Details

Time bar (total: 2.1s)

sample32.0ms

Algorithm
intervals
Results
9.0ms321×body80valid
7.0ms304×body80nan

simplify108.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0155
1225
2395
3715
41675
52985
65455
721425
850015

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.6b
(- (* y y) (* z z))
26.0b
(sqrt (- (* y y) (* z z)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
7×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div
3×expm1-log1p-u flip3-- associate-*l* flip-- log1p-expm1-u difference-of-squares
2×associate-*r/ unswap-sqr
1×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:
7.0ms
(* x (sqrt (- (* y y) (* z z))))
4.0ms
(- (* y y) (* z z))
5.0ms
(sqrt (- (* y y) (* z z)))

series184.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(* x (sqrt (- (* y y) (* z z))))
37.0ms
(- (* y y) (* z z))
59.0ms
(sqrt (- (* y y) (* z z)))

simplify101.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0202397
1786374
23192368
35001364

prune194.0ms

Filtered
71 candidates to 54 candidates (76.1%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (fma y y (- (* z z)))))
3.3b
(fma y y (- (* z z)))
26.0b
(sqrt (fma y y (- (* z z))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity sqrt-prod
6×pow1 associate-*r*
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef
Counts
3 → 49
Calls
3 calls:
9.0ms
(* x (sqrt (fma y y (- (* z z)))))
1.0ms
(fma y y (- (* z z)))
2.0ms
(sqrt (fma y y (- (* z z))))

series202.0ms

Counts
3 → 9
Calls
3 calls:
91.0ms
(* x (sqrt (fma y y (- (* z z)))))
48.0ms
(fma y y (- (* z z)))
62.0ms
(sqrt (fma y y (- (* z z))))

simplify66.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0118308
1396288
21682285
35001285

prune150.0ms

Filtered
58 candidates to 41 candidates (70.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

3.3b
(fma y y (- (* z z)))
3.3b
(fma y y (- (* z z)))
26.8b
(cbrt (fma y y (- (* z z))))
26.8b
(cbrt (fma y y (- (* z z))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
Counts
4 → 46
Calls
4 calls:
1.0ms
(fma y y (- (* z z)))
1.0ms
(fma y y (- (* z z)))
1.0ms
(cbrt (fma y y (- (* z z))))
1.0ms
(cbrt (fma y y (- (* z z))))

series375.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma y y (- (* z z)))
45.0ms
(fma y y (- (* z z)))
145.0ms
(cbrt (fma y y (- (* z z))))
132.0ms
(cbrt (fma y y (- (* z z))))

simplify146.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 4 (140.0ms)

IterNodesCost
095336
1230304
2711298
33403294
45001290

prune233.0ms

Filtered
58 candidates to 50 candidates (86.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize2.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune0.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes213.0ms

bsearch9.0ms