Details

Time bar (total: 2.6m)

sample1.4s

Algorithm
intervals
Results
1.3s3841×body80valid

simplify1.9s

Counts
1 → 1
Iterations
IterNodes
done2009
42009
31493
2392
195
031

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize115.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
144×times-frac
124×add-exp-log
113×*-un-lft-identity
89×add-cube-cbrt
50×pow1
48×div-exp prod-exp
45×swap-sqr
40×add-cbrt-cube
39×associate-*r* associate-*l*
27×unswap-sqr
24×rec-exp 1-exp pow-flip inv-pow
18×div-inv
15×pow-prod-up
12×cbrt-undiv cbrt-unprod
9×pow-prod-down pow-sqr
4×insert-posit16 add-log-exp
3×pow2 frac-times pow-plus associate-*l/ associate-*r/ un-div-inv *-commutative sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 302
Calls
4 calls:
24.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
14.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
26.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series106.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
40.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
33.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify1.5s

Counts
312 → 312
Iterations
IterNodes
done2000
32000
21064
1476
0164

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.6b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
0.4b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* 3/4 (* (/ 1 (* (fabs x) (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (+ (+ (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) 1/2) (/ 1 (fabs x))) (* (* 15/8 (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (/ 1 (fabs x))))))
0.5b
(* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))
1.0b
(sqrt PI)

rewrite8.2s

Algorithm
rewrite-expression-head
Rules
21011×associate-*r/
15479×frac-times
14436×frac-add
11944×associate-*l/
4963×add-exp-log
4387×un-div-inv
3203×prod-exp
1771×div-exp
920×flip3-+ flip-+
885×rec-exp 1-exp
449×pow1
338×add-cbrt-cube
336×pow-flip
312×pow-prod-up
171×cbrt-unprod
114×inv-pow
106×cbrt-undiv
93×pow-prod-down
64×pow-sqr
55×add-sqr-sqrt
52×pow-plus
51×times-frac
43×pow2
41×*-un-lft-identity
30×associate-*l*
28×add-cube-cbrt
17×associate-*r*
13×sqrt-prod
12×unswap-sqr
7×pow3
4×insert-posit16 add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 swap-sqr
Counts
4 → 6639
Calls
4 calls:
73.0ms
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
6.8s
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* 3/4 (* (/ 1 (* (fabs x) (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (+ (+ (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) 1/2) (/ 1 (fabs x))) (* (* 15/8 (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (/ 1 (fabs x))))))
184.0ms
(* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))
2.0ms
(sqrt PI)

series535.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
432.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* 3/4 (* (/ 1 (* (fabs x) (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (+ (+ (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) 1/2) (/ 1 (fabs x))) (* (* 15/8 (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (/ 1 (fabs x))))))
72.0ms
(* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))
0.0ms
(sqrt PI)

simplify33.3s

Counts
6649 → 6649
Iterations
IterNodes
done13415
013415

prune1.3m

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 15/8 (/ 1 (pow (fabs x) 7)))
0.3b
(/ 1 (pow (fabs x) 5))
0.3b
(* 3/4 (/ 1 (pow (fabs x) 5)))
0.4b
(* (* (exp (pow (fabs x) 2)) (+ (/ 1 (fabs x)) (+ (* 1/2 (/ 1 (pow (fabs x) 3))) (+ (* 3/4 (/ 1 (pow (fabs x) 5))) (* 15/8 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
84×times-frac
68×frac-add
66×associate-*r*
64×*-un-lft-identity
63×associate-*r/
58×add-cube-cbrt
57×add-exp-log
34×unpow-prod-down
30×un-div-inv
23×prod-exp
21×add-cbrt-cube
18×div-exp
17×sqrt-div
16×frac-times associate-*l/
14×unswap-sqr sqr-pow
13×pow1 sqrt-prod
9×pow-to-exp rec-exp 1-exp pow-exp
8×flip3-+ flip-+
7×associate-/r* associate-*l* cbrt-unprod
5×pow-prod-down
4×insert-posit16 div-inv add-log-exp
3×cbrt-undiv *-commutative associate-/l*
1×clear-num frac-2neg pow-flip inv-pow
Counts
4 → 237
Calls
4 calls:
18.0ms
(* 15/8 (/ 1 (pow (fabs x) 7)))
6.0ms
(/ 1 (pow (fabs x) 5))
14.0ms
(* 3/4 (/ 1 (pow (fabs x) 5)))
351.0ms
(* (* (exp (pow (fabs x) 2)) (+ (/ 1 (fabs x)) (+ (* 1/2 (/ 1 (pow (fabs x) 3))) (+ (* 3/4 (/ 1 (pow (fabs x) 5))) (* 15/8 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* 15/8 (/ 1 (pow (fabs x) 7)))
65.0ms
(/ 1 (pow (fabs x) 5))
53.0ms
(* 3/4 (/ 1 (pow (fabs x) 5)))
474.0ms
(* (* (exp (pow (fabs x) 2)) (+ (/ 1 (fabs x)) (+ (* 1/2 (/ 1 (pow (fabs x) 3))) (+ (* 3/4 (/ 1 (pow (fabs x) 5))) (* 15/8 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

simplify1.5s

Counts
249 → 249
Iterations
IterNodes
done2003
22003
11461
0484

prune1.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
0.4b
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
0.4b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* 3/4 (* (/ 1 (* (fabs x) (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (+ (+ (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) 1/2) (/ 1 (fabs x))) (* (* 15/8 (pow (fabs x) (+ (+ (- 2) -1) (+ (- 2) -1)))) (/ 1 (fabs x))))))
1.0b
(sqrt PI)

rewrite6.3s

Algorithm
rewrite-expression-head
Rules
2134×associate-*r/
1764×frac-add
1126×frac-times
987×associate-*l/
648×associate-+l-
432×neg-sub0 pow-sub
370×un-div-inv
216×associate-+r-
174×add-exp-log
128×flip3-+ flip-+
82×add-sqr-sqrt prod-exp
70×times-frac
61×div-exp
51×*-un-lft-identity add-cbrt-cube
49×pow1
37×add-cube-cbrt
36×associate-*l*
32×pow-flip
30×rec-exp 1-exp
29×associate-*r*
21×unswap-sqr
20×pow-prod-up
18×cbrt-unprod
15×cbrt-undiv
13×sqrt-prod
12×inv-pow
11×pow-prod-down
5×div-inv
4×pow2 pow-plus pow-sqr insert-posit16 add-log-exp
3×*-commutative
2×pow3
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 925
Calls
4 calls:
46.0ms
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
40.0ms
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
6.1s
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* 3/4 (* (/ 1 (* (fabs x) (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (+ (+ (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) 1/2) (/ 1 (fabs x))) (* (* 15/8 (pow (fabs x) (+ (+ (- 2) -1) (+ (- 2) -1)))) (/ 1 (fabs x))))))
1.0ms
(sqrt PI)

series529.0ms

Counts
4 → 10
Calls
4 calls:
51.0ms
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
46.0ms
(* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x)))
432.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* 3/4 (* (/ 1 (* (fabs x) (fabs x))) (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (+ (+ (* (* (/ 1 (* (fabs x) (fabs x))) (/ 1 (fabs x))) 1/2) (/ 1 (fabs x))) (* (* 15/8 (pow (fabs x) (+ (+ (- 2) -1) (+ (- 2) -1)))) (/ 1 (fabs x))))))
0.0ms
(sqrt PI)

simplify3.9s

Counts
935 → 935
Iterations
IterNodes
done2193
02193

prune9.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes247.0ms

bsearch0.0ms

simplify22.0ms

Iterations
IterNodes
done60
260
158
038

end0.0ms

sample4.9s

Algorithm
intervals
Results
4.6s15301×body80valid