Details

Time bar (total: 43.2s)

sample1.2s

Algorithm
intervals
Results
1.1s3269×body80valid

simplify3.4s

Counts
1 → 1
Iterations
IterNodes
done5000
31575
2409
195
031

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize121.0ms

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)

rewrite66.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 310
Calls
4 calls:
14.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
22.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
23.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series73.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
26.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
24.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify4.0s

Counts
320 → 320
Iterations
IterNodes
done5000
34141
21252
1490
0168

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))
0.4b
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.5b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x)))))
1.0b
(sqrt PI)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
103×pow1
81×times-frac add-exp-log
64×pow-div
50×add-cbrt-cube
44×add-sqr-sqrt
43×div-exp
35×*-un-lft-identity add-cube-cbrt
23×cbrt-undiv
22×associate-*l*
19×prod-exp
17×associate-/l*
16×pow2 pow-plus pow-sqr pow-prod-up pow-flip inv-pow
13×sqrt-prod
11×cbrt-unprod
6×div-inv
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* fma-udef unswap-sqr
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 183
Calls
4 calls:
0.0ms
(fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))
37.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
28.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x)))))
1.0ms
(sqrt PI)

series696.0ms

Counts
4 → 10
Calls
4 calls:
208.0ms
(fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))
61.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
427.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x)))))
0.0ms
(sqrt PI)

simplify2.6s

Counts
193 → 193
Iterations
IterNodes
done5001
22482
1771
0319

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1/2 (* (fabs x) (fabs x)))
0.4b
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
1.0b
(sqrt PI)

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×*-un-lft-identity
23×times-frac
22×associate-*l*
21×add-cube-cbrt
14×add-cbrt-cube
13×add-exp-log sqrt-prod
7×pow1
5×associate-*r*
4×expm1-log1p-u frac-times flip3-+ frac-add associate-*r/ flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp prod-exp cbrt-unprod distribute-lft-out associate-/l* unswap-sqr
2×div-inv
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 108
Calls
4 calls:
13.0ms
(/ 1/2 (* (fabs x) (fabs x)))
0.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
247.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
2.0ms
(sqrt PI)

series615.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(/ 1/2 (* (fabs x) (fabs x)))
58.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
520.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
0.0ms
(sqrt PI)

simplify2.7s

Counts
118 → 118
Iterations
IterNodes
done5002
23602
1713
0213

prune953.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

localize121.0ms

Local error

Found 4 expressions with local error:

0.4b
(sqrt (+ (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
0.4b
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
0.4b
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
11×*-un-lft-identity
8×sqrt-prod
6×pow1 add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log hypot-def insert-posit16 log1p-expm1-u add-log-exp
3×times-frac distribute-lft-out
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 frac-add flip-+ fma-udef
1×unpow-prod-down sqr-pow
Counts
4 → 64
Calls
4 calls:
128.0ms
(sqrt (+ (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
0.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series516.0ms

Counts
4 → 10
Calls
4 calls:
384.0ms
(sqrt (+ (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
70.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
61.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify2.0s

Counts
74 → 74
Iterations
IterNodes
done5000
21032
1256
0114

prune699.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

regimes338.0ms

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done28
128
023

end0.0ms

sample19.3s

Algorithm
intervals
Results
18.4s44366×body80valid