Details

Time bar (total: 10.6s)

sample22.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
11613
22612
33112
done3112

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u fma-def associate-/r* sum-log log1p-expm1-u 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 → 76
Calls
3 calls:
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
31.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series300.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (+ (* x x) (* y y)) (* z z))
59.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
191.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.0s

Counts
85 → 85
Iterations

Useful iterations: 3 (464.0ms)

IterNodesCost
01291623
12731440
210061236
343641224
done50001224

prune295.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y y (* z z))
0.3b
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
36.4b
(sqrt (fma x x (fma y y (* z z))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num fma-udef div-inv
Counts
3 → 88
Calls
3 calls:
0.0ms
(fma y y (* z z))
4.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
1.0ms
(sqrt (fma x x (fma y y (* z z))))

series445.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(fma y y (* z z))
279.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
126.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify829.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
01171869
11771705
24391629
315381629
done50001629

prune242.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y y (* z z))
0.4b
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
36.4b
(sqrt (fma x x (fma y y (* z z))))

rewrite16.0ms

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
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 72
Calls
3 calls:
0.0ms
(fma y y (* z z))
12.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
1.0ms
(sqrt (fma x x (fma y y (* z z))))

series348.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma y y (* z z))
188.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
118.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify1.5s

Counts
81 → 81
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
01121300
11931201
26141115
320191115
done50001115

prune219.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (fma x x (fma y y (* z z)))))
36.4b
(sqrt (fma x x (fma y y (* z z))))
36.4b
(sqrt (fma x x (fma y y (* z z))))
36.4b
(sqrt (fma x x (fma y y (* z z))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×cbrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 61
Calls
4 calls:
1.0ms
(cbrt (sqrt (fma x x (fma y y (* z z)))))
1.0ms
(sqrt (fma x x (fma y y (* z z))))
1.0ms
(sqrt (fma x x (fma y y (* z z))))
1.0ms
(sqrt (fma x x (fma y y (* z z))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(cbrt (sqrt (fma x x (fma y y (* z z)))))
122.0ms
(sqrt (fma x x (fma y y (* z z))))
118.0ms
(sqrt (fma x x (fma y y (* z z))))
120.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify2.7s

Counts
73 → 73
Iterations

Useful iterations: 3 (111.0ms)

IterNodesCost
060952
1108853
2268806
3940794
44512794
done5000794

prune284.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 19.8b

regimes205.0ms

Accuracy

60.7% (7.8b remaining)

Error of 26.4b against oracle of 18.6b and baseline of 38.5b

bsearch73.0ms

Steps
ItersRangePoint
8
3.196397393917939e+72
1.0649312883679304e+77
1.0479353069555717e+77
8
-1.3887243973495253e+108
-7.060621971491881e+103
-1.356128363832856e+108

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02130
12430
done2430

end0.0ms

sample445.0ms

Algorithm
intervals
Results
271.0ms8000×body80valid