Details

sample3.9s

Algorithm

intervals

sampling

Space saved by range analysis: 99.760697%

Space saved by search: 99.760697%

Guaranteed chance to sample good point: 12.109375%

Results

53.0ms	119×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	65×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	9×	body	160	valid

simplify353.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune6.0ms

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: 11.5b

Counts

2 → 1

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.1b	(+ x (- (tan (+ y z)) (tan a)))
3.7b	(tan (+ y z))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 42

Calls

3 calls:

6.0ms	(- (tan (+ y z)) (tan a))
5.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(tan (+ y z))

series102.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (tan (+ y z)) (tan a))
40.0ms	(+ x (- (tan (+ y z)) (tan a)))
25.0ms	(tan (+ y z))

simplify37.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334

prune95.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(* (tan y) (tan z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

4.0ms	(+ (tan y) (tan z))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
12.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series285.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan y) (tan z))
116.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
127.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
22.0ms	(* (tan y) (tan z))

simplify74.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	367	860
1	1074	821
2	3057	814
3	5001	814

prune123.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 0.1b

Counts

86 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*l/`
16×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`frac-sub`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`flip3-+` `frac-add` `flip-+`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 92

Calls

4 calls:

8.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
14.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
24.0ms	(* (tan y) (tan z))
21.0ms	(* (tan y) (tan z))
146.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify85.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	655	1681
1	3093	1507
2	5001	1490

prune155.0ms

Filtered

83 candidates to 104 candidates (-25.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	104	7	111

Merged error: 0.1b

Counts

111 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
0.3b	(pow (* (tan y) (tan z)) 3)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
44×	`tan-quot`
27×	`associate-*l/`
26×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-*r/`
11×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow-pow` `flip3-+` `pow-plus` `div-exp` `frac-add` `pow-exp` `associate-/r/` `*-commutative` `flip-+` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `div-sub` `cube-prod` `swap-sqr` `clear-num` `associate-/r*` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
10.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
16.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
5.0ms	(pow (* (tan y) (tan z)) 3)

series271.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (tan y) (tan z))
31.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
181.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
38.0ms	(pow (* (tan y) (tan z)) 3)

simplify125.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	812	1495
1	4454	1335
2	5001	1331

prune200.0ms

Filtered

88 candidates to 139 candidates (-58.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	139	7	146

Merged error: 0.1b

Counts

146 → 7

regimes982.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	36
1	47	36
2	47	36

end0.0ms

sample6.9s

Algorithm

intervals

sampling

Space saved by range analysis: 99.760697%

Space saved by search: 99.760697%

Guaranteed chance to sample good point: 12.109375%

Results

1.7s	3915×	body	1280	valid
559.0ms	8000×	pre	80	true
471.0ms	1944×	body	640	valid
117.0ms	685×	body	320	valid
63.0ms	1165×	body	80	valid
33.0ms	291×	body	160	valid

Details

sample3.9s

simplify353.0ms

prune6.0ms

localize25.0ms

rewrite19.0ms

series102.0ms

simplify37.0ms

prune95.0ms

localize15.0ms

rewrite34.0ms

series285.0ms

simplify74.0ms

prune123.0ms

localize20.0ms

rewrite35.0ms

series267.0ms

simplify85.0ms

prune155.0ms

localize30.0ms

rewrite41.0ms

series271.0ms

simplify125.0ms

prune200.0ms

regimes982.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.9s

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