Details

Time bar (total: 20.3s)

sample78.0ms

Algorithm
intervals
Results
55.0ms446×body80valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5001
31049
2250
170
028

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
0.1b
(fma (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0))
0.1b
(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 3) (fma (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0))))
1.0b
(sqrt PI)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×associate-*l*
20×times-frac
19×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
9×add-cbrt-cube add-exp-log
7×pow1
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-*r* unswap-sqr
2×prod-exp cbrt-unprod
1×distribute-rgt-in cbrt-undiv rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
0.0ms
(fma (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0))
21.0ms
(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 3) (fma (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0))))
1.0ms
(sqrt PI)

series484.0ms

Counts
4 → 10
Calls
4 calls:
71.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
40.0ms
(fma (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0))
373.0ms
(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 3) (fma (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0))))
0.0ms
(sqrt PI)

simplify734.0ms

Counts
91 → 91
Iterations
IterNodes
done5001
21491
1333
0152

prune873.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (pow (fabs x) 7) 0.047619047619047616 (fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x))))
0.0b
(fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x)))
0.1b
(* (fma (pow (fabs x) 5) 0.2 (fma (pow (fabs x) 7) 0.047619047619047616 (fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x))))) (* 1.0 (sqrt (/ 1 PI))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×associate-*r/ fma-udef
1×sqrt-div associate-*r* *-commutative
Counts
3 → 41
Calls
3 calls:
0.0ms
(fma (pow (fabs x) 7) 0.047619047619047616 (fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x))))
0.0ms
(fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x)))
26.0ms
(* (fma (pow (fabs x) 5) 0.2 (fma (pow (fabs x) 7) 0.047619047619047616 (fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x))))) (* 1.0 (sqrt (/ 1 PI))))

series752.0ms

Counts
3 → 9
Calls
3 calls:
189.0ms
(fma (pow (fabs x) 7) 0.047619047619047616 (fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x))))
96.0ms
(fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x)))
467.0ms
(* (fma (pow (fabs x) 5) 0.2 (fma (pow (fabs x) 7) 0.047619047619047616 (fma (pow (fabs x) 3) 0.6666666666666666 (* 2.0 (fabs x))))) (* 1.0 (sqrt (/ 1 PI))))

simplify554.0ms

Counts
50 → 50
Iterations
IterNodes
done5000
2786
1187
087

prune460.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt 1.0) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x)))))
0.3b
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (sqrt 1.0) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
929×times-frac
778×sqrt-prod
697×add-sqr-sqrt
417×*-un-lft-identity add-cube-cbrt
191×associate-*r*
63×unswap-sqr
58×associate-*l*
31×associate-/r*
30×add-cbrt-cube add-exp-log
16×div-inv
12×cbrt-undiv div-exp
8×pow1
6×prod-exp cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 608
Calls
4 calls:
26.0ms
(/ (sqrt 1.0) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x)))))
321.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (sqrt 1.0) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series1.1s

Counts
4 → 8
Calls
4 calls:
686.0ms
(/ (sqrt 1.0) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x)))))
444.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (sqrt 1.0) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.2s

Counts
616 → 616
Iterations
IterNodes
done5000
11967
0576

prune3.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0))))
0.3b
(/ (* (/ (sqrt (cbrt 1.0)) (sqrt (sqrt PI))) (sqrt 1.0)) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
112×times-frac
96×sqrt-prod
68×add-sqr-sqrt
66×*-un-lft-identity add-cube-cbrt
34×associate-/r*
27×add-cbrt-cube add-exp-log
12×cbrt-undiv div-exp
10×associate-/l*
6×pow1
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-*l/ associate-/r/ associate-/l/
Counts
4 → 172
Calls
4 calls:
25.0ms
(/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0))))
38.0ms
(/ (* (/ (sqrt (cbrt 1.0)) (sqrt (sqrt PI))) (sqrt 1.0)) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series1.1s

Counts
4 → 8
Calls
4 calls:
640.0ms
(/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0))))
504.0ms
(/ (* (/ (sqrt (cbrt 1.0)) (sqrt (sqrt PI))) (sqrt 1.0)) (/ (sqrt (sqrt PI)) (fma (pow (fabs x) 3) (fma (pow (fabs x) 2) (/ 1.0 5.0) (/ 2.0 3.0)) (* (fabs x) (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify519.0ms

Counts
180 → 180
Iterations
IterNodes
done5000
1717
0257

prune1.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done29
129
024

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.1s14027×body80valid