Details

Time bar (total: 13.4s)

sample32.0ms

Algorithm
intervals
Results
17.0ms256×body80valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
0912
11411
22410
33010
done3010

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma z z (fma x x (* y y)))
0.0b
(fma x x (* y y))
34.0b
(sqrt (fma z z (fma x x (* y y))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×pow1 add-cube-cbrt *-un-lft-identity
3×add-exp-log expm1-log1p-u sqrt-prod add-cbrt-cube log1p-expm1-u add-log-exp
2×fma-udef
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
3 → 35
Calls
3 calls:
1.0ms
(fma z z (fma x x (* y y)))
1.0ms
(fma x x (* y y))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series287.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(fma z z (fma x x (* y y)))
53.0ms
(fma x x (* y y))
165.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.9s

Counts
44 → 44
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
049471
171438
2159389
3541389
42527389
done5000389

prune227.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.0b
(+ (* z z) (fma x x (* y y)))
34.0b
(sqrt (+ (* z z) (fma x x (* y y))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×add-log-exp
4×pow1 add-cube-cbrt *-un-lft-identity
3×add-exp-log expm1-log1p-u sqrt-prod add-cbrt-cube log1p-expm1-u
2×flip3-+ sqrt-div flip-+ fma-udef
1×+-commutative rem-sqrt-square associate-+r+ fma-def sqrt-pow1 pow1/2 sum-log hypot-def
Counts
3 → 43
Calls
3 calls:
1.0ms
(fma x x (* y y))
12.0ms
(+ (* z z) (fma x x (* y y)))
10.0ms
(sqrt (+ (* z z) (fma x x (* y y))))

series287.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(fma x x (* y y))
57.0ms
(+ (* z z) (fma x x (* y y)))
181.0ms
(sqrt (+ (* z z) (fma x x (* y y))))

simplify1.7s

Counts
52 → 52
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
066675
1139576
2437523
31938523
done5000523

prune193.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.0b
(hypot z (sqrt (fma x x (* y y))))
26.9b
(sqrt (fma x x (* y y)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×pow1 add-cube-cbrt *-un-lft-identity
3×add-exp-log expm1-log1p-u sqrt-prod add-cbrt-cube log1p-expm1-u add-log-exp
2×fma-udef
1×rem-sqrt-square hypot-udef sqrt-pow1 pow1/2 hypot-def
Counts
3 → 36
Calls
3 calls:
0.0ms
(fma x x (* y y))
0.0ms
(hypot z (sqrt (fma x x (* y y))))
2.0ms
(sqrt (fma x x (* y y)))

series414.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(fma x x (* y y))
283.0ms
(hypot z (sqrt (fma x x (* y y))))
70.0ms
(sqrt (fma x x (* y y)))

simplify3.3s

Counts
45 → 45
Iterations

Useful iterations: 5 (1.8s)

IterNodesCost
048405
168370
2137235
3341231
4952231
53083219
done5000219

prune183.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot x y)
0.0b
(hypot z (hypot x y))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt hypot-udef *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(hypot x y)
1.0ms
(hypot z (hypot x y))

series721.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(hypot x y)
661.0ms
(hypot z (hypot x y))

simplify4.0s

Counts
26 → 26
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
031148
141144
246128
353128
462128
579128
6118128
7257128
8839128
93606128
done5001128

prune117.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes1.0ms