Details

Time bar (total: 5.5s)

sample79.0ms

Algorithm
intervals
Results
44.0ms99×body1280valid
16.0ms62×body640valid
4.0ms23×body320valid
4.0ms64×body80valid
1.0ms8×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.7b
(cos (+ a b))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×pow1
3×times-frac associate-*r* associate-*l* associate-/r* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 47
Calls
3 calls:
4.0ms
(* r (sin b))
11.0ms
(/ (* r (sin b)) (cos (+ a b)))
6.0ms
(cos (+ a b))

series155.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* r (sin b))
95.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify32.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0198305
1861257
25001256

prune139.0ms

Filtered
56 candidates to 40 candidates (71.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
4×prod-exp associate-/r/ cbrt-unprod add-log-exp
3×times-frac pow-prod-down associate-/r* cos-mult *-commutative sin-mult unswap-sqr
2×cbrt-undiv div-exp
1×flip3-- frac-2neg clear-num frac-sub flip-- div-inv associate-/l* sub-div
Counts
4 → 81
Calls
4 calls:
4.0ms
(* (cos a) (cos b))
4.0ms
(* r (sin b))
5.0ms
(* (sin a) (sin b))
8.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos a) (cos b))
36.0ms
(* r (sin b))
43.0ms
(* (sin a) (sin b))
217.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0367682
11616594
25001593

prune280.0ms

Filtered
93 candidates to 65 candidates (69.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
23×associate-*r*
19×times-frac
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×prod-exp cbrt-unprod add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub flip-- div-inv sub-div
1×frac-2neg associate-*r/ clear-num
Counts
4 → 105
Calls
4 calls:
4.0ms
(* (cos b) (cos a))
11.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
5.0ms
(* (sin a) (sin b))

series412.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (cos b) (cos a))
215.0ms
(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
110.0ms
(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
48.0ms
(* (sin a) (sin b))

simplify56.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04281219
118411103
250011098

prune371.0ms

Filtered
117 candidates to 86 candidates (73.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
62×add-sqr-sqrt
58×add-cube-cbrt *-un-lft-identity
16×associate-/r*
15×add-exp-log add-cbrt-cube
8×pow1
6×associate-*r* associate-*l* div-inv associate-/l*
4×cbrt-undiv div-exp associate-/l/ add-log-exp
3×cos-mult sin-mult
2×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
1×flip3-- div-sub associate-/r/ frac-sub flip-- sub-div
Counts
4 → 140
Calls
4 calls:
4.0ms
(* (cos a) (cos b))
7.0ms
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
8.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
5.0ms
(* (sin a) (sin b))

series424.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos a) (cos b))
221.0ms
(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
113.0ms
(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
47.0ms
(* (sin a) (sin b))

simplify71.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05732071
124741930
250011911

prune468.0ms

Filtered
152 candidates to 121 candidates (79.6%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes140.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01410
11410

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2895×body1280valid
493.0ms1889×body640valid
144.0ms798×body320valid
121.0ms2084×body80valid
43.0ms336×body160valid