Details

Time bar (total: 17.5s)

sample206.0ms

Algorithm
intervals
Results
106.0ms96×body1280valid
25.0ms61×body640valid
8.0ms67×body80valid
6.0ms23×body320valid
2.0ms9×body160valid

simplify26.0ms

Counts
1 → 1
Iterations
IterNodes
done21
421
320
216
112
08

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ r (cos (+ b a)))
0.2b
(* (sin b) (/ r (cos (+ b a))))
3.9b
(cos (+ b a))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×associate-/r* associate-*l* associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 67
Calls
3 calls:
9.0ms
(/ r (cos (+ b a)))
26.0ms
(* (sin b) (/ r (cos (+ b a))))
33.0ms
(cos (+ b a))

series335.0ms

Counts
3 → 9
Calls
3 calls:
108.0ms
(/ r (cos (+ b a)))
202.0ms
(* (sin b) (/ r (cos (+ b a))))
25.0ms
(cos (+ b a))

simplify924.0ms

Counts
76 → 76
Iterations
IterNodes
done5000
21471
1277
0118

prune405.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
3×associate-/r* flip3-- prod-exp frac-sub cbrt-unprod flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg diff-log associate-*r/
Counts
4 → 100
Calls
4 calls:
27.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
33.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
80.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
17.0ms
(* (sin a) (sin b))

series821.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
260.0ms
(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
375.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
67.0ms
(* (sin a) (sin b))

simplify1.6s

Counts
112 → 112
Iterations
IterNodes
done5000
22275
1445
0172

prune930.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin b) (/ r (- (* (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)
23.6b
(cbrt (pow (* (sin b) (sin a)) 3))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
16×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube add-exp-log
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 cbrt-div unpow-prod-down pow-pow unpow3 cube-prod pow-exp *-commutative rem-cube-cbrt sqr-pow
1×pow-to-exp cbrt-undiv flip3-- pow1/3 div-exp associate-*r/ cos-mult frac-sub rem-cbrt-cube div-inv flip--
Counts
4 → 95
Calls
4 calls:
126.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
20.0ms
(* (sin b) (sin a))
14.0ms
(pow (* (sin b) (sin a)) 3)
7.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

series498.0ms

Counts
4 → 12
Calls
4 calls:
289.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
53.0ms
(* (sin b) (sin a))
88.0ms
(pow (* (sin b) (sin a)) 3)
68.0ms
(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.7s

Counts
107 → 107
Iterations
IterNodes
done5001
22818
1520
0189

prune787.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ r (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
0.2b
(* (sin b) (/ r (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a)))))))
0.2b
(* (sin b) (sin a))
4.1b
(log (exp (* (sin b) (sin a))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
19×times-frac
18×associate-*r*
13×add-cbrt-cube add-exp-log
9×pow1
6×associate-*l*
5×add-log-exp
4×associate-/r/
3×log-prod associate-/r* prod-exp log-pow cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative div-inv flip--
1×exp-prod clear-num frac-2neg exp-to-pow rem-log-exp associate-*r/ sin-mult
Counts
4 → 96
Calls
4 calls:
30.0ms
(/ r (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
62.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a)))))))
19.0ms
(* (sin b) (sin a))
3.0ms
(log (exp (* (sin b) (sin a))))

series732.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(/ r (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
308.0ms
(* (sin b) (/ r (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a)))))))
64.0ms
(* (sin b) (sin a))
92.0ms
(log (exp (* (sin b) (sin a))))

simplify1.0s

Counts
108 → 108
Iterations
IterNodes
done5000
21942
1400
0169

prune680.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes418.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done17
117
014

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.9s2845×body1280valid
1.6s1942×body640valid
353.0ms759×body320valid
304.0ms2101×body80valid
83.0ms354×body160valid