Details

Time bar (total: 24.2s)

sample291.0ms

Algorithm
intervals
Results
73.0ms83×body1280valid
72.0ms24×body320valid
40.0ms72×body640valid
11.0ms61×body80valid
4.0ms16×body160valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
089
1129
2169
3209
4219
done219

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize35.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
3.4b
(cos (+ a b))

rewrite116.0ms

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×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u 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 → 73
Calls
3 calls:
61.0ms
(* r (/ (sin b) (cos (+ a b))))
23.0ms
(/ (sin b) (cos (+ a b)))
24.0ms
(cos (+ a b))

series310.0ms

Counts
3 → 9
Calls
3 calls:
194.0ms
(* r (/ (sin b) (cos (+ a b))))
75.0ms
(/ (sin b) (cos (+ a b)))
42.0ms
(cos (+ a b))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0122955
1283928
21071842
done5000836

prune654.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
23×associate-*r*
19×times-frac
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
8×associate-/r/
5×cos-mult sin-mult
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp frac-sub flip-- div-inv sub-div
1×frac-2neg associate-*r/ clear-num
Counts
4 → 113
Calls
4 calls:
20.0ms
(* (cos a) (cos b))
144.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
69.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
23.0ms
(* (sin b) (sin a))

series791.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (cos a) (cos b))
409.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
212.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
92.0ms
(* (sin b) (sin a))

simplify2.4s

Counts
125 → 125
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02002025
14821971
221771792
done50021706

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos a) (cos b))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin b) (sin a)))))))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin b) (sin a))))))
0.2b
(* (sin b) (sin a))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×associate-*r*
19×times-frac
15×add-exp-log add-cbrt-cube
10×pow1
9×associate-*l*
4×expm1-log1p-u prod-exp associate-/r/ cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv flip3-- div-exp flip-- div-inv
1×frac-2neg associate-*r/ clear-num cos-mult sin-mult
Counts
4 → 109
Calls
4 calls:
20.0ms
(* (cos a) (cos b))
104.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin b) (sin a)))))))
51.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin b) (sin a))))))
24.0ms
(* (sin b) (sin a))

series967.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (cos a) (cos b))
502.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin b) (sin a)))))))
294.0ms
(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin b) (sin a))))))
86.0ms
(* (sin b) (sin a))

simplify2.5s

Counts
121 → 121
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01942103
14611871
220661696
done50001611

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
43×*-un-lft-identity
33×add-cube-cbrt
30×times-frac
21×prod-diff
13×add-exp-log add-cbrt-cube
8×associate-/r*
7×fma-neg
6×pow1 div-inv add-log-exp
5×distribute-lft-out-- difference-of-squares
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×cbrt-undiv div-exp associate-*r* associate-*l*
2×flip3-- frac-2neg prod-exp clear-num associate-/r/ cos-mult flip-- cbrt-unprod
1×sub-neg diff-log pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 128
Calls
4 calls:
28.0ms
(* (cos b) (cos a))
59.0ms
(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
29.0ms
(/ (* (cos b) (cos a)) (sin b))
74.0ms
(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series741.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (cos b) (cos a))
158.0ms
(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
118.0ms
(/ (* (cos b) (cos a)) (sin b))
376.0ms
(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify2.6s

Counts
140 → 140
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02132538
14762234
220161957
done50001829

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes520.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01941
12341
done2341

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.4s2921×body1280valid
1.8s1832×body640valid
429.0ms2130×body80valid
407.0ms780×body320valid
158.0ms341×body160valid