8.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5002	824

prune184.0ms

Filtered

117 candidates to 77 candidates (34.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.1b

Counts

118 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

4.0ms	(- (sqrt 1.0) (tan x))
4.0ms	(+ (sqrt 1.0) (tan x))
13.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series39.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
7.0ms	(+ (sqrt 1.0) (tan x))
17.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
8.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	328	693
1	1582	618
2	5001	607

prune177.0ms

Filtered

101 candidates to 67 candidates (33.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	99	13	112

Merged error: 0.0b

Counts

112 → 13

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
15.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))
51.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	266	869
1	914	800
2	5002	784

prune144.0ms

Filtered

118 candidates to 69 candidates (41.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	116	15	131

Merged error: 0.0b

Counts

131 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`times-frac`
11×	`pow1`
10×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
5×	`sqrt-prod` `distribute-lft-out--`
4×	`tan-quot`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `frac-times` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

4.0ms	(- (sqrt 1.0) (tan x))
4.0ms	(+ (sqrt 1.0) (tan x))
8.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
7.0ms	(+ (sqrt 1.0) (tan x))
23.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
9.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	368	955
1	1554	891
2	5001	879

prune155.0ms

Filtered

110 candidates to 73 candidates (33.6%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	11	12
Picked	0	1	1
Done	0	2	2
Total	110	15	125

Merged error: 0.0b

Counts

125 → 15

regimes266.0ms

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	13	12
1	13	12

end0.0ms

sample1.0s

Algorithm

intervals

Results

382.0ms	1493×	body	1280	valid
210.0ms	1243×	body	640	valid
170.0ms	4284×	body	80	valid
78.0ms	659×	body	320	valid
27.0ms	321×	body	160	valid

Details

sample41.0ms

simplify18.0ms

prune203.0ms

localize10.0ms

rewrite25.0ms

series71.0ms

simplify44.0ms

prune184.0ms

localize11.0ms

rewrite29.0ms

series39.0ms

simplify50.0ms

prune177.0ms

localize8.0ms

rewrite32.0ms

series79.0ms

simplify38.0ms

prune144.0ms

localize13.0ms

rewrite24.0ms

series46.0ms

simplify48.0ms

prune155.0ms

regimes266.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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