Details

Time bar (total: 7.4s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
068
193
2113
done113

prune5.0ms

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)

series56.0ms

Counts
1 → 3
Calls
1 calls:
56.0ms
(hypot x y)

simplify1.2s

Counts
13 → 13
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01760
12258
22552
33052
43652
54652
66952
713252
834552
9127352
done500052

prune39.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

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)))

rewrite11.0ms

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)
7.0ms
(* (sqrt (hypot x y)) (sqrt (hypot x y)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (hypot x y))
58.0ms
(hypot x y)
50.0ms
(hypot x y)
58.0ms
(* (sqrt (hypot x y)) (sqrt (hypot x y)))

simplify1.7s

Counts
98 → 98
Iterations

Useful iterations: 4 (970.0ms)

IterNodesCost
086890
1160563
2377505
3982487
42265479
done5000479

prune198.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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-*l* unswap-sqr
12×pow1 sqrt-pow1
10×add-exp-log
9×associate-*r*
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×pow-plus *-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 157
Calls
4 calls:
2.0ms
(sqrt (sqrt (hypot x y)))
1.0ms
(sqrt (sqrt (hypot x y)))
24.0ms
(* (pow (sqrt (sqrt (hypot x y))) 3) (sqrt (sqrt (hypot x y))))
4.0ms
(pow (sqrt (sqrt (hypot x y))) 3)

series455.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(sqrt (sqrt (hypot x y)))
126.0ms
(sqrt (sqrt (hypot x y)))
54.0ms
(* (pow (sqrt (sqrt (hypot x y))) 3) (sqrt (sqrt (hypot x y))))
149.0ms
(pow (sqrt (sqrt (hypot x y))) 3)

simplify534.0ms

Counts
169 → 169
Iterations

Useful iterations: 2 (156.0ms)

IterNodesCost
01302348
13081691
210031452
done50001452

prune322.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

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))

series523.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* (cbrt (hypot x y)) (cbrt (hypot x y)))
135.0ms
(cbrt (hypot x y))
124.0ms
(cbrt (hypot x y))
126.0ms
(cbrt (hypot x y))

simplify1.3s

Counts
93 → 93
Iterations

Useful iterations: 4 (546.0ms)

IterNodesCost
078896
1148817
2373758
3996693
42655687
done5000687

prune306.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

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

sample301.0ms

Algorithm
intervals
Results
176.0ms8000×body80valid