Details

Time bar (total: 6.3s)

sample386.0ms

Algorithm
intervals
Results
40.0ms88×body1280valid
16.0ms64×body640valid
4.0ms70×body80valid
3.0ms22×body320valid
1.0ms12×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0125
1165
2205
3215
4215
done215

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

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)))
2.5b
(cos (+ a b))

rewrite41.0ms

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:
17.0ms
(* r (/ (sin b) (cos (+ a b))))
10.0ms
(/ (sin b) (cos (+ a b)))
12.0ms
(cos (+ a b))

series179.0ms

Counts
3 → 9
Calls
3 calls:
103.0ms
(* r (/ (sin b) (cos (+ a b))))
42.0ms
(/ (sin b) (cos (+ a b)))
33.0ms
(cos (+ a b))

simplify39.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0252536
11064480
25001477
done5001477

prune195.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (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))

rewrite134.0ms

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:
19.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
26.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms
(* (sin a) (sin b))

series489.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
232.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
122.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
48.0ms
(* (sin a) (sin b))

simplify53.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04051307
117611182
250011173
done50011173

prune361.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
20×associate-*r* add-cbrt-cube
18×times-frac
13×prod-exp
12×pow1
8×associate-/r/
7×cbrt-unprod sin-mult
6×div-exp cos-mult add-log-exp
4×associate-*l* pow-prod-down
3×cbrt-undiv rec-exp flip3-- 1-exp associate-/r* frac-sub flip-- associate-/l* sub-div
2×*-commutative div-inv
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ clear-num un-div-inv inv-pow unswap-sqr
Counts
4 → 110
Calls
4 calls:
17.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
34.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms
(* (sin a) (sin b))

series485.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
108.0ms
(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
236.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
50.0ms
(* (sin a) (sin b))

simplify62.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04831381
123011194
250011166
done50011166

prune338.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
0.2b
(* (sin a) (sin b))
0.3b
(pow (* (sin a) (sin b)) 3)
30.4b
(cbrt (pow (* (sin a) (sin b)) 3))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
21×add-cbrt-cube
19×associate-*r*
17×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
14×pow1 prod-exp
9×times-frac
8×cbrt-prod cbrt-unprod
5×pow-prod-down
4×div-exp associate-*l* sin-mult add-log-exp
3×cube-div pow-unpow associate-/r/
2×cbrt-undiv cube-mult unpow-prod-down rec-exp cbrt-div pow-pow 1-exp unpow3 cube-prod pow-exp *-commutative rem-cube-cbrt sqr-pow
1×pow-to-exp flip3-- pow1/3 associate-*r/ un-div-inv cos-mult frac-sub flip-- rem-cbrt-cube div-inv unswap-sqr
Counts
4 → 101
Calls
4 calls:
81.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
14.0ms
(* (sin a) (sin b))
9.0ms
(pow (* (sin a) (sin b)) 3)
4.0ms
(cbrt (pow (* (sin a) (sin b)) 3))

series412.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
53.0ms
(* (sin a) (sin b))
66.0ms
(pow (* (sin a) (sin b)) 3)
53.0ms
(cbrt (pow (* (sin a) (sin b)) 3))

simplify71.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
05181027
12650839
25002819
done5002819

prune338.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes171.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02836
12836
done2836

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2976×body1280valid
450.0ms1808×body640valid
123.0ms767×body320valid
106.0ms2095×body80valid
42.0ms356×body160valid