Details

sample3.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 75%

Results

95.0ms	74×	body	1280	valid
55.0ms	64×	body	640	valid
21.0ms	30×	body	320	valid
14.0ms	78×	body	80	valid
4.0ms	10×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	30
1	182	30
2	657	30
3	2727	30
4	5001	30

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: 0.5b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.6b	(- (cos x) (cos y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

11.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series303.0ms

Counts

4 → 10

Calls

4 calls:

279.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
12.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
12.0ms	(- (cos x) (cos y))

simplify86.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	852	1769
1	3560	1553
2	5002	1553

prune364.0ms

Filtered

70 candidates to 98 candidates (-40.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	14	99

Merged error: 0.0b

Counts

99 → 14

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.6b	(- (cos x) (cos y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg`
5×	`sqrt-prod`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 94

Calls

4 calls:

17.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series47.0ms

Counts

4 → 10

Calls

4 calls:

25.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
13.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
9.0ms	(- (cos x) (cos y))

simplify63.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	613	1094
1	2608	1002
2	5002	1002

prune315.0ms

Filtered

70 candidates to 104 candidates (-48.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.6b	(- (cos x) (cos y))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

10.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
17.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
10.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- (cos x) (cos y))

series267.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (+ (* 3.0 3.0) (neg 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
22.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
12.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
15.0ms	(- (cos x) (cos y))

simplify118.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1005	2836
1	4653	2614
2	5002	2614

prune512.0ms

Filtered

89 candidates to 124 candidates (-39.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	125	12	137

Merged error: 0.0b

Counts

137 → 12

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.6b	(- (cos x) (cos y))
1.6b	(- (cos x) (cos y))
1.6b	(- (cos x) (cos y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`diff-cos`
1×	`sqrt-prod`

Counts

4 → 60

Calls

4 calls:

4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))
4.0ms	(- (cos x) (cos y))
4.0ms	(- (cos x) (cos y))

series26.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
9.0ms	(- (cos x) (cos y))
9.0ms	(- (cos x) (cos y))
9.0ms	(- (cos x) (cos y))

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	218	417
1	571	391
2	2054	387
3	5001	387

prune218.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	70	12	82

Merged error: 0.0b

Counts

82 → 12

regimes387.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	35
1	51	35

end0.0ms

sample9.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 75%

Results

3.6s	2741×	body	1280	valid
1.7s	1868×	body	640	valid
470.0ms	750×	body	320	valid
452.0ms	2270×	body	80	valid
151.0ms	371×	body	160	valid

Details

sample3.3s

simplify52.0ms

prune5.0ms

localize32.0ms

rewrite31.0ms

series303.0ms

simplify86.0ms

prune364.0ms

localize37.0ms

rewrite39.0ms

series47.0ms

simplify63.0ms

prune315.0ms

localize40.0ms

rewrite45.0ms

series267.0ms

simplify118.0ms

prune512.0ms

localize44.0ms

rewrite18.0ms

series26.0ms

simplify55.0ms

prune218.0ms

regimes387.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.7s

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