Details

Time bar (total: 1.7s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms90×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
173

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) y)
19.3b
(sqrt (+ (* x x) y))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
add-log-exp
pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
+-commutative rem-sqrt-square fma-def sqrt-pow1 pow1/2 sum-log hypot-def
Counts
2 → 32
Calls
2 calls:
3.0ms
(+ (* x x) y)
5.0ms
(sqrt (+ (* x x) y))

series63.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(+ (* x x) y)
44.0ms
(sqrt (+ (* x x) y))

simplify52.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0153160
1518146
21716138
35002136

prune95.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize4.0ms

Local error

Found 1 expressions with local error:

19.3b
(sqrt (fma x x y))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt sqrt-prod
pow1 add-cube-cbrt *-un-lft-identity
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:
1.0ms
(sqrt (fma x x y))

series53.0ms

Counts
1 → 3
Calls
1 calls:
53.0ms
(sqrt (fma x x y))

simplify93.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (24.0ms)

IterNodesCost
07664
118559
261658
3252556
4500156

prune38.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (fma x x y)))
0.5b
(* (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))))
19.3b
(sqrt (fma x x y))
19.3b
(sqrt (fma x x y))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
associate-*r* associate-*l* pow-prod-up unswap-sqr
add-exp-log add-cbrt-cube
pow-prod-down pow-sqr
expm1-log1p-u rem-sqrt-square log1p-expm1-u add-log-exp
pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
1.0ms
(sqrt (sqrt (fma x x y)))
16.0ms
(* (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))))
1.0ms
(sqrt (fma x x y))
1.0ms
(sqrt (fma x x y))

series228.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (sqrt (fma x x y)))
47.0ms
(* (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))))
53.0ms
(sqrt (fma x x y))
48.0ms
(sqrt (fma x x y))

simplify40.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0214576
1844520
25001506

prune241.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(hypot x (pow y 1/2))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
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 (pow y 1/2))

series83.0ms

Counts
1 → 3
Calls
1 calls:
83.0ms
(hypot x (pow y 1/2))

simplify125.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
06750
116241
259840
3296439
4500139

prune37.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes64.0ms

Accuracy

98.1% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.3b

bsearch51.0ms

Steps
ItersRangePoint
9
4.342265995353652e+77
8.721286125398812e+82
1.2922566123944575e+80
9
-1.1045029026290381e+161
-1.4102566258715918e+152
-1.3778733035656446e+154

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0257
1457
2497
3517
4577
5577

end0.0ms

sample362.0ms

Algorithm
intervals
Results
146.0ms8000×body80valid
51.0ms2570×body80nan