Details

Time bar (total: 14.1s)

sample25.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0912
11411
22410
33110
done3110

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize32.0ms

Local error

Found 1 expressions with local error:

35.1b
(sqrt (fma z z (fma x x (* y y))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity
1×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
1 → 15
Calls
1 calls:
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series231.0ms

Counts
1 → 3
Calls
1 calls:
231.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.8s

Counts
18 → 18
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
026207
138180
252172
385172
4144172
5239172
6312172
7490172
81166172
done5000172

prune96.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (fma z z (fma x x (* y y)))))
0.2b
(* (fabs (cbrt (fma z z (fma x x (* y y))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
36.2b
(cbrt (fma z z (fma x x (* y y))))
36.2b
(cbrt (fma z z (fma x x (* y y))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×associate-*r*
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 74
Calls
4 calls:
4.0ms
(sqrt (cbrt (fma z z (fma x x (* y y)))))
33.0ms
(* (fabs (cbrt (fma z z (fma x x (* y y))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
2.0ms
(cbrt (fma z z (fma x x (* y y))))
2.0ms
(cbrt (fma z z (fma x x (* y y))))

series746.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(sqrt (cbrt (fma z z (fma x x (* y y)))))
227.0ms
(* (fabs (cbrt (fma z z (fma x x (* y y))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
162.0ms
(cbrt (fma z z (fma x x (* y y))))
156.0ms
(cbrt (fma z z (fma x x (* y y))))

simplify2.4s

Counts
86 → 86
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01241771
12721665
29831498
344941456
done50001456

prune471.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (exp (log (cbrt (fma z z (fma x x (* y y))))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
5.3b
(exp (log (cbrt (fma z z (fma x x (* y y))))))
36.2b
(cbrt (fma z z (fma x x (* y y))))
36.2b
(cbrt (fma z z (fma x x (* y y))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×cbrt-prod add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×sqrt-prod
7×pow1
6×add-exp-log log-prod exp-sum add-cbrt-cube
5×exp-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×log-pow
1×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Counts
4 → 75
Calls
4 calls:
13.0ms
(* (fabs (exp (log (cbrt (fma z z (fma x x (* y y))))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
5.0ms
(exp (log (cbrt (fma z z (fma x x (* y y))))))
1.0ms
(cbrt (fma z z (fma x x (* y y))))
1.0ms
(cbrt (fma z z (fma x x (* y y))))

series836.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(* (fabs (exp (log (cbrt (fma z z (fma x x (* y y))))))) (sqrt (cbrt (fma z z (fma x x (* y y))))))
182.0ms
(exp (log (cbrt (fma z z (fma x x (* y y))))))
173.0ms
(cbrt (fma z z (fma x x (* y y))))
211.0ms
(cbrt (fma z z (fma x x (* y y))))

simplify800.0ms

Counts
87 → 87
Iterations

Useful iterations: done (797.0ms)

IterNodesCost
01391904
12801711
211191505
done50001456

prune452.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.1b

localize57.0ms

Local error

Found 4 expressions with local error:

36.2b
(cbrt (fma z z (fma x x (* y y))))
36.2b
(cbrt (fma z z (fma x x (* y y))))
36.2b
(cbrt (fma z z (fma x x (* y y))))
36.2b
(cbrt (fma z z (fma x x (* y y))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
2.0ms
(cbrt (fma z z (fma x x (* y y))))
2.0ms
(cbrt (fma z z (fma x x (* y y))))
2.0ms
(cbrt (fma z z (fma x x (* y y))))
2.0ms
(cbrt (fma z z (fma x x (* y y))))

series1.3s

Counts
4 → 12
Calls
4 calls:
208.0ms
(cbrt (fma z z (fma x x (* y y))))
217.0ms
(cbrt (fma z z (fma x x (* y y))))
198.0ms
(cbrt (fma z z (fma x x (* y y))))
653.0ms
(cbrt (fma z z (fma x x (* y y))))

simplify3.0s

Counts
64 → 64
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
043960
185944
2230860
3869816
44519812
done5000812

prune456.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.1b

regimes218.0ms

Accuracy

57.5% (8.2b remaining)

Error of 26.6b against oracle of 18.5b and baseline of 37.7b

bsearch195.0ms

Steps
ItersRangePoint
8
4.093472436053604e+62
1.2817926955906846e+67
1.2621629619033288e+67
9
-1.195490085819535e-191
-8.978573997781305e-200
-1.1770060633013808e-191
9
-4.3800916202637243e-113
-3.619799235921884e-118
-6.671259440587564e-115
9
-5.754626073420363e+127
-1.0654788484896314e+122
-1.255797641178115e+124

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02040
done2040

end0.0ms

sample857.0ms

Algorithm
intervals
Results
514.0ms8000×body80valid