Details

Time bar (total: 7.8s)

sample36.0ms

Algorithm
intervals
Results
10.0ms311×body80nan
9.0ms326×body80valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
11510
22210
33910
47310
513010
624010
746210
8197610
done500010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.6b
(- (* y y) (* z z))
22.4b
(sqrt (- (* y y) (* z z)))

rewrite21.0ms

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
expm1-log1p-u flip3-- associate-*l* flip-- log1p-expm1-u difference-of-squares
associate-*r/ unswap-sqr
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 62
Calls
3 calls:
12.0ms
(* x (sqrt (- (* y y) (* z z))))
3.0ms
(- (* y y) (* z z))
5.0ms
(sqrt (- (* y y) (* z z)))

series146.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(* x (sqrt (- (* y y) (* z z))))
29.0ms
(- (* y y) (* z z))
46.0ms
(sqrt (- (* y y) (* z z)))

simplify1.5s

Counts
71 → 71
Iterations

Useful iterations: done (1.5s)

IterNodesCost
094839
1205760
2770676
33155676
done5000675

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

3.3b
(fma y y (- (* z z)))
22.4b
(sqrt (fma y y (- (* z z))))
22.4b
(sqrt (fma y y (- (* z z))))
22.4b
(sqrt (* (sqrt (fma y y (- (* z z)))) (sqrt (fma y y (- (* z z))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-pow1
22×pow1
11×pow1/2
add-sqr-sqrt
sqrt-prod
add-cube-cbrt *-un-lft-identity
pow-prod-up
add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
rem-sqrt-square pow-prod-down pow-sqr
pow2 pow-plus fma-udef
Counts
4 → 66
Calls
4 calls:
0.0ms
(fma y y (- (* z z)))
1.0ms
(sqrt (fma y y (- (* z z))))
1.0ms
(sqrt (fma y y (- (* z z))))
4.0ms
(sqrt (* (sqrt (fma y y (- (* z z)))) (sqrt (fma y y (- (* z z))))))

series194.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma y y (- (* z z)))
53.0ms
(sqrt (fma y y (- (* z z))))
52.0ms
(sqrt (fma y y (- (* z z))))
53.0ms
(sqrt (* (sqrt (fma y y (- (* z z)))) (sqrt (fma y y (- (* z z))))))

simplify4.3s

Counts
78 → 78
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
067794
1100569
2238527
3755527
43241527
done5000527

prune190.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize2.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes107.0ms

bsearch23.0ms