Details

Time bar (total: 7.6s)

sample46.0ms

Algorithm
intervals
Results
11.0ms330×body80nan
10.0ms312×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
22110
33610
46210
513310
628610
772710
8332910
done500010

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
1.6b
(- (* y y) (* z z))
22.0b
(sqrt (- (* y y) (* z z)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
sqrt-prod
add-cube-cbrt *-un-lft-identity associate-*r*
pow1
add-exp-log add-cbrt-cube add-log-exp
sqrt-div
flip3-- associate-*l* flip-- difference-of-squares
associate-*r/ unswap-sqr
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 54
Calls
3 calls:
33.0ms
(* x (sqrt (- (* y y) (* z z))))
11.0ms
(- (* y y) (* z z))
10.0ms
(sqrt (- (* y y) (* z z)))

series219.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(* x (sqrt (- (* y y) (* z z))))
52.0ms
(- (* y y) (* z z))
48.0ms
(sqrt (- (* y y) (* z z)))

simplify607.0ms

Counts
63 → 63
Iterations

Useful iterations: done (605.0ms)

IterNodesCost
085765
1211697
2930615
done5001613

prune198.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune10.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune9.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ y z))
0.2b
(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×sqrt-prod
14×sqrt-div
13×*-un-lft-identity
associate-*r*
pow1 add-cube-cbrt associate-*l*
add-exp-log frac-times flip3-+ add-cbrt-cube flip-+ unswap-sqr
flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
associate-*r/ associate-*l/ distribute-lft-out add-log-exp
rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
2 → 57
Calls
2 calls:
7.0ms
(sqrt (+ y z))
46.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

series137.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(sqrt (+ y z))
90.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

simplify2.2s

Counts
63 → 63
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
0112794
1238719
2897697
34878689
done5001689

prune192.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.2b

regimes518.0ms

bsearch49.0ms