Details

Time bar (total: 19.3s)

sample90.0ms

Algorithm
intervals
Results
25.0ms328×body80valid
19.0ms289×body80nan

simplify13.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
22110
33610
46210
513310
619110
737310
8154110
done500010

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.0b
(- (* y y) (* z z))
26.2b
(sqrt (- (* y y) (* z z)))

rewrite77.0ms

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:
50.0ms
(* x (sqrt (- (* y y) (* z z))))
9.0ms
(- (* y y) (* z z))
16.0ms
(sqrt (- (* y y) (* z z)))

series224.0ms

Counts
3 → 9
Calls
3 calls:
104.0ms
(* x (sqrt (- (* y y) (* z z))))
45.0ms
(- (* y y) (* z z))
75.0ms
(sqrt (- (* y y) (* z z)))

simplify846.0ms

Counts
63 → 63
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
085765
1185697
2443613
31486613
done5001613

prune162.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

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

prune4.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

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

prune3.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ y z))
0.0b
(sqrt (- y z))
0.1b
(* x (sqrt (+ y z)))
0.2b
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity sqrt-prod
18×sqrt-div
15×associate-*r*
13×pow1
11×add-exp-log add-cube-cbrt add-cbrt-cube
10×associate-*r/
flip3-+ flip-+
frac-times flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod add-log-exp
rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 89
Calls
4 calls:
10.0ms
(sqrt (+ y z))
8.0ms
(sqrt (- y z))
24.0ms
(* x (sqrt (+ y z)))
65.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ y z))
82.0ms
(sqrt (- y z))
93.0ms
(* x (sqrt (+ y z)))
117.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

simplify2.9s

Counts
101 → 101
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01631230
13971090
210911020
33593981
done5001981

prune302.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes462.0ms

bsearch21.0ms