Details

Time bar (total: 5.2s)

sample323.0ms

Algorithm
intervals
Results
43.0ms98×body1280valid
15.0ms55×body640valid
7.0ms26×body320valid
4.0ms64×body80valid
2.0ms13×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.6b

Counts
2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
5.0b
(cos (+ a b))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*r/ clear-num
2×cos-sum frac-2neg div-inv
1×+-commutative associate-*r* un-div-inv *-commutative
Counts
3 → 11
Calls
3 calls:
3.0ms
(* r (/ (sin b) (cos (+ a b))))
3.0ms
(/ (sin b) (cos (+ a b)))
5.0ms
(cos (+ a b))

series173.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(* r (/ (sin b) (cos (+ a b))))
37.0ms
(/ (sin b) (cos (+ a b)))
39.0ms
(cos (+ a b))

simplify43.0ms

Algorithm
egg-herbie
Counts
20 → 20
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
09073
126673
2111970
3500169

prune44.0ms

Filtered
20 candidates to 11 candidates (55.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New15520
Fresh000
Picked101
Done000
Total16521

Merged error: 0.2b

Counts
21 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.3b
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/r/
7×sin-mult
6×cos-mult
5×associate-*r*
3×flip3-- associate-*r/ clear-num frac-sub flip-- sub-div
2×frac-2neg *-commutative div-inv
1×sub-neg un-div-inv
Counts
4 → 25
Calls
4 calls:
7.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
3.0ms
(* (sin a) (sin b))
8.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
208.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms
(* (sin a) (sin b))
110.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify65.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0188316
1604314
22406285
35001276

prune125.0ms

Filtered
37 candidates to 28 candidates (75.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New29837
Fresh404
Picked101
Done000
Total34842

Merged error: 0.1b

Counts
42 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
7×associate-/r/ sin-mult
6×cos-mult
3×flip3-- frac-2neg clear-num frac-sub flip-- div-inv sub-div
1×sub-neg div-sub associate-/r* *-commutative
Counts
4 → 27
Calls
4 calls:
7.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
3.0ms
(* (sin a) (sin b))
8.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series462.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
221.0ms
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
47.0ms
(* (sin a) (sin b))
109.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify67.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0206340
1595336
22112312
35001307

prune147.0ms

Filtered
39 candidates to 31 candidates (79.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New32739
Fresh347
Picked101
Done000
Total361147

Merged error: 0.1b

Counts
47 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (- (sin b)))
0.2b
(* (sin a) (sin b))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/r/ distribute-neg-frac
7×sin-mult
6×cos-mult
5×associate-*l*
4×associate-*l/
3×neg-mul-1 flip3-- frac-sub flip-- sub-div
2×frac-2neg clear-num associate-/r* *-commutative div-inv
1×sub-neg associate-*r* distribute-rgt-neg-out
Counts
4 → 28
Calls
4 calls:
7.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms
(/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms
(* (/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (- (sin b)))
3.0ms
(* (sin a) (sin b))

series527.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
183.0ms
(/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
218.0ms
(* (/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (- (sin b)))
46.0ms
(* (sin a) (sin b))

simplify95.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
0236335
1771332
23269312
35002300

prune124.0ms

Filtered
40 candidates to 33 candidates (82.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New36440
Fresh5510
Picked011
Done000
Total411051

Merged error: 0.1b

Counts
51 → 10

regimes143.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01912
12312
22612
32612

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2919×body1280valid
485.0ms1866×body640valid
137.0ms765×body320valid
121.0ms2109×body80valid
45.0ms344×body160valid