Details

Time bar (total: 4.7s)

sample79.0ms

Algorithm
intervals
Results
43.0ms93×body1280valid
15.0ms63×body640valid
5.0ms27×body320valid
4.0ms70×body80valid
0.0ms3×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: 16.7b

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)))
4.7b
(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))

series161.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* r (sin b))
97.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify75.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 4 (72.0ms)

IterNodesCost
08464
118464
257964
3205263
4500161

prune41.0ms

Filtered
17 candidates to 10 candidates (58.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New12517
Fresh000
Picked101
Done000
Total13518

Merged error: 0.3b

Counts
18 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.2b
(- (* (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))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
8×*-commutative
5×sin-mult
4×prod-diff associate-/r/ cos-mult
2×flip3-- fma-neg frac-sub flip-- associate-/l* sub-div
1×sub-neg frac-2neg clear-num div-inv
Counts
4 → 24
Calls
4 calls:
3.0ms
(* r (sin b))
7.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms
(* (sin a) (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* r (sin b))
82.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms
(* (sin a) (sin b))
215.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0202312
1590304
21892289
35002256

prune115.0ms

Filtered
36 candidates to 25 candidates (69.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New28836
Fresh404
Picked101
Done000
Total33841

Merged error: 0.1b

Counts
41 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
5×associate-/l*
4×*-commutative
2×distribute-lft-neg-in distribute-rgt-neg-in
1×neg-sub0 neg-mul-1 frac-2neg div-sub distribute-frac-neg clear-num fma-udef div-inv sin-mult
Counts
4 → 14
Calls
4 calls:
3.0ms
(* r (sin b))
1.0ms
(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
3.0ms
(* (sin a) (sin b))
4.0ms
(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))

series390.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* r (sin b))
85.0ms
(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
44.0ms
(* (sin a) (sin b))
221.0ms
(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))

simplify92.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 4 (89.0ms)

IterNodesCost
0110164
1260163
2790162
33289161
45001158

prune99.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New23326
Fresh257
Picked011
Done000
Total25934

Merged error: 0.1b

Counts
34 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.3b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/r/ *-commutative
7×sin-mult
6×cos-mult
5×associate-*r*
4×prod-diff
3×flip3-- associate-*r/ clear-num frac-sub flip-- sub-div
2×frac-2neg fma-neg associate-*l* un-div-inv div-inv
1×sub-neg inv-pow
Counts
4 → 35
Calls
4 calls:
7.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
7.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms
(* (sin a) (sin b))
10.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series434.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
81.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms
(* (sin a) (sin b))
212.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify98.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0226384
1760373
23740342
35001341

prune122.0ms

Filtered
47 candidates to 32 candidates (68.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New45247
Fresh077
Picked101
Done011
Total461056

Merged error: 0.1b

Counts
56 → 10

regimes145.0ms

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
02111
12311
22311

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.3s2932×body1280valid
454.0ms1830×body640valid
140.0ms758×body320valid
117.0ms2147×body80valid
42.0ms334×body160valid