Details

Time bar (total: 4.9s)

sample79.0ms

Algorithm
intervals
Results
41.0ms98×body1280valid
17.0ms55×body640valid
5.0ms26×body320valid
3.0ms64×body80valid
2.0ms13×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1165
2195
3205
4205

prune2.0ms

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: 15.7b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.3b
(/ (* r (sin b)) (cos (+ a b)))
5.0b
(cos (+ a b))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
2×cos-sum *-commutative associate-/l*
1×+-commutative frac-2neg clear-num div-inv
Counts
3 → 8
Calls
3 calls:
2.0ms
(* r (sin b))
4.0ms
(/ (* r (sin b)) (cos (+ a b)))
5.0ms
(cos (+ a b))

series158.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* r (sin b))
95.0ms
(/ (* r (sin b)) (cos (+ a b)))
23.0ms
(cos (+ a b))

simplify74.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 3 (19.0ms)

IterNodesCost
08166
116966
250165
3177064
4500264

prune46.0ms

Filtered
17 candidates to 10 candidates (58.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New11617
Fresh000
Picked101
Done000
Total12618

Merged error: 0.2b

Counts
18 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
5×sin-mult
4×associate-/r/ cos-mult
3×*-commutative
2×flip3-- frac-sub flip-- associate-/l* sub-div
1×sub-neg frac-2neg clear-num div-inv
Counts
4 → 18
Calls
4 calls:
2.0ms
(* r (sin b))
7.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms
(* (sin a) (sin b))
8.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* r (sin b))
80.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms
(* (sin a) (sin b))
219.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0181253
1526251
21627235
35001225

prune100.0ms

Filtered
30 candidates to 21 candidates (70.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New22830
Fresh505
Picked011
Done000
Total27936

Merged error: 0.1b

Counts
36 → 9

localize16.0ms

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))

rewrite26.0ms

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))

series463.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
222.0ms
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
43.0ms
(* (sin a) (sin b))
116.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify65.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0206340
1595336
22112312
35001307

prune140.0ms

Filtered
39 candidates to 32 candidates (82.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New34539
Fresh347
Picked101
Done101
Total39948

Merged error: 0.1b

Counts
48 → 9

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

rewrite31.0ms

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)))
11.0ms
(/ 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))

series531.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
181.0ms
(/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
226.0ms
(* (/ r (- (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (- (sin b)))
43.0ms
(* (sin a) (sin b))

simplify96.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
0236337
1771334
23269312
35001300

prune124.0ms

Filtered
40 candidates to 33 candidates (82.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New36440
Fresh358
Picked101
Done000
Total40949

Merged error: 0.1b

Counts
49 → 9

regimes131.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01510
11510

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s2919×body1280valid
487.0ms1866×body640valid
135.0ms765×body320valid
130.0ms2109×body80valid
44.0ms344×body160valid