Details

analyze17.0s

Algorithm: search

sample126.0ms

Algorithm

intervals

Results

69.0ms	128×	body	1280	valid
18.0ms	256×	pre	80	true
15.0ms	58×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	5×	body	160	valid

simplify376.0ms

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: 13.4b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.1b	(+ x (- (tan (+ y z)) (tan a)))
2.9b	(tan (+ y z))

rewrite20.0ms

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))

series127.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (tan (+ y z)) (tan a))
42.0ms	(+ x (- (tan (+ y z)) (tan a)))
48.0ms	(tan (+ y z))

simplify38.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (12.0ms)

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

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 0.2b

Counts

52 → 8

localize16.0ms

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

rewrite38.0ms

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))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
7.0ms	(* (tan y) (tan z))

series296.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (tan y) (tan z))
123.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
129.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
22.0ms	(* (tan y) (tan z))

simplify75.0ms

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

prune158.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	67	12	79
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	74	13	87

Merged error: 0.1b

Counts

87 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

17.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
5.0ms	(* (tan y) (sin z))
20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
6.0ms	(/ (* (tan y) (sin z)) (cos z))

series293.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
16.0ms	(* (tan y) (sin z))
132.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
23.0ms	(/ (* (tan y) (sin z)) (cos z))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	391	1035
1	1334	960
2	5002	951

prune135.0ms

Filtered

61 candidates to 86 candidates (-41.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	88	11	99

Merged error: 0.1b

Counts

99 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

9.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
15.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
22.0ms	(* (tan y) (tan z))
22.0ms	(* (tan y) (tan z))
152.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	607	1601
1	2699	1448
2	5002	1435

prune121.0ms

Filtered

78 candidates to 99 candidates (-26.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Merged error: 0.1b

Counts

110 → 10

regimes567.0ms

Accuracy

0% (0.2b 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	30	22
1	30	22

end0.0ms

analyze16.1s

Algorithm: search

sample3.4s

Algorithm

intervals

Results

2.0s	3885×	body	1280	valid
512.0ms	8000×	pre	80	true
478.0ms	1980×	body	640	valid
117.0ms	704×	body	320	valid
61.0ms	1173×	body	80	valid
31.0ms	258×	body	160	valid

Details

analyze17.0s

sample126.0ms

simplify376.0ms

prune6.0ms

localize13.0ms

rewrite20.0ms

series127.0ms

simplify38.0ms

prune95.0ms

localize16.0ms

rewrite38.0ms

series296.0ms

simplify75.0ms

prune158.0ms

localize20.0ms

rewrite50.0ms

series293.0ms

simplify41.0ms

prune135.0ms

localize22.0ms

rewrite36.0ms

series470.0ms

simplify71.0ms

prune121.0ms

regimes567.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze16.1s

sample3.4s

Profiling