Details

Time bar (total: 33.3s)

sample849.0ms

Algorithm
intervals
Results
720.0ms3288×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: done (1.7s)

IterNodesCost
031103
190103
238466
3214754
done500051

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.6b

localize71.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
13×add-exp-log cube-prod
9×pow-unpow
8×pow1
7×add-cbrt-cube
6×pow-exp
4×div-inv add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×rem-cube-cbrt
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3
Counts
4 → 115
Calls
4 calls:
13.0ms
(pow (/ 1.0 (fabs x)) 3)
25.0ms
(pow (/ 1.0 (fabs x)) 4)
14.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series157.0ms

Counts
4 → 10
Calls
4 calls:
43.0ms
(pow (/ 1.0 (fabs x)) 3)
58.0ms
(pow (/ 1.0 (fabs x)) 4)
56.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.1s

Counts
125 → 125
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01591392
16051269
226301160
done50021148

prune1.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.7b

localize95.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (sqrt PI)) (+ (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x))) (* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite715.0ms

Algorithm
rewrite-expression-head
Rules
95×frac-times
90×frac-add
81×associate-*r/
51×add-sqr-sqrt
50×flip3-+ flip-+
47×times-frac
42×add-cube-cbrt *-un-lft-identity
41×cube-div
39×associate-*l/
26×unpow-prod-down
22×associate-*l*
15×add-exp-log
13×cube-prod sqrt-prod
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×pow-exp div-inv add-log-exp
3×div-exp associate-*r* unswap-sqr
2×cbrt-undiv pow-to-exp pow-pow prod-exp cbrt-unprod rem-cube-cbrt sqr-pow
1×distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down *-commutative
Counts
4 → 205
Calls
4 calls:
676.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x))) (* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))))
13.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series719.0ms

Counts
4 → 10
Calls
4 calls:
613.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x))) (* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))))
47.0ms
(pow (/ 1.0 (fabs x)) 3)
58.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify1.4s

Counts
215 → 215
Iterations

Useful iterations: done (1.4s)

IterNodesCost
054012186
1241911433
done500210551

prune2.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.75 (pow (fabs x) 5))
0.2b
(/ 1.875 (pow (fabs x) 7))
0.3b
(/ 0.5 (pow (fabs x) 3))
0.5b
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ 0.75 (pow (fabs x) 5)) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3))))

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
93×times-frac
88×*-un-lft-identity
79×add-sqr-sqrt
70×add-cube-cbrt
36×unpow-prod-down
26×associate-/r*
21×add-exp-log
18×frac-add
16×associate-*l* sqrt-prod
12×cube-prod add-cbrt-cube sqr-pow
9×div-exp distribute-lft-out associate-/l*
8×sqrt-div
7×frac-times associate-*r/ associate-*r*
6×pow1 flip3-+ flip-+
4×cube-mult unpow3 div-inv add-log-exp unswap-sqr
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 210
Calls
4 calls:
15.0ms
(/ 0.75 (pow (fabs x) 5))
15.0ms
(/ 1.875 (pow (fabs x) 7))
16.0ms
(/ 0.5 (pow (fabs x) 3))
4.0s
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ 0.75 (pow (fabs x) 5)) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3))))

series728.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ 0.75 (pow (fabs x) 5))
105.0ms
(/ 1.875 (pow (fabs x) 7))
57.0ms
(/ 0.5 (pow (fabs x) 3))
481.0ms
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ 0.75 (pow (fabs x) 5)) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3))))

simplify684.0ms

Counts
222 → 222
Iterations

Useful iterations: done (676.0ms)

IterNodesCost
04174793
110914417
done50004241

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (/ 1.0 (sqrt PI)) (+ (* (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) 1.0) (pow (fabs x) 3)) (* (fabs x) (* (pow 1.0 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))))) (* (fabs x) (pow (fabs x) 3)))
0.3b
(* (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) 1.0) (pow (fabs x) 3))
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
32×associate-*r/
30×add-cbrt-cube
29×associate-*l/
26×prod-exp
17×add-sqr-sqrt div-exp associate-/l/
16×add-cube-cbrt unpow-prod-down *-un-lft-identity frac-add
13×flip3-+ flip-+
12×associate-*r*
10×times-frac cbrt-unprod
8×cbrt-undiv frac-times
7×pow-exp
6×pow1 pow-to-exp
4×add-log-exp
3×pow-unpow cube-prod sqrt-prod
2×div-inv sqr-pow
1×cube-mult rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*l* clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 120
Calls
4 calls:
770.0ms
(/ (* (/ 1.0 (sqrt PI)) (+ (* (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) 1.0) (pow (fabs x) 3)) (* (fabs x) (* (pow 1.0 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))))) (* (fabs x) (pow (fabs x) 3)))
610.0ms
(* (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) 1.0) (pow (fabs x) 3))
10.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series680.0ms

Counts
4 → 10
Calls
4 calls:
460.0ms
(/ (* (/ 1.0 (sqrt PI)) (+ (* (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) 1.0) (pow (fabs x) 3)) (* (fabs x) (* (pow 1.0 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))))) (* (fabs x) (pow (fabs x) 3)))
155.0ms
(* (* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) 1.0) (pow (fabs x) 3))
64.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify590.0ms

Counts
130 → 130
Iterations

Useful iterations: done (580.0ms)

IterNodesCost
02934918
110144624
done50013716

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

regimes385.0ms

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02839
13639
done3639

end0.0ms

sample9.6s

Algorithm
intervals
Results
8.7s32718×body80valid