Details

Time bar (total: 2.1m)

sample46.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
7.0ms256×pre80true

simplify1.3s

Counts
1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite974.0ms

Algorithm
rewrite-expression-head
Rules
5713×*-un-lft-identity
3256×times-frac
2994×distribute-lft-out
886×add-sqr-sqrt add-cube-cbrt
197×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
5×fma-def
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1445
Calls
4 calls:
Slowest
570.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
147.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
87.0ms
(+ (+ 2 (+ beta alpha)) 1.0)
62.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
148.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
118.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
23.0ms
(+ (+ 2 (+ beta alpha)) 1.0)

simplify1.5s

Counts
1457 → 1457

prune16.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.8b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
11512×*-un-lft-identity
7123×times-frac
5934×distribute-lft-out
2633×sqrt-prod
2134×add-sqr-sqrt
1931×add-cube-cbrt
990×associate-*r*
496×associate-*l*
200×associate-/r/
174×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×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u 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 → 2836
Calls
4 calls:
Slowest
986.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
234.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
88.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
76.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

series669.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
230.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
181.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
137.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
122.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

simplify6.4s

Counts
2848 → 2848

prune46.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize79.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
3.4b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
0.6b
(/ 1 (sqrt (+ 2 (+ beta alpha))))
0.6b
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
958×*-un-lft-identity
547×times-frac
450×distribute-lft-out
208×add-sqr-sqrt add-cube-cbrt
180×sqrt-prod
44×associate-/l*
26×associate-/r* associate-/r/
17×add-exp-log
15×flip3-+ add-cbrt-cube flip-+
13×div-inv
7×div-exp
6×pow1 cbrt-undiv
5×associate-/l/
4×expm1-log1p-u clear-num frac-2neg sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×pow-flip
1×rec-exp sqrt-pow1 pow1/2 1-exp inv-pow
Counts
4 → 473
Calls
4 calls:
Slowest
141.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
78.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
53.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
19.0ms
(/ 1 (sqrt (+ 2 (+ beta alpha))))

series580.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
233.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
125.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
114.0ms
(/ 1 (sqrt (+ 2 (+ beta alpha))))
108.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

simplify2.1s

Counts
485 → 485

prune8.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize108.0ms

Local error

Found 4 expressions with local error:

10.7b
(sqrt (/ (/ 1 (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))))
3.4b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
3.2b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (sqrt (+ 2 (+ beta alpha))))
1.6b
(* (* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (sqrt (+ 2 (+ beta alpha))))) 1)) (/ (sqrt (/ (/ 1 (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0)))

rewrite880.0ms

Algorithm
rewrite-expression-head
Rules
4331×*-un-lft-identity
3153×times-frac
2088×distribute-lft-out
1986×sqrt-prod
1068×associate-*r*
1041×add-sqr-sqrt
1026×add-cube-cbrt
132×associate-/r/
88×add-exp-log
68×flip3-+ flip-+
66×div-inv
49×add-cbrt-cube
38×prod-exp
36×div-exp
18×cbrt-unprod
17×sqrt-div
15×cbrt-undiv
14×pow1
13×associate-/r*
12×1-exp
10×associate-/l*
7×rem-sqrt-square sqrt-pow1
5×frac-times associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp pow-div associate-/l/
3×pow1/2 pow-prod-down associate-*r/
2×clear-num frac-2neg pow-flip inv-pow
1×associate-*l* *-commutative
Counts
4 → 1443
Calls
4 calls:
Slowest
565.0ms
(* (* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (sqrt (+ 2 (+ beta alpha))))) 1)) (/ (sqrt (/ (/ 1 (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0)))
101.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (sqrt (+ 2 (+ beta alpha))))
57.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
49.0ms
(sqrt (/ (/ 1 (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))))

series691.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
283.0ms
(* (* (/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) 1) (/ (sqrt (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (sqrt (+ 2 (+ beta alpha))))) 1)) (/ (sqrt (/ (/ 1 (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0)))
146.0ms
(sqrt (/ (/ 1 (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))))
144.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (sqrt (+ 2 (+ beta alpha))))
117.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

simplify4.1s

Counts
1455 → 1455

prune30.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes141.0ms

Accuracy

59.9% (0.9b remaining)

Error of 2.2b against oracle of 1.2b and baseline of 3.6b

bsearch88.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.5s8000×body80valid
285.0ms8000×pre80true