Details

Time bar (total: 1.8m)

sample83.0ms

Algorithm
intervals
Results
47.0ms256×body80valid
12.0ms256×pre80true

simplify1.0s

Counts
1 → 1
Iterations
IterNodes
42384
3459
2104
133
015

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 2 (+ beta alpha)) 1.0)
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
3.8b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite522.0ms

Algorithm
rewrite-expression-head
Rules
4338×*-un-lft-identity
2696×times-frac
2176×distribute-lft-out
779×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
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 → 1234
Calls
4 calls:
88.0ms
(+ (+ 2 (+ beta alpha)) 1.0)
70.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
206.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
60.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ 2 (+ beta alpha)) 1.0)
193.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
265.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
126.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.4s

Counts
1246 → 1246
Iterations
IterNodes
24034
11422
0612

prune15.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (+ 2 (+ beta alpha)))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 1.0 (+ 2 (+ beta alpha))))
3.8b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite420.0ms

Algorithm
rewrite-expression-head
Rules
4333×*-un-lft-identity
2696×times-frac
2173×distribute-lft-out
779×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×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1232
Calls
4 calls:
34.0ms
(+ 1.0 (+ 2 (+ beta alpha)))
75.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
167.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 1.0 (+ 2 (+ beta alpha))))
56.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series926.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(+ 1.0 (+ 2 (+ beta alpha)))
186.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
213.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 1.0 (+ 2 (+ beta alpha))))
506.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.4s

Counts
1244 → 1244
Iterations
IterNodes
24047
11426
0612

prune14.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
0.3b
(* (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
3.8b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
3.8b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite565.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 1376
Calls
4 calls:
63.0ms
(sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
247.0ms
(* (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
56.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
62.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series688.0ms

Counts
4 → 12
Calls
4 calls:
289.0ms
(sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
168.0ms
(* (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
113.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
118.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.8s

Counts
1388 → 1388
Iterations
IterNodes
22874
1997
0538

prune18.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

localize60.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (/ (/ (/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) 1) 1) (* (cbrt (+ 1.0 (+ 2 (+ beta alpha)))) (cbrt (+ 1.0 (+ 2 (+ beta alpha)))))) (/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (cbrt (+ 1.0 (+ 2 (+ beta alpha))))))
4.1b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.1b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.1b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite840.0ms

Algorithm
rewrite-expression-head
Rules
7453×*-un-lft-identity
5671×times-frac
3546×distribute-lft-out
2226×cbrt-prod
1930×add-sqr-sqrt
1905×associate-*r*
1633×add-cube-cbrt
562×add-exp-log
370×div-exp
168×prod-exp
142×add-cbrt-cube
126×cbrt-undiv
118×associate-/r/
72×1-exp unswap-sqr
64×flip3-+ flip-+
60×cbrt-unprod div-inv
37×associate-*l*
20×cbrt-div
6×pow1
5×frac-times
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l/ associate-*r/
1×pow-prod-down *-commutative
Counts
4 → 2208
Calls
4 calls:
642.0ms
(* (/ (/ (/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) 1) 1) (* (cbrt (+ 1.0 (+ 2 (+ beta alpha)))) (cbrt (+ 1.0 (+ 2 (+ beta alpha)))))) (/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (cbrt (+ 1.0 (+ 2 (+ beta alpha))))))
2.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series433.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(* (/ (/ (/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) 1) 1) (* (cbrt (+ 1.0 (+ 2 (+ beta alpha)))) (cbrt (+ 1.0 (+ 2 (+ beta alpha)))))) (/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (cbrt (+ 1.0 (+ 2 (+ beta alpha))))))
68.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
82.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
92.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify6.0s

Counts
2220 → 2220
Iterations
IterNodes
15502
01555

prune40.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.1b

regimes139.0ms

Accuracy

52.7% (1.2b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.7b

bsearch100.0ms

Steps
ItersRangePoint
9
2.5691463097521214e+161
9.397070217596908e+169
2.5988416377747475e+162

simplify2.0ms

Iterations
IterNodes
220
120
016

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s8000×body80valid
687.0ms8000×pre80true