Details

sample3.6s

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

48.0ms	111×	body	1280	valid
19.0ms	73×	body	640	valid
18.0ms	256×	pre	80	true
4.0ms	21×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	10×	body	160	valid

simplify356.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 15.7b

Counts

2 → 1

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (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` `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)))
7.0ms	(tan (+ y z))

series102.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(- (tan (+ y z)) (tan a))
40.0ms	(+ x (- (tan (+ y z)) (tan a)))
25.0ms	(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

prune108.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	41	10	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	10	52

Merged error: 0.1b

Counts

52 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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` `associate-+r+` `flip3--` `flip3-+` `diff-log` `sum-log` `associate-/r/` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `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 → 90

Calls

4 calls:

8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (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))

series322.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
125.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
116.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
24.0ms	(* (tan y) (tan z))

simplify115.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	449	1259
1	1503	1211
2	4992	1203
3	5001	1203

prune173.0ms

Filtered

75 candidates to 102 candidates (-36.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Merged error: 0.1b

Counts

112 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (+ (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)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
21.0ms	(* (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)))

simplify84.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	655	1689
1	3093	1518
2	5001	1501

prune172.0ms

Filtered

83 candidates to 104 candidates (-25.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	108	8	116

Merged error: 0.1b

Counts

116 → 8

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

4.0ms	(+ (tan y) (tan z))
13.0ms	(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
10.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
5.0ms	(* (tan y) (tan z))

series221.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan y) (tan z))
123.0ms	(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
57.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
21.0ms	(* (tan y) (tan z))

simplify45.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	456	1169
1	1596	1113
2	5001	1094

prune105.0ms

Filtered

76 candidates to 101 candidates (-32.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Merged error: 0.0b

Counts

109 → 9

regimes545.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	46
1	41	46

end0.0ms

sample6.7s

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	3866×	body	1280	valid
560.0ms	8000×	pre	80	true
515.0ms	2018×	body	640	valid
125.0ms	683×	body	320	valid
62.0ms	1128×	body	80	valid
37.0ms	305×	body	160	valid

Details

sample3.6s

simplify356.0ms

prune6.0ms

localize26.0ms

rewrite21.0ms

series102.0ms

simplify38.0ms

prune108.0ms

localize17.0ms

rewrite38.0ms

series322.0ms

simplify115.0ms

prune173.0ms

localize24.0ms

rewrite35.0ms

series266.0ms

simplify84.0ms

prune172.0ms

localize16.0ms

rewrite34.0ms

series221.0ms

simplify45.0ms

prune105.0ms

regimes545.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.7s

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