Details

Time bar (total: 20.5s)

sample127.0ms

Algorithm
intervals
Results
36.0ms238×body160nan
35.0ms565×body80nan
33.0ms256×body80valid

simplify5.2s

Counts
1 → 1
Iterations
IterNodes
done5000
83499
71307
6580
5196
468
337
221
117
07

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (fma x x -1)))
31.2b
(sqrt (fma x x -1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×add-cube-cbrt add-log-exp
3×pow1 fma-def sqrt-prod
2×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
2 → 34
Calls
2 calls:
7.0ms
(+ x (sqrt (fma x x -1)))
2.0ms
(sqrt (fma x x -1))

series145.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(+ x (sqrt (fma x x -1)))
62.0ms
(sqrt (fma x x -1))

simplify3.4s

Counts
40 → 40
Iterations
IterNodes
done5000
44052
31250
2461
1172
073

prune214.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2 x (/ -1/2 x))
0.0b
(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* x (* x x))))
0.1b
(* x (* x x))
0.2b
(/ -1/8 (* x (* x x)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
128×add-sqr-sqrt
90×associate-*r*
84×times-frac
70×*-un-lft-identity
68×add-cube-cbrt
35×unswap-sqr
30×associate-*l*
28×associate-/r*
20×swap-sqr
18×pow1 add-cbrt-cube add-exp-log
16×*-commutative
6×prod-exp cbrt-unprod add-log-exp
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv fma-def div-exp pow-prod-down associate-/l*
2×cube-unmult fma-udef
1×pow2 +-commutative associate-+l+ clear-num sum-log frac-2neg flip3-+ pow-plus pow-sqr flip-+ div-inv distribute-lft-out
Counts
4 → 210
Calls
4 calls:
0.0ms
(fma 2 x (/ -1/2 x))
111.0ms
(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* x (* x x))))
28.0ms
(* x (* x x))
56.0ms
(/ -1/8 (* x (* x x)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(fma 2 x (/ -1/2 x))
60.0ms
(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* x (* x x))))
71.0ms
(* x (* x x))
55.0ms
(/ -1/8 (* x (* x x)))

simplify1.8s

Counts
222 → 222
Iterations
IterNodes
done5000
22493
1665
0251

prune626.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (fma x x -1)))
0.5b
(* (sqrt (sqrt (fma x x -1))) (sqrt (sqrt (fma x x -1))))
31.2b
(sqrt (fma x x -1))
31.2b
(sqrt (fma x x -1))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
31×pow1
20×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (sqrt (fma x x -1)))
21.0ms
(* (sqrt (sqrt (fma x x -1))) (sqrt (sqrt (fma x x -1))))
1.0ms
(sqrt (fma x x -1))
2.0ms
(sqrt (fma x x -1))

series336.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(sqrt (sqrt (fma x x -1)))
67.0ms
(* (sqrt (sqrt (fma x x -1))) (sqrt (sqrt (fma x x -1))))
69.0ms
(sqrt (fma x x -1))
56.0ms
(sqrt (fma x x -1))

simplify3.0s

Counts
144 → 144
Iterations
IterNodes
done5000
44906
31631
2626
1289
0137

prune578.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done13
113
011

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.9s7741×body160nan
1.4s16814×body80nan
781.0ms8000×body80valid