Details

Time bar (total: 3.5m)

sample77.0ms

Algorithm
intervals
Results
43.0ms256×body80valid
13.0ms256×pre80true

simplify1.5s

Counts
1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize38.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 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)

rewrite677.0ms

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
275.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
135.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
84.0ms
(+ (+ 2 (+ beta alpha)) 1.0)
69.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(/ (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
169.0ms
(/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
135.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
24.0ms
(+ (+ 2 (+ beta alpha)) 1.0)

simplify1.4s

Counts
1457 → 1457

prune17.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize71.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
4.6b
(/ (+ 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)))) (+ (+ 2 (+ beta alpha)) 1.0))
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)))

rewrite1.6s

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
1.0s
(* (/ (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)))
197.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
81.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
70.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

series707.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
256.0ms
(* (/ (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)))
215.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
127.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
108.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

simplify6.2s

Counts
2848 → 2848

prune48.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize88.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
4.6b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
4.6b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
4.6b
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

rewrite383.0ms

Algorithm
rewrite-expression-head
Rules
292×*-un-lft-identity
144×distribute-lft-out
100×times-frac
52×add-sqr-sqrt add-cube-cbrt
20×associate-/r* associate-/l*
12×add-cbrt-cube add-exp-log
8×flip3-+ associate-/r/ flip-+ associate-/l/
4×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
4 → 216
Calls
4 calls:
Slowest
109.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
101.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
83.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
82.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

series511.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
134.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
119.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))
109.0ms
(/ (+ 1.0 (+ beta (fma beta alpha alpha))) (+ 2 (+ beta alpha)))

simplify1.6s

Counts
228 → 228

prune4.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize68.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
4.5b
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
0.6b
(/ (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
0.6b
(/ (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
20268×*-un-lft-identity
15850×times-frac
9842×sqrt-prod
9378×distribute-lft-out
5216×add-sqr-sqrt
5210×add-cube-cbrt
570×associate-/l*
184×associate-/r/
168×sqrt-div
102×div-inv
94×flip3-+ flip-+
27×add-exp-log
22×add-cbrt-cube
18×associate-/r*
17×div-exp
12×cbrt-undiv
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 1-exp hypot-def associate-/l/
Counts
4 → 5806
Calls
4 calls:
Slowest
281.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
209.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
32.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
23.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))

series563.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
199.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ beta (fma beta alpha alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
78.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))
78.0ms
(sqrt (+ 1.0 (+ beta (fma beta alpha alpha))))

simplify9.2s

Counts
5818 → 5818

prune1.9m

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.8b

regimes117.0ms

Accuracy

45% (1.4b remaining)

Error of 2.5b against oracle of 1.1b and baseline of 3.7b

bsearch186.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8000×body80valid
334.0ms8000×pre80true