Details

Time bar (total: 23.8s)

sample213.0ms

Algorithm
intervals
Results
69.0ms51×body640valid
60.0ms100×body1280valid
7.0ms28×body320valid
6.0ms68×body80valid
4.0ms9×body160valid

simplify19.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
089
1129
2169
3209
4219
done219

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))
4.3b
(cos (+ a b))

rewrite69.0ms

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:
32.0ms
(/ (sin b) (cos (+ a b)))
19.0ms
(* r (/ (sin b) (cos (+ a b))))
12.0ms
(cos (+ a b))

series278.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(/ (sin b) (cos (+ a b)))
171.0ms
(* r (/ (sin b) (cos (+ a b))))
40.0ms
(cos (+ a b))

simplify5.5s

Counts
76 → 76
Iterations

Useful iterations: 4 (3.8s)

IterNodesCost
0116909
1249883
2634793
31708785
44906783
done5000783

prune311.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

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:
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
35.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
110.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms
(* (sin a) (sin b))

series670.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
176.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
319.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
63.0ms
(* (sin a) (sin b))

simplify2.3s

Counts
112 → 112
Iterations

Useful iterations: 3 (997.0ms)

IterNodesCost
01702072
14032024
211671834
333731715
done50001715

prune620.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b
(* (sin b) (sin a))
0.3b
(pow (* (sin b) (sin a)) 3)
30.3b
(cbrt (pow (* (sin b) (sin a)) 3))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
16×add-cube-cbrt *-un-lft-identity
14×add-exp-log add-cbrt-cube
11×pow1
10×times-frac
8×cbrt-prod
6×associate-*l*
4×prod-exp cbrt-unprod sin-mult add-log-exp
3×cube-div pow-unpow pow-prod-down associate-/r/ unswap-sqr
2×cube-mult unpow-prod-down cbrt-div pow-pow unpow3 cube-prod pow-exp *-commutative rem-cube-cbrt sqr-pow
1×cbrt-undiv pow-to-exp flip3-- pow1/3 associate-*r/ div-exp cos-mult frac-sub flip-- rem-cbrt-cube div-inv
Counts
4 → 95
Calls
4 calls:
151.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
23.0ms
(* (sin b) (sin a))
20.0ms
(pow (* (sin b) (sin a)) 3)
5.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

series653.0ms

Counts
4 → 12
Calls
4 calls:
384.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
68.0ms
(* (sin b) (sin a))
125.0ms
(pow (* (sin b) (sin a)) 3)
76.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.2s

Counts
107 → 107
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01881602
14341318
214331188
done50001186

prune636.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×sub-neg frac-2neg diff-log clear-num div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
35.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
20.0ms
(* r (sin b))
25.0ms
(* (sin a) (sin b))
72.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series588.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(- (* (cos b) (cos a)) (* (sin a) (sin b)))
58.0ms
(* r (sin b))
69.0ms
(* (sin a) (sin b))
319.0ms
(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify3.3s

Counts
88 → 88
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01401256
13411224
210891076
338841021
done50001021

prune435.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes241.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01418
12016
done2016

end0.0ms

sample6.0s

Algorithm
intervals
Results
3.4s2954×body1280valid
991.0ms1762×body640valid
548.0ms308×body160valid
422.0ms843×body320valid
276.0ms2134×body80valid