Details

Time bar (total: 11.8s)

sample35.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify21.0ms

Counts
1 → 1
Iterations
IterNodes
done22
322
221
115
011

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.8b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1
3×associate-/r* insert-posit16 associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
3 → 68
Calls
3 calls:
10.0ms
(+ (* x x) (* y y))
68.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
51.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series376.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(+ (* x x) (* y y))
61.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
266.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify723.0ms

Counts
77 → 77
Iterations
IterNodes
done2001
2930
1298
0131

prune406.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.2b

localize51.0ms

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))
36.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.8b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

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:
152.0ms
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
23.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
22.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
64.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series625.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
153.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
133.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
262.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify877.0ms

Counts
141 → 141
Iterations
IterNodes
done2000
21236
1543
0182

prune704.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 19.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
0.2b
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
36.8b
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
51×times-frac add-exp-log
37×*-un-lft-identity
34×add-cube-cbrt
24×cbrt-prod
22×associate-*r*
20×prod-exp
19×add-cbrt-cube
16×div-exp
9×pow1 unswap-sqr
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×associate-/r* add-log-exp
4×rec-exp 1-exp insert-posit16
3×sqrt-div div-inv associate-/l*
2×frac-times sqrt-pow1 flip3-+ pow-prod-down associate-*l/ associate-*r/ flip-+ associate-/l/
1×+-commutative clear-num sum-log frac-2neg pow1/2 *-commutative sqrt-prod
Counts
4 → 140
Calls
4 calls:
9.0ms
(+ (* x x) (* y y))
125.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
102.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
68.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

series959.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (* x x) (* y y))
185.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
195.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
522.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

simplify648.0ms

Counts
152 → 152
Iterations
IterNodes
done2001
1700
0232

prune723.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cbrt 3.0) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
36.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.8b
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (cbrt 3.0) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×*-un-lft-identity add-cube-cbrt
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×associate-/r* add-exp-log associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 insert-posit16 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/r/
1×frac-times cbrt-undiv clear-num frac-2neg div-exp pow-prod-down associate-*l/ associate-*r/ div-inv
Counts
4 → 110
Calls
4 calls:
28.0ms
(/ (cbrt 3.0) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
22.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
24.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
46.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (cbrt 3.0) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))))

series869.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (cbrt 3.0) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
160.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
132.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
418.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (cbrt 3.0) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))))

simplify945.0ms

Counts
122 → 122
Iterations
IterNodes
done2002
31998
2611
1267
0149

prune799.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.2b

regimes659.0ms

Accuracy

63.1% (6.4b remaining)

Error of 24.6b against oracle of 18.2b and baseline of 35.6b

bsearch69.0ms

Steps
ItersRangePoint
6
1.3755500145718548e+155
6.181162647627959e+155
1.3936358732915887e+155
7
-1.1481705486358557e+130
-6.049533408753237e+128
-1.1295859422058697e+130

simplify15.0ms

Iterations
IterNodes
done37
237
134
026

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.2s8000×body80valid