Details

Time bar (total: 52.6s)

sample908.0ms

Algorithm
intervals
Results
797.0ms3534×body80valid

simplify2.7s

Counts
1 → 1
Iterations
IterNodes
done5000
32139
2384
190
031

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
120×times-frac
89×*-un-lft-identity add-cube-cbrt
40×add-cbrt-cube add-exp-log
39×swap-sqr associate-*r* associate-*l*
26×pow1
12×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×add-log-exp
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 214
Calls
4 calls:
37.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)

series101.0ms

Counts
4 → 10
Calls
4 calls:
47.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify3.0s

Counts
224 → 224
Iterations
IterNodes
done5000
23353
1462
0143

prune2.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.7b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (sqrt PI)) (+ (* (/ 1.0 (fabs x)) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (/ 1.0 (* (fabs x) (fabs x))) (/ 15.0 8.0))))))) (/ 1.0 (fabs x))))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1221×frac-times
974×frac-add
861×associate-*r/
329×associate-*l/
108×add-sqr-sqrt
100×times-frac
82×flip3-+ flip-+
75×*-un-lft-identity add-cube-cbrt
48×associate-*l*
33×add-cbrt-cube add-exp-log
29×associate-*r*
26×swap-sqr
21×pow1
13×sqrt-prod
11×unswap-sqr
10×prod-exp cbrt-unprod
9×cbrt-undiv div-exp div-inv
4×add-log-exp
3×pow-prod-down *-commutative
2×pow2 pow-plus pow-sqr pow-prod-up
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 609
Calls
4 calls:
1.1s
(* (/ 1.0 (sqrt PI)) (+ (* (/ 1.0 (fabs x)) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (/ 1.0 (* (fabs x) (fabs x))) (/ 15.0 8.0))))))) (/ 1.0 (fabs x))))
33.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
27.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms
(sqrt PI)

series587.0ms

Counts
4 → 10
Calls
4 calls:
511.0ms
(* (/ 1.0 (sqrt PI)) (+ (* (/ 1.0 (fabs x)) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (/ 1.0 (* (fabs x) (fabs x))) (/ 15.0 8.0))))))) (/ 1.0 (fabs x))))
36.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
40.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify7.8s

Counts
619 → 619
Iterations
IterNodes
done5002
01898

prune7.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
136×frac-add
86×associate-*r/
85×un-div-inv
56×add-sqr-sqrt
52×add-exp-log
47×pow1
44×associate-*r*
41×times-frac
35×*-un-lft-identity
31×sqrt-div add-cube-cbrt
30×frac-times associate-*l/
25×add-cbrt-cube
23×prod-exp
16×sqrt-prod
14×flip3-+ flip-+
12×pow-plus div-exp pow-prod-up pow-flip unswap-sqr
11×unpow-prod-down
9×cbrt-unprod
8×pow-prod-down
7×associate-*l*
6×rec-exp 1-exp
5×sqr-pow
4×pow2 cbrt-undiv pow-sqr add-log-exp
3×pow-to-exp pow-exp *-commutative div-inv associate-/l*
2×pow3
1×clear-num associate-/r* frac-2neg inv-pow
Counts
4 → 223
Calls
4 calls:
27.0ms
(/ 1 (* (* (fabs x) (fabs x)) (fabs x)))
14.0ms
(* (* (fabs x) (fabs x)) (fabs x))
19.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
1.4s
(* (+ (* 1.0 (/ 1 (fabs x))) (+ (* 0.5 (/ 1 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (sqrt (/ 1 PI)))

series618.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 1 (* (* (fabs x) (fabs x)) (fabs x)))
46.0ms
(* (* (fabs x) (fabs x)) (fabs x))
72.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
452.0ms
(* (+ (* 1.0 (/ 1 (fabs x))) (+ (* 0.5 (/ 1 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (sqrt (/ 1 PI)))

simplify1.8s

Counts
235 → 235
Iterations
IterNodes
done5000
11380
0455

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
42×add-sqr-sqrt
35×times-frac
32×add-cube-cbrt
30×frac-add
25×pow1 add-exp-log
22×add-cbrt-cube
17×associate-*l*
16×sqrt-prod
14×flip3-+ flip-+
12×unpow-prod-down sqrt-div
11×frac-times associate-*r/
10×associate-*r*
8×associate-/r* distribute-lft-out
7×prod-exp cbrt-unprod
6×pow-plus div-exp pow-prod-up associate-/l*
5×unswap-sqr
4×cbrt-undiv pow-prod-down add-log-exp sqr-pow
3×div-inv
2×pow2 clear-num frac-2neg pow-sqr *-commutative
1×distribute-rgt-in pow-to-exp distribute-lft-in pow3 associate-*l/ pow-exp
Counts
4 → 159
Calls
4 calls:
23.0ms
(/ 0.5 (* (* (fabs x) (fabs x)) (fabs x)))
14.0ms
(* (* (fabs x) (fabs x)) (fabs x))
6.0ms
(/ 0.75 (pow (fabs x) 5))
1.2s
(* (sqrt (/ 1 PI)) (+ (+ (/ 1.0 (fabs x)) (/ 0.5 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 0.75 (pow (fabs x) 5)) (/ 1.875 (pow (fabs x) 7)))))

series629.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 0.5 (* (* (fabs x) (fabs x)) (fabs x)))
41.0ms
(* (* (fabs x) (fabs x)) (fabs x))
77.0ms
(/ 0.75 (pow (fabs x) 5))
467.0ms
(* (sqrt (/ 1 PI)) (+ (+ (/ 1.0 (fabs x)) (/ 0.5 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 0.75 (pow (fabs x) 5)) (/ 1.875 (pow (fabs x) 7)))))

simplify2.1s

Counts
171 → 171
Iterations
IterNodes
done5001
11130
0340

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes420.0ms

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done36
136
027

end0.0ms

sample14.8s

Algorithm
intervals
Results
13.8s52303×body80valid