Details

sample236.0ms

Algorithm

intervals

Results

121.0ms	81×	body	1280	valid
56.0ms	60×	body	640	valid
18.0ms	82×	body	80	valid
12.0ms	18×	body	320	valid
7.0ms	15×	body	160	valid

simplify54.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.8b	(- (cos x) (cos y))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

22.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
30.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))

series236.0ms

Counts

4 → 10

Calls

4 calls:

89.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
90.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
56.0ms	(- (cos x) (cos y))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	584	813
1	2075	753
2	5001	753

prune597.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.8b	(- (cos x) (cos y))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

26.0ms	(/ (+ 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 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
22.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
27.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms	(- (cos x) (cos y))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.9s	(/ (+ 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 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
94.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
95.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
54.0ms	(- (cos x) (cos y))

simplify108.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1029	2159
1	4404	1906
2	5001	1906

prune785.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
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 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.8b	(- (cos x) (cos y))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

21.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
28.0ms	(/ (/ (+ 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 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
30.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms	(- (cos x) (cos y))

series2.0s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
1.8s	(/ (/ (+ 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 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
91.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
55.0ms	(- (cos x) (cos y))

simplify146.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1189	5142
1	4792	4885
2	5001	4885

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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))) (- (cos x) (cos y)))
0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.8b	(- (cos x) (cos y))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

158.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
26.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
28.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms	(- (cos x) (cos y))

series459.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
90.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
90.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
57.0ms	(- (cos x) (cos y))

simplify44.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	977	2200
1	5001	2033

prune932.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	35
1	50	35

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.9s	2779×	body	1280	valid
1.7s	1808×	body	640	valid
491.0ms	2324×	body	80	valid
487.0ms	713×	body	320	valid
166.0ms	376×	body	160	valid