Details

Time bar (total: 2.7s)

sample32.0ms

Algorithm
intervals
Results
8.0ms310×body80valid
7.0ms298×body80nan

simplify103.0ms

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: 24.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.8b
(- (* y y) (* z z))
24.3b
(sqrt (- (* y y) (* z z)))

rewrite19.0ms

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:
8.0ms
(* x (sqrt (- (* y y) (* z z))))
4.0ms
(- (* y y) (* z z))
5.0ms
(sqrt (- (* y y) (* z z)))

series178.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(* x (sqrt (- (* y y) (* z z))))
38.0ms
(- (* y y) (* z z))
56.0ms
(sqrt (- (* y y) (* z z)))

simplify101.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0202397
1786374
23192368
35001364

prune245.0ms

Filtered
71 candidates to 54 candidates (76.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (* y y) (* z z))
2.8b
(- (* y y) (* z z))
24.3b
(sqrt (- (* y y) (* z z)))
24.3b
(sqrt (- (* y y) (* z z)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 70
Calls
4 calls:
4.0ms
(- (* y y) (* z z))
4.0ms
(- (* y y) (* z z))
4.0ms
(sqrt (- (* y y) (* z z)))
5.0ms
(sqrt (- (* y y) (* z z)))

series175.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* y y) (* z z))
34.0ms
(- (* y y) (* z z))
53.0ms
(sqrt (- (* y y) (* z z)))
54.0ms
(sqrt (- (* y y) (* z z)))

simplify61.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0135420
1482394
21632388
35001378

prune291.0ms

Filtered
82 candidates to 66 candidates (80.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

24.3b
(sqrt (- (* y y) (* z z)))
25.1b
(cbrt (- (* y y) (* z z)))
25.1b
(cbrt (- (* y y) (* z z)))
25.1b
(cbrt (- (* y y) (* z z)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-prod add-cbrt-cube flip-- log1p-expm1-u add-log-exp difference-of-squares
3×pow1/3
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 66
Calls
4 calls:
4.0ms
(sqrt (- (* y y) (* z z)))
4.0ms
(cbrt (- (* y y) (* z z)))
4.0ms
(cbrt (- (* y y) (* z z)))
4.0ms
(cbrt (- (* y y) (* z z)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(sqrt (- (* y y) (* z z)))
128.0ms
(cbrt (- (* y y) (* z z)))
121.0ms
(cbrt (- (* y y) (* z z)))
122.0ms
(cbrt (- (* y y) (* z z)))

simplify153.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0174545
1481515
21379506
34872499
45001499

prune372.0ms

Filtered
78 candidates to 72 candidates (92.3%)
Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.4b

localize3.0ms

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

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.4b

regimes419.0ms

bsearch49.0ms