Details

Time bar (total: 14.0s)

sample38.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01114
11613
22612
33312
done3312

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (fma z z (fma x x (* y y))) 3.0)
35.2b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite11.0ms

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×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
2 → 56
Calls
2 calls:
5.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
4.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series310.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
231.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify1.6s

Counts
62 → 62
Iterations

Useful iterations: 3 (393.0ms)

IterNodesCost
01011118
11681062
2454977
32048974
done5002974

prune323.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
35.1b
(sqrt (fma z z (fma x x (* y y))))

rewrite53.0ms

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:
46.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series454.0ms

Counts
2 → 6
Calls
2 calls:
269.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
185.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.6s

Counts
68 → 68
Iterations

Useful iterations: 3 (860.0ms)

IterNodesCost
0991192
11761089
25191032
334711030
done50011030

prune322.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
35.1b
(sqrt (fma z z (fma x x (* y y))))

rewrite18.0ms

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 add-cbrt-cube
3×pow1
2×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 div-inv
Counts
2 → 78
Calls
2 calls:
10.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series538.0ms

Counts
2 → 6
Calls
2 calls:
338.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
199.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.6s

Counts
84 → 84
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01041761
11611588
24641546
320791546
done50011544

prune327.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 14.8b

localize21.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
5.9b
(exp (log (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))
35.1b
(sqrt (fma z z (fma x x (* y y))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
81×sqrt-prod
72×times-frac
59×add-sqr-sqrt
58×add-cube-cbrt *-un-lft-identity
40×log-prod exp-sum
6×associate-/r* associate-/l*
5×pow1 add-exp-log add-cbrt-cube
4×exp-prod
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×div-inv
1×cbrt-undiv rem-sqrt-square log-div sqrt-undiv frac-2neg sqrt-pow1 pow1/2 exp-diff div-exp clear-num log-pow rem-exp-log
Counts
3 → 133
Calls
3 calls:
8.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
20.0ms
(exp (log (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))
3.0ms
(sqrt (fma z z (fma x x (* y y))))

series914.0ms

Counts
3 → 9
Calls
3 calls:
338.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
399.0ms
(exp (log (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))
177.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.8s

Counts
142 → 142
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02103398
13382914
28732813
339312695
done50012689

prune540.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 14.8b

regimes458.0ms

Accuracy

45.8% (13.7b remaining)

Error of 26.3b against oracle of 12.6b and baseline of 37.9b

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03590
14090
done4090

end0.0ms

sample977.0ms

Algorithm
intervals
Results
616.0ms8000×body80valid