Details

Time bar (total: 10.0s)

sample24.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0912
11411
22410
33110
done3110

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize13.0ms

Local error

Found 1 expressions with local error:

35.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt
3×sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ hypot-def log1p-expm1-u add-log-exp
Counts
1 → 18
Calls
1 calls:
59.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series138.0ms

Counts
1 → 3
Calls
1 calls:
138.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify962.0ms

Counts
21 → 21
Iterations

Useful iterations: done (961.0ms)

IterNodesCost
043331
198272
2311243
31216235
done5000234

prune132.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot (sqrt (+ (* x x) (* y y))) z)
30.8b
(sqrt (+ (* x x) (* y y)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-sqrt-square hypot-udef sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
Counts
2 → 28
Calls
2 calls:
0.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
9.0ms
(sqrt (+ (* x x) (* y y)))

series295.0ms

Counts
2 → 6
Calls
2 calls:
245.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
49.0ms
(sqrt (+ (* x x) (* y y)))

simplify1.5s

Counts
34 → 34
Iterations

Useful iterations: 3 (197.0ms)

IterNodesCost
053389
1116220
2286194
3682188
41810188
done5000188

prune212.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot x y)
0.0b
(hypot (hypot x y) z)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt hypot-udef *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(hypot x y)
0.0ms
(hypot (hypot x y) z)

series419.0ms

Counts
2 → 6
Calls
2 calls:
78.0ms
(hypot x y)
341.0ms
(hypot (hypot x y) z)

simplify1.4s

Counts
26 → 26
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
030148
138144
243128
350128
465128
5132128
6282128
7644128
81968128
done5000128

prune148.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

6.6b
(- (fma x x (* y y)) (* z z))
9.5b
(fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4))
12.6b
(sqrt (fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4)))
44.0b
(/ (hypot (pow z 3) (pow (fma x x (* y y)) 3/2)) (sqrt (fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
18×times-frac
15×sqrt-prod
6×add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×fma-neg prod-diff associate-/l*
2×fma-udef
1×cbrt-undiv sub-neg rem-sqrt-square sqrt-undiv hypot-udef flip3-- frac-2neg sqrt-pow1 pow1/2 diff-log div-exp associate--l+ clear-num flip-- div-inv difference-of-squares
Counts
4 → 89
Calls
4 calls:
7.0ms
(- (fma x x (* y y)) (* z z))
0.0ms
(fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4))
2.0ms
(sqrt (fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4)))
8.0ms
(/ (hypot (pow z 3) (pow (fma x x (* y y)) 3/2)) (sqrt (fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4))))

series1.4s

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (fma x x (* y y)) (* z z))
481.0ms
(fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4))
300.0ms
(sqrt (fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4)))
501.0ms
(/ (hypot (pow z 3) (pow (fma x x (* y y)) 3/2)) (sqrt (fma (fma x x (* y y)) (- (fma x x (* y y)) (* z z)) (pow z 4))))

simplify1.2s

Counts
101 → 101
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01483454
13083239
213933012
done50012998

prune713.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes248.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
done55

end0.0ms

sample1.0s

Algorithm
intervals
Results
642.0ms8000×body80valid