Details

sample188.0ms

Algorithm

intervals

Results

104.0ms	101×	body	1280	valid
37.0ms	46×	body	640	valid
13.0ms	28×	body	320	valid
10.0ms	70×	body	80	valid
3.0ms	11×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize40.0ms

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))
3.7b	(- (cos x) (cos y))

rewrite94.0ms

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:

57.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
28.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))

series297.0ms

Counts

4 → 10

Calls

4 calls:

142.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
95.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
59.0ms	(- (cos x) (cos y))

simplify68.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	622	1094
1	2643	1002
2	5003	1002

prune578.0ms

Filtered

104 candidates to 70 candidates (67.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.7b	(- (cos x) (cos y))

rewrite114.0ms

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:

24.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
55.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
28.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms	(- (cos x) (cos y))

series387.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
145.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
94.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
53.0ms	(- (cos x) (cos y))

simplify84.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (18.0ms)

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

prune833.0ms

Filtered

132 candidates to 89 candidates (67.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

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	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
3.7b	(- (cos x) (cos y))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

249.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
28.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
3.0ms	(- (cos x) (cos y))

series279.0ms

Counts

4 → 10

Calls

4 calls:

132.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
91.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
57.0ms	(- (cos x) (cos y))

simplify66.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	590	1161
1	2523	1065
2	5002	1065

prune768.0ms

Filtered

109 candidates to 71 candidates (65.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
1.0b	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
3.4b	(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
3.7b	(- (cos x) (cos y))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

18.0ms	(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
9.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
25.0ms	(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
3.0ms	(- (cos x) (cos y))

series354.0ms

Counts

4 → 10

Calls

4 calls:

114.0ms	(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
0.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
182.0ms	(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
58.0ms	(- (cos x) (cos y))

simplify74.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	574	1389
1	2427	1208
2	5001	1191

prune806.0ms

Filtered

107 candidates to 76 candidates (71.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes229.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	54
1	64	54

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.0s	2702×	body	1280	valid
1.3s	1819×	body	640	valid
379.0ms	776×	body	320	valid
327.0ms	2328×	body	80	valid
120.0ms	375×	body	160	valid