Details

Time bar (total: 4.9m)

sample78.0ms

Algorithm
intervals
Results
41.0ms256×body80valid
19.0ms256×pre80true

simplify1.1s

Counts
1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize51.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ (+ 1.0 (+ beta alpha)) 2)

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
4332×*-un-lft-identity
2696×times-frac
2173×distribute-lft-out
778×add-sqr-sqrt add-cube-cbrt
166×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
13×add-log-exp
10×cbrt-undiv div-exp
6×sum-log
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1221
Calls
4 calls:
Slowest
306.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
185.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
165.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
65.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series486.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
165.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
106.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
24.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.4s

Counts
1233 → 1233

prune13.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize59.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(* (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))
0.1b
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
8779×*-un-lft-identity
5938×times-frac
4324×distribute-lft-out
2233×sqrt-prod
1897×add-sqr-sqrt
1694×add-cube-cbrt
840×associate-*r*
421×associate-*l*
200×associate-/r/
147×associate-/l*
102×flip3-+ flip-+
101×div-inv
45×unswap-sqr
27×add-exp-log
22×add-cbrt-cube
16×associate-/r*
10×div-exp
7×cbrt-undiv
6×pow1 prod-exp
5×associate-/l/
4×cbrt-unprod insert-posit16 add-log-exp
3×clear-num frac-2neg
2×1-exp
1×frac-times sqrt-div pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 2416
Calls
4 calls:
Slowest
1.4s
(* (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))
261.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
178.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
172.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))
172.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
108.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
94.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify5.8s

Counts
2428 → 2428

prune39.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize102.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite731.0ms

Algorithm
rewrite-expression-head
Rules
196×*-un-lft-identity
84×distribute-lft-out
80×times-frac
48×add-sqr-sqrt add-cube-cbrt
20×associate-/r*
16×associate-/l*
12×add-cbrt-cube add-exp-log
8×flip3-+ associate-/r/ flip-+ associate-/l/
4×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 div-inv add-log-exp
Counts
4 → 184
Calls
4 calls:
Slowest
212.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
192.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
162.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
156.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
119.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
118.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
111.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.7s

Counts
196 → 196

prune4.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize51.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.6b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
0.2b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.1b
(/ (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
62484×*-un-lft-identity
48332×times-frac
29618×distribute-lft-out
17150×sqrt-prod
13956×add-sqr-sqrt add-cube-cbrt
1962×associate-/l*
1210×associate-/r/
606×flip3-+ flip-+
605×div-inv
148×sqrt-div
34×add-cbrt-cube add-exp-log
27×associate-/r*
20×cbrt-undiv div-exp
5×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Counts
4 → 14314
Calls
4 calls:
Slowest
821.0ms
(/ (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
251.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
213.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
188.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series776.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
238.0ms
(/ (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
225.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
193.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
120.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify17.2s

Counts
14326 → 14326

prune3.3m

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes83.0ms

Accuracy

0% (2.4b remaining)

Error of 3.6b against oracle of 1.2b and baseline of 3.6b

bsearch3.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s8000×body80valid
203.0ms8000×pre80true