Details

Time bar (total: 23.3s)

sample86.0ms

Algorithm
intervals
Results
26.0ms321×body80valid
19.0ms356×body80nan

simplify13.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
11510
22210
33910
47110
516410
627510
751810
8191210
done500110

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.4b
(- (* y y) (* z z))
22.8b
(sqrt (- (* y y) (* z z)))

rewrite81.0ms

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:
39.0ms
(* x (sqrt (- (* y y) (* z z))))
13.0ms
(- (* y y) (* z z))
27.0ms
(sqrt (- (* y y) (* z z)))

series299.0ms

Counts
3 → 9
Calls
3 calls:
161.0ms
(* x (sqrt (- (* y y) (* z z))))
65.0ms
(- (* y y) (* z z))
73.0ms
(sqrt (- (* y y) (* z z)))

simplify1.5s

Counts
71 → 71
Iterations

Useful iterations: done (1.5s)

IterNodesCost
094839
1199758
2491676
31629676
done5002671

prune279.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (* y y) (* z z))
2.4b
(- (* y y) (* z z))
22.8b
(sqrt (- (* y y) (* z z)))
22.8b
(sqrt (- (* y y) (* z z)))

rewrite73.0ms

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:
18.0ms
(- (* y y) (* z z))
24.0ms
(- (* y y) (* z z))
15.0ms
(sqrt (- (* y y) (* z z)))
13.0ms
(sqrt (- (* y y) (* z z)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* y y) (* z z))
50.0ms
(- (* y y) (* z z))
81.0ms
(sqrt (- (* y y) (* z z)))
80.0ms
(sqrt (- (* y y) (* z z)))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
062912
1132824
2347722
31112722
done5001712

prune399.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (* y y) (* z z))
2.4b
(- (* y y) (* z z))
23.7b
(cbrt (- (* y y) (* z z)))
23.7b
(cbrt (- (* y y) (* z z)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod add-log-exp
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg fma-neg pow1/3 diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
11.0ms
(- (* y y) (* z z))
18.0ms
(- (* y y) (* z z))
10.0ms
(cbrt (- (* y y) (* z z)))
11.0ms
(cbrt (- (* y y) (* z z)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* y y) (* z z))
56.0ms
(- (* y y) (* z z))
158.0ms
(cbrt (- (* y y) (* z z)))
140.0ms
(cbrt (- (* y y) (* z z)))

simplify1.5s

Counts
78 → 78
Iterations

Useful iterations: done (1.5s)

IterNodesCost
077964
1170926
2433804
31257788
done5000772

prune416.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes373.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 25.3b

bsearch302.0ms

Steps
ItersRangePoint
11
-8.501644981951623e-221
-2.751809256330958e-243
-2.794570820839951e-243

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21411
done1411

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.1s10075×body80valid
603.0ms10255×body80nan