Details

Time bar (total: 17.5s)

sample39.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
done22
322
221
115
011

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
4×add-cbrt-cube add-exp-log
3×pow1 associate-/r* associate-/l*
2×rem-sqrt-square insert-posit16 div-inv add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp flip-+
Counts
2 → 56
Calls
2 calls:
87.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series317.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
228.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.2s

Counts
62 → 62
Iterations
IterNodes
done5008
33007
2651
1219
0109

prune335.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
36.9b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
37.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
58×times-frac
38×*-un-lft-identity
36×sqrt-prod
32×add-cube-cbrt
22×associate-*r* associate-*l*
21×add-exp-log
16×add-cbrt-cube
15×unswap-sqr
11×pow1
7×sqrt-div div-exp
6×prod-exp
4×cbrt-undiv sqrt-pow1 cbrt-unprod insert-posit16 add-log-exp
3×pow1/2
2×frac-times rem-sqrt-square flip3-+ 1-exp pow-prod-down associate-*l/ associate-*r/ flip-+ div-inv
1×*-commutative
Counts
4 → 129
Calls
4 calls:
146.0ms
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
30.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
40.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
46.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series583.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
228.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
146.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
140.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.0s

Counts
141 → 141
Iterations
IterNodes
done5191
34206
21156
1538
0182

prune816.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.0b

localize45.0ms

Local error

Found 4 expressions with local error:

36.9b
(sqrt (* (/ (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
37.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 sqrt-prod
9×sqrt-div
7×*-un-lft-identity add-cube-cbrt
5×sqrt-pow1
4×add-cbrt-cube pow1/2 add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square flip3-+ flip-+
1×frac-times pow-prod-down associate-*l/ associate-*r/
Counts
4 → 63
Calls
4 calls:
199.0ms
(sqrt (* (/ (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
46.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
45.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
47.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series663.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(sqrt (* (/ (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
151.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
136.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
152.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.6s

Counts
75 → 75
Iterations
IterNodes
done5001
43397
31066
2369
1149
072

prune377.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 18.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
0.4b
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
37.1b
(sqrt (+ (* x x) (+ (* y y) (* z z))))
37.1b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod
73×add-sqr-sqrt
44×times-frac
36×*-un-lft-identity add-cube-cbrt
25×associate-*r*
16×sqrt-div
12×unswap-sqr
11×pow1
9×associate-*l*
6×add-cbrt-cube add-exp-log
5×rem-sqrt-square sqrt-pow1 pow1/2
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×pow-prod-down
2×frac-times associate-*l/ div-inv
1×sqrt-unprod prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
36.0ms
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
105.0ms
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
35.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
27.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
200.0ms
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
133.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
155.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify2.1s

Counts
146 → 146
Iterations
IterNodes
done5010
33293
21005
1362
0189

prune754.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 18.0b

regimes755.0ms

Accuracy

65.1% (6.1b remaining)

Error of 24.2b against oracle of 18.1b and baseline of 35.7b

bsearch122.0ms

Steps
ItersRangePoint
11
5.0707754921117725e+147
1.3010579244045132e+167
1.2721613999661422e+154
9
-1.854306054422796e+154
-6.720912415933141e+146
-1.3226326560428921e+154

simplify9.0ms

Iterations
IterNodes
done30
230
128
022

end0.0ms

sample1.1s

Algorithm
intervals
Results
918.0ms8000×body80valid