Details

analyze17.0s

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

sample107.0ms

Algorithm

intervals

Results

49.0ms	117×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	66×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	9×	body	160	valid

simplify445.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	185	9
1	185	9

prune5.0ms

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: 13.5b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.0b	(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:

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

series118.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ x (- (tan (+ y z)) (tan a)))
51.0ms	(- (tan (+ y z)) (tan a))
26.0ms	(tan (+ y z))

simplify66.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4916	561
1	4916	561

prune96.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 0.2b

Counts

50 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

9.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
14.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series335.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
132.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
123.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
23.0ms	(* (tan y) (tan z))

simplify54.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5084	1882

prune189.0ms

Filtered

75 candidates to 100 candidates (-33.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	91	9	100
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 0.1b

Counts

108 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

16×	`tan-quot` `associate-*l/` `frac-add`
14×	`add-sqr-sqrt` `associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `add-log-exp`
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×	`+-commutative` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*` `sum-log` `flip--` `div-inv`

Counts

4 → 92

Calls

4 calls:

11.0ms	(+ (* (+ (tan y) (tan z)) (cos a)) (* (sin a) (+ (* (tan y) (tan z)) -1)))
18.0ms	(/ (+ (* (+ (tan y) (tan z)) (cos a)) (* (sin a) (+ (* (tan y) (tan z)) -1))) (* (- 1 (* (tan y) (tan z))) (cos a)))
7.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series281.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* (+ (tan y) (tan z)) (cos a)) (* (sin a) (+ (* (tan y) (tan z)) -1)))
154.0ms	(/ (+ (* (+ (tan y) (tan z)) (cos a)) (* (sin a) (+ (* (tan y) (tan z)) -1))) (* (- 1 (* (tan y) (tan z))) (cos a)))
23.0ms	(* (tan y) (tan z))
23.0ms	(* (tan y) (tan z))

simplify47.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4994	2336
1	4994	2336

prune179.0ms

Filtered

84 candidates to 104 candidates (-23.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	104	14	118

Merged error: 0.1b

Counts

118 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (* (tan y) (* (tan z) (tan z))))
0.2b	(* (tan y) (* (tan z) (tan z)))
0.3b	(* (tan z) (tan z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

52×	`tan-quot`
27×	`pow1`
24×	`frac-times` `associate-*r/`
22×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l` `associate-l/`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`associate-r`
4×	`*-commutative` `add-log-exp`
3×	`swap-sqr` `unswap-sqr`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 111

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
12.0ms	(* (tan y) (* (tan y) (* (tan z) (tan z))))
8.0ms	(* (tan y) (* (tan z) (tan z)))
6.0ms	(* (tan z) (tan z))

series96.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (tan y) (tan z))
36.0ms	(* (tan y) (* (tan y) (* (tan z) (tan z))))
28.0ms	(* (tan y) (* (tan z) (tan z)))
9.0ms	(* (tan z) (tan z))

simplify34.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5327	1077

prune113.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	123	14	137

Merged error: 0.1b

Counts

137 → 14

regimes986.0ms

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	53	32
1	53	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	3965×	body	1280	valid
533.0ms	8000×	pre	80	true
468.0ms	1931×	body	640	valid
109.0ms	665×	body	320	valid
60.0ms	1165×	body	80	valid
31.0ms	274×	body	160	valid

Details

analyze17.0s

sample107.0ms

simplify445.0ms

prune5.0ms

localize13.0ms

rewrite21.0ms

series118.0ms

simplify66.0ms

prune96.0ms

localize17.0ms

rewrite44.0ms

series335.0ms

simplify54.0ms

prune189.0ms

localize22.0ms

rewrite44.0ms

series281.0ms

simplify47.0ms

prune179.0ms

localize25.0ms

rewrite34.0ms

series96.0ms

simplify34.0ms

prune113.0ms

regimes986.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling