Details

Time bar (total: 2.3m)

sample43.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
5.0ms256×pre80true

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
014404
133404
2114354
3509354
43214354
done5000354

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma 2.0 1.0 (+ alpha beta)))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
3.1b
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

rewrite159.0ms

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:
9.0ms
(+ 1.0 (fma 2.0 1.0 (+ alpha beta)))
28.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
57.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
30.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ 1.0 (fma 2.0 1.0 (+ alpha beta)))
192.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
262.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (+ 1.0 (fma 2.0 1.0 (+ alpha beta))))
102.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

simplify4.3s

Counts
434 → 434
Iterations

Useful iterations: done (4.2s)

IterNodesCost
0517284613
11171271663
22986268623
done5002267903

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.7b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
0.4b
(/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
3.1b
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
3.1b
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
112×sqrt-prod
98×*-un-lft-identity
84×times-frac
72×add-sqr-sqrt
66×add-cube-cbrt
16×distribute-lft-out
14×associate-/l*
12×associate-/r*
8×add-cbrt-cube sqrt-div add-exp-log
6×pow1
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
4 → 182
Calls
4 calls:
14.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
19.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
9.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
11.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
155.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (sqrt (fma 2.0 1.0 (+ alpha beta))))
72.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
71.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))

simplify2.4s

Counts
194 → 194
Iterations

Useful iterations: done (2.3s)

IterNodesCost
015396478
129690234
264989760
3186089534
done500289484

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.7b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))))
0.1b
(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))))))
3.1b
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
3.1b
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

rewrite4.4s

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:
75.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))))
512.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))))))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
26.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

series926.0ms

Counts
4 → 12
Calls
4 calls:
420.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))))
270.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))) (/ (+ 1.0 (fma 2.0 1.0 (+ alpha beta))) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))))))
100.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
136.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))

simplify26.1s

Counts
13051 → 13051
Iterations

Useful iterations: 0 (12.7s)

IterNodesCost
01202218088501
done1202218088501

prune1.5m

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.7b

localize88.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
3.1b
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
3.1b
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
9.3b
(sqrt (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
155×times-frac
124×sqrt-prod
113×*-un-lft-identity
98×add-sqr-sqrt
83×add-cube-cbrt
15×distribute-lft-out
7×pow1
6×rem-sqrt-square add-cbrt-cube add-exp-log
5×sqrt-div div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-/r* sqrt-pow1 flip3-+ pow1/2 flip-+
2×hypot-def associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp
Counts
4 → 168
Calls
4 calls:
10.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
10.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
25.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
37.0ms
(sqrt (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))))

series526.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
71.0ms
(sqrt (+ 1.0 (fma beta alpha (+ alpha beta))))
134.0ms
(/ (+ 1.0 (fma beta alpha (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta)))
257.0ms
(sqrt (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ alpha beta)))) (fma 2.0 1.0 (+ alpha beta))) (fma 2.0 1.0 (+ alpha beta))))

simplify2.8s

Counts
180 → 180
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0396101771
178695310
2194093465
done500293325

prune1.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.7b

regimes200.0ms

Accuracy

55.2% (1.2b remaining)

Error of 2.2b against oracle of 1.0b and baseline of 3.6b

bsearch87.0ms

Steps
ItersRangePoint
7
1.2249560232862804e+194
2.9325347846936822e+196
1.2474579348782378e+194

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
019606
122606
done22606

end0.0ms

sample1.3s

Algorithm
intervals
Results
794.0ms8000×body80valid
268.0ms8000×pre80true