Details

sample186.0ms

Algorithm

intervals

Results

91.0ms	81×	body	1280	valid
43.0ms	53×	body	640	valid
14.0ms	28×	body	320	valid
12.0ms	80×	body	80	valid
5.0ms	14×	body	160	valid

simplify50.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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

localize37.0ms

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)))))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite32.0ms

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

series1.4s

Counts

4 → 10

Calls

4 calls:

1.2s	(/ (+ 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)))))
86.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
55.0ms	(- (cos x) (cos y))

simplify89.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (19.0ms)

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

prune527.0ms

Filtered

98 candidates to 70 candidates (71.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	10	99

Merged error: 0.0b

Counts

99 → 10

localize31.0ms

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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite41.0ms

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))

series263.0ms

Counts

4 → 10

Calls

4 calls:

129.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
84.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
50.0ms	(- (cos x) (cos y))

simplify64.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	587	1081
1	2535	989
2	5003	989

prune480.0ms

Filtered

104 candidates to 70 candidates (67.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	104	10	114

Merged error: 0.0b

Counts

114 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.4b	(- (cos x) (cos y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

10.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
19.0ms	(* (* (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))

series372.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
124.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
87.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
50.0ms	(- (cos x) (cos y))

simplify77.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	751	1321
1	3282	1206
2	5001	1206

prune669.0ms

Filtered

132 candidates to 89 candidates (67.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	132	10	142

Merged error: 0.0b

Counts

142 → 10

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))
2.4b	(- (cos x) (cos y))
2.4b	(- (cos x) (cos y))

rewrite19.0ms

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))
5.0ms	(- (cos x) (cos y))

series162.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
55.0ms	(- (cos x) (cos y))
55.0ms	(- (cos x) (cos y))
52.0ms	(- (cos x) (cos y))

simplify57.0ms

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

prune346.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	70	10	80

Merged error: 0.0b

Counts

80 → 10

regimes248.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	34
1	46	34

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.4s	2778×	body	1280	valid
1.4s	1825×	body	640	valid
399.0ms	753×	body	320	valid
376.0ms	2342×	body	80	valid
108.0ms	302×	body	160	valid