Details

Time bar (total: 12.3s)

sample77.0ms

Algorithm
intervals
Results
40.0ms96×body1280valid
16.0ms62×body640valid
4.0ms23×body320valid
3.0ms62×body80valid
2.0ms13×body160valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089
1129
2169
3199
4209
done209

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
4.1b
(cos (+ a b))

rewrite16.0ms

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×times-frac associate-*r* associate-*l* associate-/r* 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 → 47
Calls
3 calls:
3.0ms
(* r (sin b))
4.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))

series162.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(* r (sin b))
99.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify1.7s

Counts
56 → 56
Iterations

Useful iterations: 3 (421.0ms)

IterNodesCost
090535
1199525
2556447
32202443
done5000443

prune133.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.2b
(- (* (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))

rewrite23.0ms

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:
3.0ms
(* r (sin b))
5.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms
(* (sin a) (sin b))

series375.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* r (sin b))
81.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
214.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms
(* (sin a) (sin b))

simplify2.0s

Counts
88 → 88
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01401256
13431224
210941076
34105989
done5000988

prune283.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (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))))))
0.2b
(* (sin a) (sin b))
2.7b
(log (exp (* (sin a) (sin b))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
7×pow1
6×log-prod add-log-exp
3×times-frac associate-*r* associate-*l* associate-/r* log-pow associate--r+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ flip-- cbrt-unprod
1×sub-neg exp-prod exp-to-pow frac-2neg diff-log rem-log-exp pow-prod-down clear-num *-commutative div-inv sin-mult associate-/l* unswap-sqr
Counts
4 → 71
Calls
4 calls:
5.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
10.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
4.0ms
(* (sin a) (sin b))
2.0ms
(log (exp (* (sin a) (sin b))))

series397.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
222.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
44.0ms
(* (sin a) (sin b))
47.0ms
(log (exp (* (sin a) (sin b))))

simplify1.9s

Counts
83 → 83
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01401338
13201165
29871023
33863968
done5000967

prune311.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
27×associate-*l*
23×add-sqr-sqrt
19×add-exp-log add-cbrt-cube
15×frac-times *-un-lft-identity
14×associate-*r*
13×add-cube-cbrt
12×pow1
11×associate-/r/
10×sin-mult
8×flip3-- flip3-+ frac-add cos-mult flip-- flip-+
7×associate-*r/ associate-*l/ prod-exp cbrt-unprod
4×pow-prod-down *-commutative add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in times-frac
2×cbrt-undiv sub-neg div-exp
1×div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 119
Calls
4 calls:
40.0ms
(* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))
5.0ms
(* (sin a) (sin b))
4.0ms
(* (sin a) (sin b))
75.0ms
(* (/ r (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))
48.0ms
(* (sin a) (sin b))
44.0ms
(* (sin a) (sin b))
191.0ms
(* (/ r (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.2s

Counts
131 → 131
Iterations

Useful iterations: 2 (396.0ms)

IterNodesCost
02114035
17423917
236203505
done50003505

prune611.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes187.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01418
11718
done1718

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s2940×body1280valid
460.0ms1823×body640valid
130.0ms761×body320valid
118.0ms2119×body80valid
50.0ms359×body160valid