Details

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 99.761164%

Space saved by search: 99.761164%

Guaranteed chance to sample good point: 0%

Results

54.0ms	113×	body	1280	valid
22.0ms	64×	body	640	valid
18.0ms	256×	pre	80	true
6.0ms	30×	body	320	valid
2.0ms	35×	body	80	valid
2.0ms	14×	body	160	valid

simplify362.0ms

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: 11.5b

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)))
2.3b	(tan (+ y z))

rewrite19.0ms

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)))
5.0ms	(tan (+ y z))

series114.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(- (tan (+ y z)) (tan a))
40.0ms	(+ x (- (tan (+ y z)) (tan a)))
41.0ms	(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

prune91.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.1b

Counts

52 → 6

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

rewrite35.0ms

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:

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

series287.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (tan y) (tan z))
116.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
126.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
22.0ms	(* (tan y) (tan z))

simplify73.0ms

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

prune131.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 0.1b

Counts

85 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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))
13.0ms	(/ (- (* (+ (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))
7.0ms	(* (tan y) (tan z))

series225.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (+ (tan y) (tan z)) (cos a))
147.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
21.0ms	(* (tan y) (tan z))
21.0ms	(* (tan y) (tan z))

simplify72.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	587	1304
1	2694	1144
2	5001	1128

prune156.0ms

Filtered

83 candidates to 108 candidates (-30.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	108	9	117

Merged error: 0.1b

Counts

117 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
9.2b	(cbrt (* (tan y) (tan z)))
9.2b	(cbrt (* (tan y) (tan z)))
9.2b	(cbrt (* (tan y) (tan z)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
33×	`cbrt-div`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

9.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
4.0ms	(cbrt (* (tan y) (tan z)))
4.0ms	(cbrt (* (tan y) (tan z)))
4.0ms	(cbrt (* (tan y) (tan z)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
37.0ms	(cbrt (* (tan y) (tan z)))
39.0ms	(cbrt (* (tan y) (tan z)))
38.0ms	(cbrt (* (tan y) (tan z)))

simplify107.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	253	864
1	868	775
2	3898	700
3	5001	694

prune97.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	94	9	103

Merged error: 0.1b

Counts

103 → 9

regimes1.1s

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	26	20
1	26	20

end0.0ms

sample6.7s

Algorithm

intervals

sampling

Space saved by range analysis: 99.761164%

Space saved by search: 99.761164%

Guaranteed chance to sample good point: 0%

Results

1.8s	3865×	body	1280	valid
542.0ms	8000×	pre	80	true
534.0ms	1994×	body	640	valid
140.0ms	741×	body	320	valid
68.0ms	1123×	body	80	valid
35.0ms	277×	body	160	valid

Details

sample3.6s

simplify362.0ms

prune6.0ms

localize13.0ms

rewrite19.0ms

series114.0ms

simplify37.0ms

prune91.0ms

localize16.0ms

rewrite35.0ms

series287.0ms

simplify73.0ms

prune131.0ms

localize21.0ms

rewrite35.0ms

series225.0ms

simplify72.0ms

prune156.0ms

localize23.0ms

rewrite23.0ms

series173.0ms

simplify107.0ms

prune97.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.7s

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