Details

Time bar (total: 12.9s)

sample23.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify26.0ms

Counts
1 → 1
Iterations
IterNodes
done25
325
222
115
011

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y y) (+ (* x x) (* z z)))
0.0b
(+ (* x x) (* z z))
0.1b
(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
35.3b
(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×sqrt-prod
11×add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1
4×sum-log
3×associate-/r* flip3-+ flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+r+ clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
4 → 78
Calls
4 calls:
29.0ms
(+ (* y y) (+ (* x x) (* z z)))
12.0ms
(+ (* x x) (* z z))
101.0ms
(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
45.0ms
(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

series463.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* y y) (+ (* x x) (* z z)))
49.0ms
(+ (* x x) (* z z))
77.0ms
(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
285.0ms
(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

simplify981.0ms

Counts
90 → 90
Iterations
IterNodes
done5001
22059
1373
0138

prune635.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y y) (+ (* x x) (* z z)))
0.0b
(+ (* x x) (* z z))
0.4b
(/ (sqrt (+ (* y y) (+ (* x x) (* z z)))) (sqrt 3.0))
35.2b
(sqrt (+ (* y y) (+ (* x x) (* z z))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
11×add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
5×pow1
4×sum-log flip3-+ sqrt-div flip-+
2×+-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square associate-+r+ sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 102
Calls
4 calls:
27.0ms
(+ (* y y) (+ (* x x) (* z z)))
12.0ms
(+ (* x x) (* z z))
49.0ms
(/ (sqrt (+ (* y y) (+ (* x x) (* z z)))) (sqrt 3.0))
24.0ms
(sqrt (+ (* y y) (+ (* x x) (* z z))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (* y y) (+ (* x x) (* z z)))
41.0ms
(+ (* x x) (* z z))
317.0ms
(/ (sqrt (+ (* y y) (+ (* x x) (* z z)))) (sqrt 3.0))
127.0ms
(sqrt (+ (* y y) (+ (* x x) (* z z))))

simplify1.2s

Counts
114 → 114
Iterations
IterNodes
done5001
22136
1376
0151

prune589.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.9b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (pow y 2) (* z z)) (* x x))
0.4b
(* (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) (sqrt (/ 1 3.0)))
35.2b
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))

rewrite279.0ms

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-cbrt-cube add-exp-log
4×flip3-+ flip-+
3×sum-log sqrt-pow1 pow1/2 pow-prod-down
2×frac-times associate-*l/
1×+-commutative rem-sqrt-square associate-+l+ sqrt-unprod prod-exp associate-*r/ *-commutative cbrt-unprod div-inv
Counts
3 → 77
Calls
3 calls:
80.0ms
(+ (+ (pow y 2) (* z z)) (* x x))
130.0ms
(* (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) (sqrt (/ 1 3.0)))
65.0ms
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))

series451.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(+ (+ (pow y 2) (* z z)) (* x x))
240.0ms
(* (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) (sqrt (/ 1 3.0)))
149.0ms
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))

simplify1.0s

Counts
86 → 86
Iterations
IterNodes
done5002
21597
1308
0134

prune591.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) 3.0))
0.4b
(* (sqrt (sqrt (+ (+ (pow y 2) (* z z)) (* x x)))) (sqrt (/ (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) 3.0)))
35.2b
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))
35.2b
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))

rewrite460.0ms

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod
73×add-sqr-sqrt
44×times-frac
36×*-un-lft-identity add-cube-cbrt
25×associate-*r*
16×sqrt-div
12×unswap-sqr
11×pow1
9×associate-*l*
6×add-cbrt-cube add-exp-log
5×rem-sqrt-square sqrt-pow1 pow1/2
4×flip3-+ flip-+ add-log-exp
3×pow-prod-down
2×frac-times associate-*l/ div-inv
1×sqrt-unprod prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 130
Calls
4 calls:
60.0ms
(sqrt (/ (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) 3.0))
257.0ms
(* (sqrt (sqrt (+ (+ (pow y 2) (* z z)) (* x x)))) (sqrt (/ (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) 3.0)))
65.0ms
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))
72.0ms
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))

series828.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(sqrt (/ (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) 3.0))
283.0ms
(* (sqrt (sqrt (+ (+ (pow y 2) (* z z)) (* x x)))) (sqrt (/ (sqrt (+ (+ (pow y 2) (* z z)) (* x x))) 3.0)))
186.0ms
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))
121.0ms
(sqrt (+ (+ (pow y 2) (* z z)) (* x x)))

simplify885.0ms

Counts
142 → 142
Iterations
IterNodes
done5001
21423
1355
0185

prune880.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.6b

regimes1.3s

Accuracy

38.4% (19.6b remaining)

Error of 26.0b against oracle of 6.4b and baseline of 38.2b

bsearch185.0ms

Steps
ItersRangePoint
6
2.6913520219809045e+92
3.9657822087457923e+93
3.650529274743424e+93
6
6.722994943076513e-143
9.582574548702874e-142
1.9059416657880497e-142
6
-3.392970635093907e-140
-3.053173983632099e-141
-1.6418988825485982e-140
8
-5.250355123902004e+120
-1.540786475003901e+118
-8.482917924797484e+119

simplify17.0ms

Iterations
IterNodes
done58
258
156
043

end0.0ms

sample1.2s

Algorithm
intervals
Results
938.0ms8000×body80valid