Details

Time bar (total: 16.2s)

sample294.0ms

Algorithm
intervals
Results
134.0ms56×body640valid
64.0ms91×body1280valid
10.0ms25×body320valid
7.0ms75×body80valid
2.0ms9×body160valid

simplify67.0ms

Counts
1 → 1
Iterations
IterNodes
done20
420
319
216
112
08

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ b a)))
2.3b
(cos (+ b a))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
3×associate-/r* times-frac associate-*r* associate-*l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum clear-num frac-2neg pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 47
Calls
3 calls:
9.0ms
(* r (sin b))
17.0ms
(/ (* r (sin b)) (cos (+ b a)))
18.0ms
(cos (+ b a))

series225.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(* r (sin b))
125.0ms
(/ (* r (sin b)) (cos (+ b a)))
42.0ms
(cos (+ b a))

simplify907.0ms

Counts
56 → 56
Iterations
IterNodes
done5000
2944
1210
093

prune362.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×associate-/r/ cos-mult
3×associate-/r* times-frac prod-exp cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×clear-num sub-neg frac-2neg diff-log div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
13.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
15.0ms
(* r (sin b))
18.0ms
(* (sin b) (sin a))
45.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series608.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
69.0ms
(* r (sin b))
63.0ms
(* (sin b) (sin a))
327.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify954.0ms

Counts
88 → 88
Iterations
IterNodes
done5000
21831
1374
0146

prune583.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
34×add-cbrt-cube add-exp-log
30×sin-mult
29×cos-mult
24×frac-times
19×times-frac associate-/l/
18×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
13×associate-/r* flip3-+ frac-add flip-+
12×cbrt-undiv div-exp
10×associate-/r/
8×pow1 flip3-- prod-exp associate-*r/ frac-sub cbrt-unprod flip-- sub-div
6×associate-*r* associate-*l* associate-*l/
4×div-inv add-log-exp
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in pow-prod-down *-commutative associate-/l* unswap-sqr
Counts
4 → 147
Calls
4 calls:
9.0ms
(* (sin b) (sin a))
44.0ms
(/ (* r (sin b)) (/ (* (+ (* (sin b) (sin a)) (* (cos a) (cos b))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))))
129.0ms
(* (+ (* (sin b) (sin a)) (* (cos a) (cos b))) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
83.0ms
(/ (* (+ (* (sin b) (sin a)) (* (cos a) (cos b))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))

series746.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sin b) (sin a))
323.0ms
(/ (* r (sin b)) (/ (* (+ (* (sin b) (sin a)) (* (cos a) (cos b))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))))
224.0ms
(* (+ (* (sin b) (sin a)) (* (cos a) (cos b))) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
120.0ms
(/ (* (+ (* (sin b) (sin a)) (* (cos a) (cos b))) (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (+ (* (sin b) (sin a)) (* (cos a) (cos b))))

simplify534.0ms

Counts
159 → 159
Iterations
IterNodes
done5000
1877
0274

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
63×add-cbrt-cube add-exp-log
29×add-sqr-sqrt cbrt-undiv div-exp
28×times-frac
23×*-un-lft-identity add-cube-cbrt
16×prod-exp associate-/r/ cbrt-unprod
10×pow1
9×associate-*r* associate-*l*
8×associate-/l*
5×div-inv sin-mult
4×frac-times associate-*l/ associate-*r/ add-log-exp
3×associate-/r* pow-prod-down *-commutative unswap-sqr
2×cos-mult
1×clear-num frac-2neg flip3-- frac-sub flip-- sub-div associate-/l/
Counts
4 → 129
Calls
4 calls:
19.0ms
(* (sin a) (sin b))
18.0ms
(* (sin a) (sin b))
19.0ms
(* (sin b) (sin a))
86.0ms
(/ (/ (* r (sin b)) (* (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (sin a) (sin b)) (* (cos a) (cos b)))))) (- (* (sin b) (sin a)) (* (cos a) (cos b))))

series760.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (sin a) (sin b))
91.0ms
(* (sin a) (sin b))
87.0ms
(* (sin b) (sin a))
516.0ms
(/ (/ (* r (sin b)) (* (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (sin a) (sin b)) (* (cos a) (cos b)))))) (- (* (sin b) (sin a)) (* (cos a) (cos b))))

simplify600.0ms

Counts
141 → 141
Iterations
IterNodes
done5001
1878
0273

prune851.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes369.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done28
328
226
124
020

end0.0ms

sample5.9s

Algorithm
intervals
Results
3.6s2928×body1280valid
1.1s1797×body640valid
372.0ms758×body320valid
295.0ms2178×body80valid
133.0ms339×body160valid