Details

Time bar (total: 1.0m)

sample52.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify5.1s

Counts
1 → 1
Iterations
IterNodes
done5000
43214
3509
2114
133
014

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
4.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg flip3-+ flip-+
2×associate-/r/
1×+-commutative associate-+r+ sum-log fma-udef
Counts
4 → 426
Calls
4 calls:
8.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
49.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
62.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
40.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series754.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
267.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
315.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
140.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify5.6s

Counts
438 → 438
Iterations
IterNodes
done5005
23093
11185
0520

prune4.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.6b

localize65.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 3.0 (+ beta alpha)))
4.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
872×times-frac
765×*-un-lft-identity
360×add-sqr-sqrt add-cube-cbrt
229×distribute-lft-out
72×associate-/l*
31×div-inv
19×add-cbrt-cube add-exp-log
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 460
Calls
3 calls:
51.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
148.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 3.0 (+ beta alpha)))
49.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series662.0ms

Counts
3 → 9
Calls
3 calls:
226.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
271.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 3.0 (+ beta alpha)))
165.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify5.8s

Counts
469 → 469
Iterations
IterNodes
done5001
23062
11162
0506

prune4.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
0.1b
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
0.1b
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 3.0 (+ beta alpha)))
4.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity add-exp-log
55×add-sqr-sqrt
54×times-frac
38×add-cbrt-cube add-cube-cbrt
28×div-exp
16×associate-*l* prod-exp
15×cbrt-undiv
13×associate-*r* distribute-lft-out
11×associate-/r*
8×cbrt-unprod associate-/l*
7×pow1
6×unswap-sqr associate-/l/
5×rec-exp 1-exp div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×frac-times flip3-+ associate-*l/ associate-*r/ associate-/r/ un-div-inv flip-+
1×pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 177
Calls
4 calls:
7.0ms
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
79.0ms
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
114.0ms
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 3.0 (+ beta alpha)))
39.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series1.1s

Counts
4 → 12
Calls
4 calls:
441.0ms
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
256.0ms
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
264.0ms
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 3.0 (+ beta alpha)))
133.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify4.8s

Counts
189 → 189
Iterations
IterNodes
done5003
22739
1680
0242

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize199.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
0.6b
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) 1) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
4.5b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.5b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
6212×times-frac
3778×*-un-lft-identity
3312×sqrt-prod
2632×add-sqr-sqrt
2626×add-cube-cbrt
576×distribute-lft-out
284×associate-/l*
66×div-inv
27×add-exp-log
22×add-cbrt-cube
17×div-exp
14×associate-/r*
12×cbrt-undiv
8×sqrt-div
6×pow1
4×expm1-log1p-u flip3-+ associate-/r/ flip-+ 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 → 2372
Calls
4 calls:
139.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
200.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) 1) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
21.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
21.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
333.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) 1) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
78.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
109.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify8.6s

Counts
2384 → 2384
Iterations
IterNodes
done5001
14297
01835

prune11.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

regimes423.0ms

Accuracy

54.2% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch50.0ms

Steps
ItersRangePoint
4
3.989259968505067e+165
5.908223814084248e+165
5.248579992166405e+165

simplify13.0ms

Iterations
IterNodes
done24
124
019

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.1s8000×body80valid
262.0ms8000×pre80true