Details

Time bar (total: 30.4s)

sample433.0ms

Algorithm
intervals
Results
91.0ms91×body1280valid
42.0ms67×body640valid
10.0ms23×body320valid
9.0ms60×body80valid
5.0ms15×body160valid

simplify53.0ms

Counts
1 → 1
Iterations
IterNodes
done20
520
419
317
214
112
08

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize41.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
5.5b
(cos (+ a b))

rewrite106.0ms

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×expm1-log1p-u times-frac associate-*r* associate-*l* associate-/r* log1p-expm1-u 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 → 53
Calls
3 calls:
55.0ms
(* r (sin b))
23.0ms
(/ (* r (sin b)) (cos (+ a b)))
23.0ms
(cos (+ a b))

series395.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(* r (sin b))
235.0ms
(/ (* r (sin b)) (cos (+ a b)))
72.0ms
(cos (+ a b))

simplify3.6s

Counts
62 → 62
Iterations
IterNodes
done5000
32460
2599
1213
096

prune598.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

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×expm1-log1p-u associate-/r/ cos-mult log1p-expm1-u
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 fma-neg diff-log prod-diff clear-num div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
21.0ms
(* r (sin b))
41.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
68.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
34.0ms
(* (sin a) (sin b))

series926.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* r (sin b))
192.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
529.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms
(* (sin a) (sin b))

simplify2.9s

Counts
98 → 98
Iterations
IterNodes
done5000
21204
1386
0152

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

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))))
0.3b
(* (sin a) (sin b))

rewrite319.0ms

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
4×expm1-log1p-u log1p-expm1-u
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 fma-neg diff-log associate-*r/ prod-diff clear-num
Counts
4 → 110
Calls
4 calls:
42.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
171.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
59.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
39.0ms
(* (sin a) (sin b))

series1.5s

Counts
4 → 12
Calls
4 calls:
172.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
959.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
251.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
109.0ms
(* (sin a) (sin b))

simplify2.9s

Counts
122 → 122
Iterations
IterNodes
done5000
21541
1460
0181

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.3b
(* (sin a) (sin b))
2.8b
(log (exp (* (sin a) (sin b))))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×pow1
7×add-log-exp
6×log-prod prod-diff log-pow
4×expm1-log1p-u log1p-expm1-u
3×times-frac associate-*r* associate-*l* associate-/r* associate--r+
2×cbrt-undiv exp-prod flip3-- exp-to-pow div-exp prod-exp associate-/r/ flip-- cbrt-unprod
1×sub-neg frac-2neg fma-neg diff-log rem-log-exp pow-prod-down clear-num *-commutative div-inv sin-mult associate-/l* unswap-sqr
Counts
4 → 86
Calls
4 calls:
42.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
56.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
27.0ms
(* (sin a) (sin b))
11.0ms
(log (exp (* (sin a) (sin b))))

series920.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
511.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
112.0ms
(* (sin a) (sin b))
104.0ms
(log (exp (* (sin a) (sin b))))

simplify2.9s

Counts
98 → 98
Iterations
IterNodes
done5000
21329
1420
0167

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes637.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done17
117
014

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.1s2850×body1280valid
2.2s1867×body640valid
428.0ms747×body320valid
419.0ms2196×body80valid
301.0ms340×body160valid