Details

analyze17.3s

Algorithm

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0%	0.2%	99.8%	3
0%	0.2%	99.8%	4
0%	0.2%	99.8%	5
0%	0.2%	99.8%	6
0%	0.2%	99.8%	7
0%	0.2%	99.8%	8
0%	0.2%	99.8%	9
0%	0.2%	99.8%	10
0%	0.2%	99.8%	11
0%	0.2%	99.8%	12
0%	0.2%	99.8%	13
0%	0.2%	99.8%	14

sample110.0ms

Algorithm

intervals

Results

51.0ms	118×	body	1280	valid
18.0ms	256×	pre	80	true
17.0ms	71×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	6×	body	160	valid

simplify441.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	185	9
1	185	9

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: 13.0b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
1.1b	(tan (+ y z))

rewrite21.0ms

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` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `associate-+r+` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 40

Calls

3 calls:

5.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series111.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ x (- (tan (+ y z)) (tan a)))
46.0ms	(- (tan (+ y z)) (tan a))
25.0ms	(tan (+ y z))

simplify69.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4916	561
1	4916	561

prune101.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	40	9	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Merged error: 0.1b

Counts

50 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.3b	(* (tan y) (tan z))

rewrite36.0ms

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` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `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 → 65

Calls

4 calls:

6.0ms	(+ (tan y) (tan z))
12.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series282.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (tan y) (tan z))
124.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
115.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(* (tan y) (tan z))

simplify33.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4951	1271
1	4951	1271

prune159.0ms

Filtered

60 candidates to 77 candidates (-28.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	75	11	86

Merged error: 0.1b

Counts

86 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

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` `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-` `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 → 72

Calls

4 calls:

20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan z) (sin y)) (cos y)))) (tan a)))
6.0ms	(/ (* (tan z) (sin y)) (cos y))
18.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan z) (sin y)) (cos y)))) (tan a))
5.0ms	(* (tan z) (sin y))

series281.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan z) (sin y)) (cos y)))) (tan a)))
22.0ms	(/ (* (tan z) (sin y)) (cos y))
117.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan z) (sin y)) (cos y)))) (tan a))
15.0ms	(* (tan z) (sin y))

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4941	1475
1	4941	1475

prune142.0ms

Filtered

65 candidates to 84 candidates (-29.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 0.1b

Counts

95 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
0.3b	(* (tan y) (tan z))
0.4b	(pow (* (tan y) (tan z)) 3)
22.7b	(cbrt (pow (* (tan y) (tan z)) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

22.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
5.0ms	(* (tan y) (tan z))
5.0ms	(pow (* (tan y) (tan z)) 3)
4.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

series196.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
21.0ms	(* (tan y) (tan z))
37.0ms	(pow (* (tan y) (tan z)) 3)
22.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

simplify45.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4941	1085
1	4941	1085

prune108.0ms

Filtered

67 candidates to 93 candidates (-38.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 0.1b

Counts

103 → 10

regimes667.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3878×	body	1280	valid
543.0ms	8000×	pre	80	true
498.0ms	1989×	body	640	valid
127.0ms	739×	body	320	valid
58.0ms	1132×	body	80	valid
32.0ms	262×	body	160	valid

Details

analyze17.3s

sample110.0ms

simplify441.0ms

prune6.0ms

localize13.0ms

rewrite21.0ms

series111.0ms

simplify69.0ms

prune101.0ms

localize16.0ms

rewrite36.0ms

series282.0ms

simplify33.0ms

prune159.0ms

localize21.0ms

rewrite51.0ms

series281.0ms

simplify59.0ms

prune142.0ms

localize21.0ms

rewrite38.0ms

series196.0ms

simplify45.0ms

prune108.0ms

regimes667.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling