Details

Time bar (total: 2.4s)

sample32.0ms

Algorithm
intervals
Results
8.0ms310×body80valid
7.0ms298×body80nan

simplify76.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0145
1215
2365
3625
41335
52115
63975
717985
850015

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize7.0ms

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)))

rewrite15.0ms

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×flip3-- associate-*l* flip-- difference-of-squares
2×associate-*r/ unswap-sqr
1×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:
7.0ms
(* x (sqrt (- (* y y) (* z z))))
3.0ms
(- (* y y) (* z z))
4.0ms
(sqrt (- (* y y) (* z z)))

series152.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(* x (sqrt (- (* y y) (* z z))))
29.0ms
(- (* y y) (* z z))
48.0ms
(sqrt (- (* y y) (* z z)))

simplify74.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0187364
1732340
23010337
35002337

prune333.0ms

Filtered
63 candidates to 46 candidates (73.0%)
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)))

rewrite16.0ms

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 flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 58
Calls
4 calls:
4.0ms
(- (* y y) (* z z))
3.0ms
(- (* y y) (* z z))
4.0ms
(sqrt (- (* y y) (* z z)))
4.0ms
(sqrt (- (* y y) (* z z)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* y y) (* z z))
32.0ms
(- (* y y) (* z z))
47.0ms
(sqrt (- (* y y) (* z z)))
45.0ms
(sqrt (- (* y y) (* z z)))

simplify49.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0122378
1432350
21459350
35001348

prune206.0ms

Filtered
70 candidates to 54 candidates (77.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

localize17.0ms

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)))

rewrite19.0ms

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 flip3-- sqrt-prod add-cbrt-cube flip-- add-log-exp difference-of-squares
3×pow1/3
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
4.0ms
(sqrt (- (* y y) (* z z)))
4.0ms
(cbrt (- (* y y) (* z z)))
7.0ms
(cbrt (- (* y y) (* z z)))
4.0ms
(cbrt (- (* y y) (* z z)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(sqrt (- (* y y) (* z z)))
106.0ms
(cbrt (- (* y y) (* z z)))
107.0ms
(cbrt (- (* y y) (* z z)))
107.0ms
(cbrt (- (* y y) (* z z)))

simplify138.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 4 (132.0ms)

IterNodesCost
0162508
1438478
21208472
34422471
45001468

prune278.0ms

Filtered
70 candidates to 61 candidates (87.1%)
Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.4b

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

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.4b

regimes366.0ms

bsearch48.0ms