Details

Time bar (total: 15.8s)

sample80.0ms

Algorithm
intervals
Results
22.0ms547×body80nan
21.0ms256×body80valid
18.0ms208×body160nan

simplify5.0s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b
(log (+ x (sqrt (fma x x -1))))
30.6b
(sqrt (fma x x -1))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 log-prod add-cube-cbrt
3×add-exp-log sqrt-prod
2×expm1-log1p-u log-div add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp log-pow flip-+ distribute-lft-out
Counts
2 → 34
Calls
2 calls:
13.0ms
(log (+ x (sqrt (fma x x -1))))
4.0ms
(sqrt (fma x x -1))

series277.0ms

Counts
2 → 6
Calls
2 calls:
190.0ms
(log (+ x (sqrt (fma x x -1))))
87.0ms
(sqrt (fma x x -1))

simplify1.6s

Counts
40 → 40
Iterations
IterNodes
done5003
31955
2589
1215
0102

prune198.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* x x))
0.1b
(/ (/ 1/4 x) x)
0.2b
(+ (log x) (log 2))
0.4b
(/ 3/32 (* (* x x) (* x x)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
120×pow1
78×times-frac
55×*-un-lft-identity
51×add-sqr-sqrt add-cube-cbrt
39×add-cbrt-cube add-exp-log
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
16×prod-exp cbrt-unprod associate-/l*
13×pow2
8×cbrt-undiv div-exp
6×log-prod div-inv
5×log-pow
4×expm1-log1p-u associate-/r* fma-def insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
3×associate-+l+ associate-+r+
2×clear-num frac-2neg
1×+-commutative sum-log flip3-+ swap-sqr associate-*r* associate-*l* *-commutative flip-+ unswap-sqr associate-/l/
Counts
4 → 197
Calls
4 calls:
36.0ms
(* (* x x) (* x x))
15.0ms
(/ (/ 1/4 x) x)
11.0ms
(+ (log x) (log 2))
31.0ms
(/ 3/32 (* (* x x) (* x x)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* x x) (* x x))
34.0ms
(/ (/ 1/4 x) x)
294.0ms
(+ (log x) (log 2))
59.0ms
(/ 3/32 (* (* x x) (* x x)))

simplify1.4s

Counts
209 → 209
Iterations
IterNodes
done5001
21693
1688
0269

prune852.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.2b
(log (+ x (fma (/ -1 x) 1/2 (fma (/ 1/8 (* x x)) (/ -1 x) x))))
0.6b
(/ 1/8 (* x x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
8×add-exp-log
7×*-un-lft-identity add-cbrt-cube
5×add-sqr-sqrt add-cube-cbrt
4×log-prod
3×pow1 times-frac associate-/l*
2×expm1-log1p-u cbrt-undiv log-div div-exp insert-posit16 log1p-expm1-u add-log-exp
1×clear-num associate-/r* frac-2neg flip3-+ rem-log-exp prod-exp log-pow cbrt-unprod flip-+ div-inv distribute-lft-out
Counts
2 → 42
Calls
2 calls:
9.0ms
(log (+ x (fma (/ -1 x) 1/2 (fma (/ 1/8 (* x x)) (/ -1 x) x))))
16.0ms
(/ 1/8 (* x x))

series180.0ms

Counts
2 → 6
Calls
2 calls:
132.0ms
(log (+ x (fma (/ -1 x) 1/2 (fma (/ 1/8 (* x x)) (/ -1 x) x))))
48.0ms
(/ 1/8 (* x x))

simplify1.8s

Counts
48 → 48
Iterations
IterNodes
done5000
32602
2692
1244
0111

prune182.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done16
116
014

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s7582×body160nan
940.0ms16009×body80nan
655.0ms8000×body80valid