Details

Time bar (total: 10.0m)

sample1.3s

Algorithm
intervals
Results
1.1s3361×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: done (1.9s)

IterNodesCost
031103
190103
240165
3232051
done500049

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize92.0ms

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)

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
120×times-frac
89×add-cube-cbrt *-un-lft-identity
40×add-exp-log add-cbrt-cube
39×swap-sqr associate-*r* associate-*l*
26×pow1
12×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ sqrt-prod pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 222
Calls
4 calls:
40.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
41.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)

series92.0ms

Counts
4 → 10
Calls
4 calls:
38.0ms
(* (/ 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)

simplify3.1s

Counts
232 → 232
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01503287
14802982
234322630
done50002463

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.7b

localize105.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1.0 (fabs x)) (* (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 3.0 4.0) (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 15.0 8.0) (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 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)

rewrite2.8m

Algorithm
rewrite-expression-head
Rules
1654197×frac-times
1295595×associate-*l/
875949×associate-*r/
784606×frac-add
16258×flip3-+ flip-+
87×add-sqr-sqrt
80×times-frac
62×add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
35×add-exp-log
29×associate-*r*
27×associate-*l*
26×swap-sqr
24×pow1
13×prod-exp cbrt-unprod
9×cbrt-undiv div-exp
8×div-inv unswap-sqr
5×pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod *-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 → 272724
Calls
4 calls:
53.6s
(* (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1.0 (fabs x)) (* (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 3.0 4.0) (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 15.0 8.0) (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms
(sqrt PI)

series504.0ms

Counts
4 → 10
Calls
4 calls:
441.0ms
(* (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1.0 (fabs x)) (* (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 3.0 4.0) (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 15.0 8.0) (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify4.3m

Counts
272734 → 272734
Iterations

Useful iterations: 0 (1.4m)

IterNodesCost
045356041863220
done45356041863220

prune2.8m