Details

Time bar (total: 15.1s)

sample43.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify31.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0912
11411
22410
33010
done3010

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
30.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
7×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow1 fma-def sum-log
3×add-exp-log expm1-log1p-u flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×+-commutative sqrt-div
1×rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2 hypot-def
Counts
3 → 50
Calls
3 calls:
9.0ms
(+ (* x x) (* y y))
57.0ms
(+ (+ (* x x) (* y y)) (* z z))
43.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series264.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ (* x x) (* y y))
60.0ms
(+ (+ (* x x) (* y y)) (* z z))
160.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.2s

Counts
59 → 59
Iterations

Useful iterations: done (2.2s)

IterNodesCost
080808
1219673
2736586
32816574
done5001572

prune278.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(hypot (sqrt (+ (* x x) (* y y))) z)
27.7b
(sqrt (+ (* x x) (* y y)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-log-exp
4×pow1 add-cube-cbrt *-un-lft-identity
3×add-exp-log expm1-log1p-u sqrt-prod add-cbrt-cube log1p-expm1-u
2×flip3-+ sqrt-div flip-+
1×+-commutative rem-sqrt-square hypot-udef fma-def sqrt-pow1 pow1/2 sum-log hypot-def
Counts
3 → 42
Calls
3 calls:
17.0ms
(+ (* x x) (* y y))
1.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
19.0ms
(sqrt (+ (* x x) (* y y)))

series388.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ (* x x) (* y y))
278.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
57.0ms
(sqrt (+ (* x x) (* y y)))

simplify3.2s

Counts
51 → 51
Iterations

Useful iterations: 3 (390.0ms)

IterNodesCost
065571
1150371
2421312
31187308
43439308
done5000308

prune228.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

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)

series331.0ms

Counts
2 → 6
Calls
2 calls:
84.0ms
(hypot x y)
247.0ms
(hypot (hypot x y) z)

simplify3.7s

Counts
26 → 26
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
030148
138144
243128
350128
459128
576128
6115128
7252128
8816128
93627128
done5000128

prune106.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (fma z z (fma x x (* y y)))))
0.3b
(* (fabs (cbrt (fma z z (fma x x (* y y))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
31.4b
(cbrt (fma z z (fma x x (* y y))))
31.4b
(cbrt (fma z z (fma x x (* y y))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×associate-*r*
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 74
Calls
4 calls:
2.0ms
(sqrt (cbrt (fma z z (fma x x (* y y)))))
13.0ms
(* (fabs (cbrt (fma z z (fma x x (* y y))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
1.0ms
(cbrt (fma z z (fma x x (* y y))))
1.0ms
(cbrt (fma z z (fma x x (* y y))))

series689.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(sqrt (cbrt (fma z z (fma x x (* y y)))))
211.0ms
(* (fabs (cbrt (fma z z (fma x x (* y y))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
156.0ms
(cbrt (fma z z (fma x x (* y y))))
158.0ms
(cbrt (fma z z (fma x x (* y y))))

simplify2.0s

Counts
86 → 86
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01241771
12641665
27441498
320691456
done50011454

prune368.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes169.0ms

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

sample935.0ms

Algorithm
intervals
Results
578.0ms8000×body80valid