Details

Time bar (total: 11.9s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22114
32214
done2214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize12.0ms

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)
33.1b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite61.0ms

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:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
31.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series249.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
50.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
163.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.8s

Counts
76 → 76
Iterations

Useful iterations: 3 (404.0ms)

IterNodesCost
01231541
12601473
29781346
340361330
done50001330

prune209.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
33.0b
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-log-exp
7×add-sqr-sqrt
5×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×associate-*r/
3×flip3-+ associate-*r* associate-*l* sum-log flip-+
2×sqrt-pow1 sqrt-div pow-prod-down
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 48
Calls
3 calls:
15.0ms
(+ (+ (* x x) (* y y)) (* z z))
33.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
10.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series247.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
52.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
160.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify467.0ms

Counts
57 → 57
Iterations

Useful iterations: done (466.0ms)

IterNodesCost
090992
1246945
21147841
done5000825

prune133.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
33.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×sqrt-prod
16×*-un-lft-identity associate-*r*
14×add-cube-cbrt
13×times-frac
9×sqrt-div
8×pow1 add-log-exp unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×sqrt-pow1 pow1/2 pow-prod-down sum-log
2×frac-times associate-*l/
1×+-commutative rem-sqrt-square associate-+l+ sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
3 → 77
Calls
3 calls:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
42.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
16.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series300.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (+ (* x x) (* y y)) (* z z))
164.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.9s

Counts
86 → 86
Iterations

Useful iterations: 3 (717.0ms)

IterNodesCost
01351793
12921673
211251554
345751526
done50001526

prune229.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 15.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow y 2) (pow z 2))
0.0b
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
0.4b
(/ (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) (sqrt 3.0))
33.0b
(sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
115×*-un-lft-identity
78×sqrt-prod
54×times-frac
47×distribute-lft-out
40×add-sqr-sqrt
39×add-cube-cbrt
29×unpow-prod-down
11×add-log-exp
9×associate-/l*
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div sum-log flip-+
2×+-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square associate-+r+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 131
Calls
4 calls:
10.0ms
(+ (pow y 2) (pow z 2))
32.0ms
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
91.0ms
(/ (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) (sqrt 3.0))
55.0ms
(sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2))))

series386.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (pow y 2) (pow z 2))
40.0ms
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
219.0ms
(/ (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) (sqrt 3.0))
100.0ms
(sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2))))

simplify3.2s

Counts
143 → 143
Iterations

Useful iterations: 3 (592.0ms)

IterNodesCost
01533074
13132758
211272672
348262664
done50002664

prune295.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 15.0b

regimes393.0ms

Accuracy

62.9% (7.3b remaining)

Error of 25.3b against oracle of 18.0b and baseline of 37.7b

bsearch75.0ms

Steps
ItersRangePoint
9
1.5308671146039946e+53
1.176638228465725e+60
1.1586965865467858e+60
9
-6.5309962722429555e+122
-4.4188440889263735e+116
-1.1663424956880876e+121

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02533
13333
done3333

end0.0ms

sample435.0ms

Algorithm
intervals
Results
270.0ms8000×body80valid