Details

Time bar (total: 22.4s)

sample112.0ms

Algorithm
intervals
Results
40.0ms510×body80nan
34.0ms235×body160nan
19.0ms256×body80valid

simplify6.4s

Counts
1 → 1
Iterations
IterNodes
done5000
83739
71640
6693
5212
468
337
221
117
07

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

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)))
32.5b
(sqrt (fma x x -1))

rewrite17.0ms

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:
8.0ms
(log (+ x (sqrt (fma x x -1))))
7.0ms
(+ x (sqrt (fma x x -1)))
2.0ms
(sqrt (fma x x -1))

series336.0ms

Counts
3 → 9
Calls
3 calls:
168.0ms
(log (+ x (sqrt (fma x x -1))))
82.0ms
(+ x (sqrt (fma x x -1)))
85.0ms
(sqrt (fma x x -1))

simplify1.7s

Counts
61 → 61
Iterations
IterNodes
done5001
32464
2759
1268
0119

prune314.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite472.0ms

Algorithm
rewrite-expression-head
Rules
212×*-un-lft-identity
210×times-frac
136×prod-diff
126×add-sqr-sqrt
119×add-cube-cbrt
71×associate-+r+
44×distribute-lft-out
19×div-inv
18×add-log-exp
17×add-exp-log
16×add-cbrt-cube
13×associate-/l*
6×cbrt-undiv log-prod div-exp distribute-lft-out--
5×pow1 sum-log
4×expm1-log1p-u fma-neg diff-log insert-posit16 log1p-expm1-u
3×fma-def flip3-+ flip-+ difference-of-squares
2×log-div sub-neg prod-exp associate--l+ frac-sub cbrt-unprod
1×+-commutative clear-num associate-+r- associate-/r* frac-2neg flip3-- rem-log-exp log-pow flip-- associate-/l/
Counts
4 → 259
Calls
4 calls:
182.0ms
(+ x (- (+ x (/ -1/2 x)) (/ (/ 1/8 x) (* x x))))
144.0ms
(log (+ x (- (+ x (/ -1/2 x)) (/ (/ 1/8 x) (* x x)))))
112.0ms
(- (+ x (/ -1/2 x)) (/ (/ 1/8 x) (* x x)))
20.0ms
(/ (/ 1/8 x) (* x x))

series280.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ x (- (+ x (/ -1/2 x)) (/ (/ 1/8 x) (* x x))))
97.0ms
(log (+ x (- (+ x (/ -1/2 x)) (/ (/ 1/8 x) (* x x)))))
60.0ms
(- (+ x (/ -1/2 x)) (/ (/ 1/8 x) (* x x)))
72.0ms
(/ (/ 1/8 x) (* x x))

simplify2.2s

Counts
271 → 271
Iterations
IterNodes
done5053
23277
11028
0408

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 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 → 85
Calls
4 calls:
1.0ms
(cbrt x)
4.0ms
(cbrt x)
1.0ms
(cbrt x)
16.0ms
(* (cbrt x) (cbrt x))

series1.2s

Counts
4 → 12
Calls
4 calls:
284.0ms
(cbrt x)
303.0ms
(cbrt x)
291.0ms
(cbrt x)
280.0ms
(* (cbrt x) (cbrt x))

simplify3.3s

Counts
97 → 97
Iterations
IterNodes
done5000
44201
31199
2389
1142
067

prune581.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.2b 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

sample4.2s

Algorithm
intervals
Results
1.7s16024×body80nan
1.3s7610×body160nan
805.0ms8000×body80valid