Details

Time bar (total: 3.9m)

sample75.0ms

Algorithm
intervals
Results
44.0ms256×body80valid
12.0ms256×pre80true

simplify1.1s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize47.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 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)

rewrite971.0ms

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
381.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
200.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
188.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
107.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series507.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
211.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
150.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
125.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
20.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.6s

Counts
1233 → 1233

prune15.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.8b

localize77.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
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)))

rewrite1.9s

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
988.0ms
(* (/ (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)))
336.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
203.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
193.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series688.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
232.0ms
(* (/ (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)))
200.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
132.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
123.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify6.0s

Counts
2428 → 2428

prune40.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize59.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.9b
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (+ 2 (+ beta alpha)))))
0.5b
(* (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (+ 2 (+ beta alpha))))

rewrite861.0ms

Algorithm
rewrite-expression-head
Rules
199×*-un-lft-identity
109×times-frac
85×distribute-lft-out
58×sqrt-prod
55×add-sqr-sqrt
51×add-cube-cbrt
37×associate-/l*
18×flip3-+ flip-+
16×associate-/r/
15×add-cbrt-cube add-exp-log
13×sqrt-div
11×associate-/r*
8×frac-times associate-*r*
6×pow1 associate-*l*
5×div-inv associate-/l/
4×cbrt-undiv div-exp associate-*l/ associate-*r/ insert-posit16 add-log-exp
3×clear-num frac-2neg
2×prod-exp cbrt-unprod unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 211
Calls
4 calls:
Slowest
262.0ms
(* (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (+ 2 (+ beta alpha))))
245.0ms
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (+ 2 (+ beta alpha)))))
176.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
175.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (+ 2 (+ beta alpha)))))
107.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
89.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
80.0ms
(* (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (+ 2 (+ beta alpha))))

simplify1.0s

Counts
223 → 223

prune3.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize80.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
4.5b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
4.5b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.6b
(/ (sqrt (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
16544×*-un-lft-identity
16524×sqrt-prod
14005×times-frac
7239×distribute-lft-out
4771×add-sqr-sqrt
4769×add-cube-cbrt
509×associate-/l*
187×sqrt-div
184×associate-/r/
95×flip3-+ flip-+
92×div-inv
14×associate-/r*
8×add-cbrt-cube add-exp-log
6×pow1
4×insert-posit16 add-log-exp
3×associate-/l/
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp
1×sqrt-undiv
Counts
4 → 5156
Calls
4 calls:
Slowest
304.0ms
(/ (sqrt (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
179.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
96.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
63.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(/ (sqrt (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
114.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
75.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
60.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify10.3s

Counts
5168 → 5168

prune2.4m

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes147.0ms

Accuracy

57.2% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.7b

bsearch124.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8000×body80valid
375.0ms8000×pre80true