Details

Time bar (total: 14.3s)

sample45.0ms

Algorithm
intervals
Results
21.0ms256×body80valid

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22214
32514
done2514

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite178.0ms

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×rem-sqrt-square 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 → 54
Calls
2 calls:
127.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
49.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series305.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
243.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify695.0ms

Counts
60 → 60
Iterations

Useful iterations: done (691.0ms)

IterNodesCost
01071270
12241209
29791112
done50011102

prune382.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
29×sqrt-prod
16×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt times-frac
9×sqrt-div
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×frac-times associate-*l/ add-log-exp
1×rem-sqrt-square sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 64
Calls
2 calls:
157.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series348.0ms

Counts
2 → 6
Calls
2 calls:
203.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
145.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify4.6s

Counts
70 → 70
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01181522
12411403
27431320
343591298
done50001298

prune355.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.2b

localize20.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log sqrt-div add-cbrt-cube
3×pow1
2×flip3-+ flip-+ associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 78
Calls
2 calls:
79.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
48.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series403.0ms

Counts
2 → 6
Calls
2 calls:
269.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
133.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.4s

Counts
84 → 84
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01192087
12171888
27031834
332481816
done50011814

prune380.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.1b

localize7.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ x (sqrt 3.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
7.0ms
(/ x (sqrt 3.0))

series98.0ms

Counts
1 → 3
Calls
1 calls:
98.0ms
(/ x (sqrt 3.0))

simplify987.0ms

Counts
42 → 42
Iterations

Useful iterations: done (985.0ms)

IterNodesCost
066371
1108334
2277324
31023324
done5001322

prune192.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 10.1b

regimes1.2s

Accuracy

53.3% (13.6b remaining)

Error of 25.8b against oracle of 12.2b and baseline of 41.2b

bsearch270.0ms

Steps
ItersRangePoint
9
9.23219417715695e+129
1.278698893362856e+135
9.324766710132622e+129
9
1.4535525082619025e+99
1.808291141957747e+108
1.6350700005414168e+108
7
8.968674946987851e-17
1.899433490407338e-14
9.136096463042233e-17
10
-3.109808602001194e-144
-1.3454629880417017e-161
-1.6711070948620834e-161
5
-1.1259454966916272e+94
-2.918087972802078e+93
-1.1005165876387523e+94

simplify18.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04274
14874
done4874

end0.0ms

sample1.0s

Algorithm
intervals
Results
651.0ms8000×body80valid