Details

Time bar (total: 17.7s)

sample36.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify33.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0912
11411
22410
33010
done3010

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize13.0ms

Local error

Found 1 expressions with local error:

34.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite58.0ms

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:
57.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series122.0ms

Counts
1 → 3
Calls
1 calls:
122.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.9s

Counts
21 → 21
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
043331
198272
2300243
31040235
44140234
done5000234

prune103.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot (sqrt (+ (* x x) (* y y))) z)
28.7b
(sqrt (+ (* x x) (* y y)))

rewrite11.0ms

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)
10.0ms
(sqrt (+ (* x x) (* y y)))

series275.0ms

Counts
2 → 6
Calls
2 calls:
224.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
50.0ms
(sqrt (+ (* x x) (* y y)))

simplify4.1s

Counts
34 → 34
Iterations

Useful iterations: 3 (177.0ms)

IterNodesCost
053389
1115220
2268194
3586188
41444188
54140188
done5000188

prune145.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

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)
1.0ms
(hypot (hypot x y) z)

series333.0ms

Counts
2 → 6
Calls
2 calls:
76.0ms
(hypot x y)
257.0ms
(hypot (hypot x y) z)

simplify3.5s

Counts
26 → 26
Iterations

Useful iterations: 2 (20.0ms)

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

prune80.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4)))
15.3b
(- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4))
20.9b
(sqrt (- (fma x x (* y y)) (* z z)))
21.0b
(/ (sqrt (- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4))) (sqrt (- (fma x x (* y y)) (* z z))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
98×sqrt-prod
77×add-sqr-sqrt
63×times-frac
44×add-cube-cbrt *-un-lft-identity
41×difference-of-squares
13×unpow-prod-down
11×sqr-pow
9×associate-/l*
8×sqrt-div
7×prod-diff associate-/r*
6×pow1 add-exp-log add-cbrt-cube add-log-exp
5×flip3-- flip--
4×expm1-log1p-u log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 associate--l+ associate-/r/ fma-udef associate-/l/
1×cbrt-undiv distribute-rgt-in sub-neg sqrt-undiv frac-2neg distribute-lft-in fma-neg diff-log div-exp clear-num div-inv
Counts
4 → 163
Calls
4 calls:
32.0ms
(sqrt (- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4)))
21.0ms
(- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4))
12.0ms
(sqrt (- (fma x x (* y y)) (* z z)))
50.0ms
(/ (sqrt (- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4))) (sqrt (- (fma x x (* y y)) (* z z))))

series790.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(sqrt (- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4)))
175.0ms
(- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4))
179.0ms
(sqrt (- (fma x x (* y y)) (* z z)))
250.0ms
(/ (sqrt (- (* (fma x x (* y y)) (fma x x (* y y))) (pow z 4))) (sqrt (- (fma x x (* y y)) (* z z))))

simplify3.7s

Counts
175 → 175
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
02736702
14856059
211875707
349705585
done50005585

prune531.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes60.0ms

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

sample750.0ms

Algorithm
intervals
Results
449.0ms8000×body80valid