Details

Time bar (total: 2.3m)

sample41.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
5.0ms256×pre80true

simplify2.4s

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize38.0ms

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))))
2.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite142.0ms

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 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 → 422
Calls
4 calls:
5.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
36.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
48.0ms
(/ (/ (/ (+ 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))))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series574.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
154.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
247.0ms
(/ (/ (/ (+ 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))))
138.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify2.7s

Counts
434 → 434
Iterations
IterNodes
done5001
22978
11172
0516

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (/ (+ 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))) (sqrt (/ (/ (+ 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 2.0 1.0 (+ beta alpha))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
2.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
2.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
63159×times-frac
36802×*-un-lft-identity
23660×sqrt-prod
22324×add-sqr-sqrt add-cube-cbrt
7239×distribute-lft-out
1880×div-inv
286×associate-/r*
67×associate-/l*
58×sqrt-div associate-/r/
15×add-cbrt-cube add-exp-log
7×associate-/l/
6×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
3×flip3-+ flip-+
Counts
4 → 13039
Calls
4 calls:
387.0ms
(/ (sqrt (/ (/ (+ 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))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))))
34.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
19.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series897.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(/ (sqrt (/ (/ (+ 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))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))))
398.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
121.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
134.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify24.6s

Counts
13051 → 13051
Iterations
IterNodes
done12022
012022

prune1.4m

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize85.0ms

Local error

Found 4 expressions with local error:

1.1b
(sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
2.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
2.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
10.0b
(sqrt (/ (/ 1 (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
180×sqrt-prod
150×*-un-lft-identity
134×add-sqr-sqrt
114×add-cube-cbrt
17×distribute-lft-out
10×pow1 rem-sqrt-square div-inv
9×associate-/r*
8×sqrt-pow1 add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u pow1/2 log1p-expm1-u add-log-exp pow-div associate-/l/
2×cbrt-undiv clear-num frac-2neg flip3-+ sqrt-div div-exp flip-+ pow-flip inv-pow
Counts
4 → 233
Calls
4 calls:
10.0ms
(sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
20.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
23.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
16.0ms
(sqrt (/ (/ 1 (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))

series776.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
120.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
139.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
269.0ms
(sqrt (/ (/ 1 (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))

simplify2.2s

Counts
245 → 245
Iterations
IterNodes
done5001
22551
11025
0509

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.2b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
0.3b
(* (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
2.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
2.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite554.0ms

Algorithm
rewrite-expression-head
Rules
1426×times-frac
1160×sqrt-prod
967×*-un-lft-identity
947×add-sqr-sqrt
597×add-cube-cbrt
220×swap-sqr
161×distribute-lft-out
118×associate-*r* associate-*l*
49×unswap-sqr
42×div-inv
27×associate-/l*
22×add-cbrt-cube add-exp-log
12×associate-/r*
11×pow1
7×cbrt-undiv div-exp
5×sqrt-undiv associate-/l/
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×flip3-+ flip-+
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 758
Calls
4 calls:
19.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
381.0ms
(* (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
19.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
17.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series725.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
218.0ms
(* (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
121.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
124.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify2.7s

Counts
770 → 770
Iterations
IterNodes
done5000
12022
0586

prune4.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.2b

regimes192.0ms

Accuracy

57% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch78.0ms

Steps
ItersRangePoint
7
1.9526692800653698e+163
1.145851839445724e+165
7.550165460766495e+163

simplify4.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample1.2s

Algorithm
intervals
Results
772.0ms8000×body80valid
223.0ms8000×pre80true