Details

Time bar (total: 17.5s)

sample51.0ms

Algorithm
intervals
Results
28.0ms256×body80valid

simplify32.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize23.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 58
Calls
2 calls:
127.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
69.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series355.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
278.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.1s

Counts
64 → 64
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01111328
12221181
26661015
324691009
done50001008

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))
35.4b
(sqrt (fma z z (fma x x (* y y))))
35.4b
(sqrt (fma z z (fma x x (* y y))))
35.5b
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))))

rewrite71.0ms

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
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow1/2 sqrt-div
2×rem-sqrt-square
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 108
Calls
4 calls:
16.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))
2.0ms
(sqrt (fma z z (fma x x (* y y))))
2.0ms
(sqrt (fma z z (fma x x (* y y))))
47.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
384.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))
170.0ms
(sqrt (fma z z (fma x x (* y y))))
168.0ms
(sqrt (fma z z (fma x x (* y y))))
528.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma z z (fma x x (* y y)))) (cbrt 3.0))))

simplify4.6s

Counts
120 → 120
Iterations

Useful iterations: 3 (197.0ms)

IterNodesCost
01322478
11952082
23411983
36191947
412241947
520231947
635301947
done50001947

prune613.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.5b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
35.5b
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
75×times-frac sqrt-prod
52×*-un-lft-identity
48×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
8×pow1
7×add-exp-log
6×associate-/r* add-cbrt-cube
5×sqrt-div
4×div-inv
3×expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u associate-/l* add-log-exp
1×cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
3 → 148
Calls
3 calls:
11.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
126.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
7.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

series1.1s

Counts
3 → 9
Calls
3 calls:
162.0ms
(/ (fma z z (fma x x (* y y))) (cbrt 3.0))
425.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0))))
529.0ms
(sqrt (/ (fma z z (fma x x (* y y))) (cbrt 3.0)))

simplify1.5s

Counts
157 → 157
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02033869
13343691
27533516
318403516
done50013488

prune634.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.4b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b
(* x (sqrt 0.3333333333333333))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u add-log-exp
Counts
1 → 24
Calls
1 calls:
20.0ms
(* x (sqrt 0.3333333333333333))

series62.0ms

Counts
1 → 3
Calls
1 calls:
61.0ms
(* x (sqrt 0.3333333333333333))

simplify2.8s

Counts
27 → 27
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
039168
171151
2126143
3173143
4219143
5359143
6834143
72754143
done5001143

prune62.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 7.4b

regimes443.0ms

Accuracy

38.4% (19.1b remaining)

Error of 25.9b against oracle of 6.8b and baseline of 37.8b

bsearch130.0ms

Steps
ItersRangePoint
11
5.840439438579558e+61
3.5877520487646245e+82
2.467313987424883e+82
6
-1.2093633317186018e+82
-1.201978405841871e+81
-1.1896418808192102e+82

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03160
14160
24360
done4360

end0.0ms

sample876.0ms

Algorithm
intervals
Results
563.0ms8000×body80valid