Details

Time bar (total: 16.7s)

sample179.0ms

Algorithm
intervals
Results
54.0ms276×body160nan
50.0ms577×body80nan
48.0ms256×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: 27.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (sqrt (fma x x -1))))
0.0b
(+ x (sqrt (fma x x -1)))
26.4b
(sqrt (fma x x -1))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube sqrt-prod insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 52
Calls
3 calls:
4.0ms
(log (+ x (sqrt (fma x x -1))))
5.0ms
(+ x (sqrt (fma x x -1)))
1.0ms
(sqrt (fma x x -1))

series317.0ms

Counts
3 → 9
Calls
3 calls:
162.0ms
(log (+ x (sqrt (fma x x -1))))
75.0ms
(+ x (sqrt (fma x x -1)))
79.0ms
(sqrt (fma x x -1))

simplify1.6s

Counts
61 → 61
Iterations
IterNodes
done5000
32305
2739
1268
0119

prune281.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ -1/8 (* (* x x) x)) (/ 1/2 x))
0.1b
(* (* x x) x)
1.0b
(/ -1/8 (* (* x x) x))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
109×times-frac
91×prod-diff
89×add-sqr-sqrt
85×*-un-lft-identity
83×add-cube-cbrt
22×pow1 div-inv
17×add-cbrt-cube add-exp-log
7×fma-neg
6×pow-plus prod-exp pow-prod-up cbrt-unprod
5×add-log-exp
3×expm1-log1p-u cbrt-undiv div-exp associate-*r* pow-prod-down insert-posit16 log1p-expm1-u associate-/l*
2×pow2 pow-sqr difference-of-squares
1×clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log associate-*l* pow3 *-commutative frac-sub flip-- distribute-lft-out-- unswap-sqr
Counts
3 → 174
Calls
3 calls:
115.0ms
(- (/ -1/8 (* (* x x) x)) (/ 1/2 x))
15.0ms
(* (* x x) x)
25.0ms
(/ -1/8 (* (* x x) x))

series207.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(- (/ -1/8 (* (* x x) x)) (/ 1/2 x))
40.0ms
(* (* x x) x)
60.0ms
(/ -1/8 (* (* x x) x))

simplify1.7s

Counts
183 → 183
Iterations
IterNodes
done5000
21818
1668
0277

prune540.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (fma x x -1)))
26.4b
(sqrt (fma x x -1))
26.4b
(sqrt (fma x x -1))
26.4b
(sqrt (fma x x -1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×cbrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 65
Calls
4 calls:
2.0ms
(cbrt (sqrt (fma x x -1)))
1.0ms
(sqrt (fma x x -1))
1.0ms
(sqrt (fma x x -1))
1.0ms
(sqrt (fma x x -1))

series320.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (sqrt (fma x x -1)))
60.0ms
(sqrt (fma x x -1))
58.0ms
(sqrt (fma x x -1))
60.0ms
(sqrt (fma x x -1))

simplify1.4s

Counts
77 → 77
Iterations
IterNodes
done5000
31521
2507
1201
092

prune345.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done12
112
011

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.8s7978×body160nan
1.2s16699×body80nan
826.0ms8000×body80valid