Details

Time bar (total: 8.5s)

sample23.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify2.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* sum-log associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 67
Calls
3 calls:
31.0ms
(+ (+ (* x x) (* y y)) (* z z))
104.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
45.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series364.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(+ (+ (* x x) (* y y)) (* z z))
86.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
230.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify116.0ms

Counts
76 → 76

prune431.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
36.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.7b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite291.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 106
Calls
4 calls:
75.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
61.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
62.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
86.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
300.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
113.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
136.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
463.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify59.0ms

Counts
118 → 118

prune463.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
36.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite336.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
9×pow1 add-log-exp
8×add-exp-log
7×add-cbrt-cube
6×associate-/r*
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down sum-log associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times associate-+l+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
48.0ms
(+ (+ (* x x) (* y y)) (* z z))
88.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
153.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
38.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (+ (* x x) (* y y)) (* z z))
189.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
450.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
405.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify53.0ms

Counts
169 → 169

prune724.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (sqrt (/ 1 (cbrt 3.0))) z)
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (cbrt 3.0))) z))
1.0b
(/ 1 (cbrt 3.0))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
43×times-frac
38×*-un-lft-identity
36×add-cube-cbrt
35×associate-*l*
34×sqrt-prod
23×cbrt-prod
14×add-exp-log
11×pow1 add-cbrt-cube
6×associate-/r* unswap-sqr
5×sqrt-div
4×associate-*r* pow-prod-down associate-*l/ prod-exp cbrt-unprod
3×div-inv associate-/l* add-log-exp
2×pow-flip div-exp *-commutative
1×cbrt-undiv frac-times rec-exp frac-2neg pow1/3 1-exp associate-*r/ clear-num inv-pow
Counts
3 → 118
Calls
3 calls:
38.0ms
(* (sqrt (/ 1 (cbrt 3.0))) z)
125.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (cbrt 3.0))) z))
10.0ms
(/ 1 (cbrt 3.0))

series325.0ms

Counts
3 → 7
Calls
3 calls:
127.0ms
(* (sqrt (/ 1 (cbrt 3.0))) z)
198.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (cbrt 3.0))) z))
0.0ms
(/ 1 (cbrt 3.0))

simplify83.0ms

Counts
125 → 125

prune382.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 18.9b

regimes858.0ms

Accuracy

59.2% (8.1b remaining)

Error of 26.6b against oracle of 18.6b and baseline of 38.3b

bsearch331.0ms

Steps
ItersRangePoint
10
7.323427609233628e+139
7.187798267153574e+149
1.4439299756457442e+146
6
1.3891154800348428e+38
1.3980828701306097e+39
1.5921435257149642e+38
9
1.8485205844676482
779548.5780578556
770005.7426888434
10
-6.3260321363592525e-87
-8.715213317225141e-102
-3.477829585500689e-87
8
-3.949908300579693e-44
-9.026186484768267e-47
-9.175538176234307e-47
10
-1.3581248764839886e+149
-1.4388293188308112e+134
-4.3499399230850033e+145

simplify127.0ms

end0.0ms

sample987.0ms

Algorithm
intervals
Results
626.0ms8000×body80valid