Details

Time bar (total: 6.7s)

sample335.0ms

Algorithm
intervals
Results
44.0ms84×body1280valid
18.0ms62×body640valid
6.0ms72×body80valid
5.0ms24×body320valid
2.0ms14×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0125
1165
2205
3215
4215

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
3.4b
(cos (+ a b))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
5×pow1
3×associate-*l* associate-/r* associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 67
Calls
3 calls:
9.0ms
(* r (/ (sin b) (cos (+ a b))))
3.0ms
(/ (sin b) (cos (+ a b)))
7.0ms
(cos (+ a b))

series159.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(* r (/ (sin b) (cos (+ a b))))
39.0ms
(/ (sin b) (cos (+ a b)))
25.0ms
(cos (+ a b))

simplify39.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0252536
11064480
25001477

prune197.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×associate-*r*
19×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
3×flip3-- prod-exp associate-/r* frac-sub flip-- cbrt-unprod associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×sub-neg frac-2neg diff-log associate-*r/ clear-num
Counts
4 → 100
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms
(* (sin a) (sin b))

series452.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
216.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
111.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
47.0ms
(* (sin a) (sin b))

simplify58.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04051307
117611182
250011173

prune359.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
27×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity associate-*r*
22×add-cbrt-cube
18×times-frac
14×pow1 prod-exp
8×associate-/r/ cbrt-unprod
7×associate-*l*
6×div-exp
5×pow-prod-down sin-mult
4×cos-mult add-log-exp
3×cbrt-undiv rec-exp 1-exp associate-/r* *-commutative associate-/l*
2×flip3-- frac-sub flip-- div-inv sub-div unswap-sqr
1×pow-flip frac-2neg associate-*r/ clear-num un-div-inv inv-pow
Counts
4 → 114
Calls
4 calls:
3.0ms
(* r (sin b))
4.0ms
(* (sin a) (sin b))
12.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series398.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* r (sin b))
46.0ms
(* (sin a) (sin b))
98.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
215.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04741265
124191084
250011056

prune340.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
0.2b
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
40×cos-mult sin-mult
35×add-exp-log pow-prod-down add-cbrt-cube
34×associate-*r*
32×associate-/r/
27×add-sqr-sqrt
25×times-frac
23×associate-*r/
22×add-cube-cbrt *-un-lft-identity associate-*l/
18×frac-times prod-exp frac-sub cbrt-unprod
10×sub-div
8×pow-sqr pow-prod-up
7×difference-of-squares
5×associate-*l*
4×pow-plus associate-/r* add-log-exp
3×*-commutative associate-/l*
2×cbrt-undiv pow2 flip3-- swap-sqr div-exp flip-- div-inv unswap-sqr
1×frac-2neg clear-num
Counts
4 → 172
Calls
4 calls:
34.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
110.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
15.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
13.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
292.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
54.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
58.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify101.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07102847
134682471
250012471

prune509.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes160.0ms

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
02011
12011

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.4s2963×body1280valid
549.0ms1803×body640valid
168.0ms784×body320valid
160.0ms2081×body80valid
58.0ms371×body160valid