Details

Time bar (total: 11.6s)

sample19.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
01114
11613
22612
33112
done3112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize10.0ms

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))

rewrite62.0ms

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))
32.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series279.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(+ (+ (* x x) (* y y)) (* z z))
54.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
180.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.1s

Counts
85 → 85
Iterations

Useful iterations: 3 (450.0ms)

IterNodesCost
01291623
12731440
210061236
343641224
done50001224

prune302.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
33.0b
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×expm1-log1p-u sqrt-pow1 pow-prod-down fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
3.0ms
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
2.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series259.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(* 0.3333333333333333 (fma x x (fma y y (* z z))))
196.0ms
(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify1.2s

Counts
41 → 41
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
065567
1128533
2440473
32121473
done5001473

prune115.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.1b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 pow1/2 pow-prod-down
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 62
Calls
2 calls:
16.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
1.0ms
(sqrt (fma x x (fma y y (* z z))))

series320.0ms

Counts
2 → 6
Calls
2 calls:
196.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
124.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify3.1s

Counts
68 → 68
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0991192
11751097
25191030
311011030
426031030
done50001030

prune188.0ms

Pruning

6 alts after pruning (4 fresh and 2 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 3.0))
33.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
35×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
8×add-log-exp
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube
4×pow1 sqrt-div
3×expm1-log1p-u fma-def flip3-+ sum-log flip-+ log1p-expm1-u
2×associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square associate-+l+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
3 → 101
Calls
3 calls:
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
23.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
17.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series385.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ (+ (* x x) (* y y)) (* z z))
238.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
107.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.9s

Counts
110 → 110
Iterations

Useful iterations: 3 (425.0ms)

IterNodesCost
01422440
12792095
29501879
339581861
done50001861

prune343.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.5b

regimes389.0ms

Accuracy

78.7% (3.6b remaining)

Error of 15.7b against oracle of 12.2b and baseline of 28.9b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01729
11829
done1829

end0.0ms

sample467.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid