Details

Time bar (total: 14.2s)

sample113.0ms

Algorithm
intervals
Results
78.0ms440×body80valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5001
31049
2250
170
028

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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 (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0))
0.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
22.0ms
(* (/ 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))))
2.0ms
(sqrt PI)

series537.0ms

Counts
4 → 10
Calls
4 calls:
50.0ms
(fma (/ 1.0 5.0) (* (fabs x) (fabs x)) (/ 2.0 3.0))
75.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
411.0ms
(* (/ 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)

simplify826.0ms

Counts
91 → 91
Iterations
IterNodes
done5001
21492
1333
0152

prune794.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×associate-*r* sqrt-prod
14×*-un-lft-identity
13×add-cube-cbrt
11×times-frac
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l* fma-udef
1×sqrt-div pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod div-inv
Counts
4 → 67
Calls
4 calls:
0.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))
0.0ms
(fma (pow (fabs x) 5) 0.2 (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x)))))
19.0ms
(* (fma (pow (fabs x) 5) 0.2 (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))) (sqrt (/ 1 PI)))
0.0ms
(fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x)))

series916.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))
238.0ms
(fma (pow (fabs x) 5) 0.2 (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x)))))
359.0ms
(* (fma (pow (fabs x) 5) 0.2 (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x))))) (sqrt (/ 1 PI)))
133.0ms
(fma 0.047619047619047616 (pow (fabs x) 7) (* 2.0 (fabs x)))

simplify590.0ms

Counts
79 → 79
Iterations
IterNodes
done5001
2715
1220
0120

prune707.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ 1.0 5.0) (pow (fabs x) 2) (/ 2.0 3.0))
0.1b
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
0.3b
(/ (* 1.0 (fma (pow (fabs x) 3) (fma (/ 1.0 5.0) (pow (fabs x) 2) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x)))) (sqrt PI))
1.0b
(sqrt PI)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
6×associate-/r* times-frac
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp fma-udef
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 64
Calls
4 calls:
0.0ms
(fma (/ 1.0 5.0) (pow (fabs x) 2) (/ 2.0 3.0))
0.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
11.0ms
(/ (* 1.0 (fma (pow (fabs x) 3) (fma (/ 1.0 5.0) (pow (fabs x) 2) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x)))) (sqrt PI))
2.0ms
(sqrt PI)

series578.0ms

Counts
4 → 10
Calls
4 calls:
41.0ms
(fma (/ 1.0 5.0) (pow (fabs x) 2) (/ 2.0 3.0))
97.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
440.0ms
(/ (* 1.0 (fma (pow (fabs x) 3) (fma (/ 1.0 5.0) (pow (fabs x) 2) (/ 2.0 3.0)) (* (fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0) (fabs x)))) (sqrt PI))
0.0ms
(sqrt PI)

simplify778.0ms

Counts
74 → 74
Iterations
IterNodes
done5000
21146
1266
0126

prune663.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
0.1b
(* (/ 1.0 (expm1 (log1p (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
(expm1 (log1p (sqrt PI)))
1.0b
(sqrt PI)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×*-un-lft-identity associate-*l* add-cube-cbrt
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* sqrt-prod fma-udef
2×prod-exp cbrt-unprod unswap-sqr
1×distribute-rgt-in cbrt-undiv rem-sqrt-square expm1-log1p distribute-lft-in sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv expm1-udef
Counts
4 → 72
Calls
4 calls:
1.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
22.0ms
(* (/ 1.0 (expm1 (log1p (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
(expm1 (log1p (sqrt PI)))
2.0ms
(sqrt PI)

series796.0ms

Counts
4 → 8
Calls
4 calls:
94.0ms
(fma (pow (fabs x) 6) (/ 1.0 21.0) 2.0)
702.0ms
(* (/ 1.0 (expm1 (log1p (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
(expm1 (log1p (sqrt PI)))
0.0ms
(sqrt PI)

simplify666.0ms

Counts
80 → 80
Iterations
IterNodes
done5000
21297
1312
0143

prune710.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes107.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done26
126
024

end0.0ms

sample3.3s

Algorithm
intervals
Results
3.0s14022×body80valid