Details

Time bar (total: 10.5s)

sample14.0ms

Algorithm
intervals
Results
6.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
068
193
2113
done113

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b
(hypot x y)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt hypot-udef *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(hypot x y)

series59.0ms

Counts
1 → 3
Calls
1 calls:
59.0ms
(hypot x y)

simplify1.8s

Counts
13 → 13
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01760
12258
22552
33052
43652
55952
611752
742852
8128852
done500052

prune42.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot x y))
0.0b
(hypot x y)
0.0b
(hypot x y)
0.5b
(* (sqrt (hypot x y)) (sqrt (hypot x y)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
20×pow1
13×add-cube-cbrt *-un-lft-identity
9×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×hypot-udef
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 86
Calls
4 calls:
1.0ms
(sqrt (hypot x y))
0.0ms
(hypot x y)
0.0ms
(hypot x y)
8.0ms
(* (sqrt (hypot x y)) (sqrt (hypot x y)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(sqrt (hypot x y))
52.0ms
(hypot x y)
55.0ms
(hypot x y)
56.0ms
(* (sqrt (hypot x y)) (sqrt (hypot x y)))

simplify2.9s

Counts
98 → 98
Iterations

Useful iterations: done (2.9s)

IterNodesCost
086890
1163565
2558505
33139486
done5001485

prune203.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (hypot x y)))
0.1b
(sqrt (sqrt (hypot x y)))
0.2b
(* (sqrt (sqrt (hypot x y))) (pow (sqrt (sqrt (hypot x y))) 3))
0.7b
(pow (sqrt (sqrt (hypot x y))) 3)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
107×sqrt-prod
74×add-sqr-sqrt
27×unpow-prod-down cube-prod
25×add-cube-cbrt *-un-lft-identity
24×associate-*r* unswap-sqr
12×pow1 sqrt-pow1
10×add-exp-log
9×associate-*l*
7×add-cbrt-cube
6×pow1/2
5×pow-pow sqr-pow
4×expm1-log1p-u rem-sqrt-square log1p-expm1-u add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp unpow3 pow-exp
1×*-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 156
Calls
4 calls:
1.0ms
(sqrt (sqrt (hypot x y)))
1.0ms
(sqrt (sqrt (hypot x y)))
25.0ms
(* (sqrt (sqrt (hypot x y))) (pow (sqrt (sqrt (hypot x y))) 3))
4.0ms
(pow (sqrt (sqrt (hypot x y))) 3)

series688.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (sqrt (hypot x y)))
128.0ms
(sqrt (sqrt (hypot x y)))
284.0ms
(* (sqrt (sqrt (hypot x y))) (pow (sqrt (sqrt (hypot x y))) 3))
152.0ms
(pow (sqrt (sqrt (hypot x y))) 3)

simplify1.3s

Counts
168 → 168
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
01322357
13142020
213661423
done50001423

prune318.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (hypot x y)) (cbrt (hypot x y)))
0.6b
(cbrt (hypot x y))
0.6b
(cbrt (hypot x y))
0.6b
(cbrt (hypot x y))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt (hypot x y)) (cbrt (hypot x y)))
1.0ms
(cbrt (hypot x y))
1.0ms
(cbrt (hypot x y))
1.0ms
(cbrt (hypot x y))

series480.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (cbrt (hypot x y)) (cbrt (hypot x y)))
114.0ms
(cbrt (hypot x y))
118.0ms
(cbrt (hypot x y))
123.0ms
(cbrt (hypot x y))

simplify1.7s

Counts
93 → 93
Iterations

Useful iterations: 3 (397.0ms)

IterNodesCost
078896
1151821
2549758
32368693
done5001693

prune299.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033
done33

end0.0ms

sample327.0ms

Algorithm
intervals
Results
184.0ms8000×body80valid