Details

Time bar (total: 25.5s)

sample897.0ms

Algorithm
intervals
Results
765.0ms3182×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: done (1.7s)

IterNodesCost
031103
190103
238466
3214754
done500051

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b
(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)

rewrite50.0ms

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:
14.0ms
(pow (/ 1.0 (fabs x)) 3)
18.0ms
(pow (/ 1.0 (fabs x)) 4)
7.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series176.0ms

Counts
4 → 10
Calls
4 calls:
63.0ms
(pow (/ 1.0 (fabs x)) 3)
65.0ms
(pow (/ 1.0 (fabs x)) 4)
47.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify1.8s

Counts
125 → 125
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01591392
16051269
226301160
done50021148

prune928.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.4b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
47×times-frac
46×*-un-lft-identity
44×add-cube-cbrt
41×unpow-prod-down
32×associate-*l*
28×cube-prod
18×add-exp-log
9×add-cbrt-cube
7×pow1
6×pow-unpow pow-exp unswap-sqr
5×cube-div div-inv
4×associate-*r* prod-exp add-log-exp sqr-pow
3×frac-times pow-to-exp associate-*r/ div-exp sqrt-prod
2×cube-mult pow-pow flip3-+ unpow3 frac-add flip-+ rem-cube-cbrt
1×cbrt-undiv distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l/ *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 151
Calls
4 calls:
155.0ms
(* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))
7.0ms
(pow (/ 1.0 (fabs x)) 3)
7.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series337.0ms

Counts
4 → 10
Calls
4 calls:
230.0ms
(* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))
54.0ms
(pow (/ 1.0 (fabs x)) 3)
52.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify3.6s

Counts
161 → 161
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
02222788
19082646
248892455
done50012455

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
0.3b
(/ (* (+ (/ 1.875 (pow (fabs x) 4)) 0.5) 1.0) (pow (fabs x) 3))
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite816.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
31×times-frac
29×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
19×unpow-prod-down
14×add-cbrt-cube
13×associate-*r*
12×associate-/r*
8×pow1 div-exp
6×cube-prod
5×prod-exp
4×associate-*l* associate-*l/ pow-exp add-log-exp
3×cbrt-undiv pow-to-exp pow-unpow flip3-+ sqrt-prod cbrt-unprod flip-+ div-inv sqr-pow
2×cube-mult frac-times unpow3 associate-/l/ unswap-sqr
1×rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out associate-/l*
Counts
4 → 123
Calls
4 calls:
701.0ms
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
99.0ms
(/ (* (+ (/ 1.875 (pow (fabs x) 4)) 0.5) 1.0) (pow (fabs x) 3))
7.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series378.0ms

Counts
4 → 10
Calls
4 calls:
134.0ms
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
196.0ms
(/ (* (+ (/ 1.875 (pow (fabs x) 4)) 0.5) 1.0) (pow (fabs x) 3))
48.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify539.0ms

Counts
133 → 133
Iterations

Useful iterations: done (532.0ms)

IterNodesCost
02512349
17642199
done50001961

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
30×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
13×add-exp-log
9×pow-unpow
8×pow1
6×pow-exp
4×add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod div-inv sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 97
Calls
4 calls:
7.0ms
(pow (/ 1.0 (fabs x)) 4)
7.0ms
(pow (/ 1.0 (fabs x)) 4)
12.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series121.0ms

Counts
4 → 10
Calls
4 calls:
42.0ms
(pow (/ 1.0 (fabs x)) 4)
41.0ms
(pow (/ 1.0 (fabs x)) 4)
37.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.0s

Counts
107 → 107
Iterations

Useful iterations: 3 (859.0ms)

IterNodesCost
01021132
12731041
2867999
33630978
done5000978

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

regimes381.0ms

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03374
14374
done4374

end0.0ms

sample7.7s

Algorithm
intervals
Results
7.0s25472×body80valid