Details

Time bar (total: 1.1m)

sample80.0ms

Algorithm
intervals
Results
46.0ms256×body80valid
12.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
43908
3592
2148
163
015

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* alpha beta) (+ beta alpha))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
3.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite843.0ms

Algorithm
rewrite-expression-head
Rules
4323×*-un-lft-identity
2696×times-frac
2167×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*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1217
Calls
4 calls:
13.0ms
(+ (* alpha beta) (+ beta alpha))
187.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
371.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
174.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (* alpha beta) (+ beta alpha))
181.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
210.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
121.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.7s

Counts
1229 → 1229
Iterations
IterNodes
12460
0609

prune14.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
0.3b
(* (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
3.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
7619×*-un-lft-identity
3793×times-frac
3499×distribute-lft-out
2030×sqrt-prod
869×add-sqr-sqrt
803×swap-sqr add-cube-cbrt
139×associate-*r* associate-*l*
88×associate-/r/
46×flip3-+ flip-+
44×div-inv
20×pow1
16×unswap-sqr
10×associate-/r* add-cbrt-cube add-exp-log
9×sqrt-pow1 pow1/2
8×associate-/l*
5×sqrt-div pow-prod-up
4×insert-posit16 add-log-exp associate-/l/
3×rem-sqrt-square pow-prod-down pow-sqr
2×cbrt-undiv clear-num frac-2neg div-exp
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 1368
Calls
4 calls:
137.0ms
(sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
532.0ms
(* (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
206.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
145.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series671.0ms

Counts
4 → 12
Calls
4 calls:
263.0ms
(sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
179.0ms
(* (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
121.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
108.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.4s

Counts
1380 → 1380
Iterations
IterNodes
23990
11754
0533

prune19.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize74.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
0.7b
(* (sqrt (/ 1 (sqrt (+ 2 (+ beta alpha))))) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
3.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite873.0ms

Algorithm
rewrite-expression-head
Rules
1196×*-un-lft-identity
880×times-frac
608×sqrt-prod
499×distribute-lft-out
440×add-sqr-sqrt
320×add-cube-cbrt
217×associate-*r*
44×associate-/r/
36×unswap-sqr
34×associate-/l*
33×associate-*l*
24×flip3-+ flip-+
22×div-inv
18×associate-/r*
15×add-cbrt-cube add-exp-log
10×sqrt-div
8×pow1
5×cbrt-undiv div-exp associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
2×sqrt-pow1 pow1/2
1×frac-times sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 656
Calls
4 calls:
162.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
337.0ms
(* (sqrt (/ 1 (sqrt (+ 2 (+ beta alpha))))) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
181.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
170.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series1.1s

Counts
4 → 12
Calls
4 calls:
236.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
291.0ms
(* (sqrt (/ 1 (sqrt (+ 2 (+ beta alpha))))) (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
431.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
131.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.2s

Counts
668 → 668
Iterations
IterNodes
12259
0560

prune11.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* alpha beta) (+ beta alpha))
0.0b
(* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))
2.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha))))
3.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite870.0ms

Algorithm
rewrite-expression-head
Rules
148×*-un-lft-identity
86×times-frac
64×distribute-lft-out
39×add-sqr-sqrt
37×add-cube-cbrt
30×associate-/l*
20×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
14×associate-/r/
9×add-log-exp
8×frac-times
7×cbrt-undiv div-exp
6×pow1 associate-/r* associate-*l*
5×associate-*r*
4×associate-*l/ associate-*r/ insert-posit16 div-inv
3×sum-log prod-exp cbrt-unprod associate-/l/
2×clear-num frac-2neg
1×distribute-rgt-in +-commutative associate-+r+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 175
Calls
4 calls:
27.0ms
(+ (* alpha beta) (+ beta alpha))
325.0ms
(* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))
273.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha))))
238.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (* alpha beta) (+ beta alpha))
46.0ms
(* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))
227.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha))))
103.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.4s

Counts
187 → 187
Iterations
IterNodes
24600
11279
0257

prune1.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.2b

regimes99.0ms

Accuracy

48.4% (1.3b remaining)

Error of 2.6b against oracle of 1.3b and baseline of 3.9b

bsearch109.0ms

Steps
ItersRangePoint
7
1.1200243465581616e+123
6.941568694875892e+124
2.8836479899208303e+124

simplify12.0ms

Iterations
IterNodes
242
142
030

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s8000×body80valid
690.0ms8000×pre80true