Details

sample11.5s

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

43.0ms	109×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	64×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	42×	body	80	valid
2.0ms	12×	body	160	valid

simplify359.0ms

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: 15.3b

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)))
4.6b	(tan (+ y z))

rewrite28.0ms

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:

15.0ms	(- (tan (+ y z)) (tan a))
5.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(tan (+ y z))

series104.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (tan (+ y z)) (tan a))
41.0ms	(+ x (- (tan (+ y z)) (tan a)))
26.0ms	(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

prune94.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

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))
0.2b	(+ (tan y) (tan z))
0.2b	(* (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` `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:

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))
4.0ms	(+ (tan y) (tan z))
7.0ms	(* (tan y) (tan z))

series290.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
120.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
21.0ms	(+ (tan y) (tan z))
22.0ms	(* (tan y) (tan z))

simplify74.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (24.0ms)

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

prune149.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

19.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
4.0ms	(+ (tan y) (tan z))
5.0ms	(/ (* (sin y) (tan z)) (cos y))
5.0ms	(* (sin y) (tan z))

series181.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
21.0ms	(+ (tan y) (tan z))
23.0ms	(/ (* (sin y) (tan z)) (cos y))
17.0ms	(* (sin y) (tan z))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	383	781
1	1350	706
2	5001	697

prune134.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	81	11	92

Merged error: 0.0b

Counts

92 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (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

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

Counts

4 → 96

Calls

4 calls:

7.0ms	(* (+ (tan y) (tan z)) (cos a))
5.0ms	(* (tan y) (tan z))
7.0ms	(* (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)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ (tan y) (tan z)) (cos a))
22.0ms	(* (tan y) (tan z))
23.0ms	(* (tan y) (tan z))
148.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify70.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	587	1304
1	2701	1144
2	5003	1128

prune122.0ms

Filtered

83 candidates to 108 candidates (-30.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	108	11	119

Merged error: 0.0b

Counts

119 → 11

regimes515.0ms

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	22	13
1	22	13

end0.0ms

sample14.9s

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

1.6s	3845×	body	1280	valid
571.0ms	8000×	pre	80	true
481.0ms	1950×	body	640	valid
124.0ms	722×	body	320	valid
61.0ms	1154×	body	80	valid
38.0ms	329×	body	160	valid

Details

sample11.5s

simplify359.0ms

prune6.0ms

localize13.0ms

rewrite28.0ms

series104.0ms

simplify37.0ms

prune94.0ms

localize16.0ms

rewrite36.0ms

series290.0ms

simplify74.0ms

prune149.0ms

localize21.0ms

rewrite35.0ms

series181.0ms

simplify39.0ms

prune134.0ms

localize21.0ms

rewrite36.0ms

series228.0ms

simplify70.0ms

prune122.0ms

regimes515.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample14.9s

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