Details

sample317.0ms

Algorithm

intervals

Results

9.0ms	35×	body	1280	valid
8.0ms	39×	body	640	valid
5.0ms	151×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify13.0ms

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

prune6.0ms

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:

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

rewrite46.0ms

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:

26.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series242.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
41.0ms	(- 1.0 (* (tan x) (tan x)))
45.0ms	(* (tan x) (tan x))
49.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune410.0ms

Filtered

117 candidates to 77 candidates (34.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series228.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- 1.0 (* (tan x) (tan x)))
109.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
37.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	545	2148
1	2567	1966
2	5001	1864

prune524.0ms

Filtered

177 candidates to 89 candidates (49.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	177	12	189

Merged error: 0.0b

Counts

189 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

16.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
4.0ms	(+ (sqrt 1.0) (tan x))
11.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series461.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(+ (sqrt 1.0) (tan x))
146.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
38.0ms	(* (tan x) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	517	1120
1	2851	938
2	5001	923

prune511.0ms

Filtered

117 candidates to 81 candidates (30.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	117	12	129

Merged error: 0.0b

Counts

129 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac`
60×	`unpow-prod-down`
50×	`add-sqr-sqrt`
48×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `unpow2` `sqr-pow`
13×	`pow1`
9×	`div-exp`
8×	`pow-to-exp` `pow-exp` `associate-/r` `add-cbrt-cube` `associate-/l`
6×	`pow-unpow`
4×	`tan-quot` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`pow-pow`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 164

Calls

4 calls:

7.0ms	(/ (pow (sin x) 2) (pow (cos x) 2))
2.0ms	(pow (sin x) 2)
5.0ms	(* (tan x) (tan x))
2.0ms	(pow (cos x) 2)

series146.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (pow (sin x) 2) (pow (cos x) 2))
23.0ms	(pow (sin x) 2)
38.0ms	(* (tan x) (tan x))
25.0ms	(pow (cos x) 2)

simplify49.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	375	1244
1	1542	1063
2	5002	1029

prune746.0ms

Filtered

176 candidates to 88 candidates (50.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	176	12	188

Merged error: 0.0b

Counts

188 → 12

regimes267.0ms

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	12	10
1	12	10

end0.0ms

sample988.0ms

Algorithm

intervals

Results

390.0ms	1532×	body	1280	valid
201.0ms	1229×	body	640	valid
153.0ms	4317×	body	80	valid
74.0ms	628×	body	320	valid
24.0ms	294×	body	160	valid

Details

sample317.0ms

simplify13.0ms

prune6.0ms

localize10.0ms

rewrite46.0ms

series242.0ms

simplify44.0ms

prune410.0ms

localize9.0ms

rewrite28.0ms

series228.0ms

simplify75.0ms

prune524.0ms

localize10.0ms

rewrite40.0ms

series461.0ms

simplify78.0ms

prune511.0ms

localize15.0ms

rewrite23.0ms

series146.0ms

simplify49.0ms

prune746.0ms

regimes267.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample988.0ms

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