Details

Time bar (total: 28.9s)

sample1.0s

Algorithm
intervals
Results
898.0ms3217×body80valid

simplify3.4s

Counts
1 → 1
Iterations
IterNodes
done5000
31575
2409
195
031

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize87.0ms

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)

rewrite93.0ms

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:
28.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
28.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
28.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series75.0ms

Counts
4 → 10
Calls
4 calls:
22.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
28.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
25.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify4.4s

Counts
320 → 320
Iterations
IterNodes
done5000
34141
21252
1490
0168

prune2.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.5b

localize92.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.4b
(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))))
0.5b
(* (/ (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)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
51×times-frac
42×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
30×add-exp-log
22×associate-*l*
21×pow1 add-cbrt-cube
13×div-exp sqrt-prod associate-/l*
8×pow-div
7×cbrt-undiv
6×prod-exp
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u div-inv pow-flip inv-pow add-log-exp
3×associate-*r* fma-udef unswap-sqr
2×pow2 rec-exp pow-plus 1-exp pow-sqr pow-prod-up
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 → 135
Calls
4 calls:
21.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
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
(* (/ (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)))))
2.0ms
(sqrt PI)

series704.0ms

Counts
4 → 10
Calls
4 calls:
53.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
247.0ms
(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))))
403.0ms
(* (/ (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
145 → 145
Iterations
IterNodes
done5005
21828
1588
0239

prune948.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt times-frac
48×*-un-lft-identity
47×add-cube-cbrt
25×add-exp-log
24×unpow-prod-down
19×add-cbrt-cube
16×associate-*l* sqrt-prod
15×associate-/r*
9×div-exp associate-/l*
8×sqr-pow
6×pow1
5×cbrt-undiv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
3×clear-num frac-2neg associate-*r*
2×pow-to-exp pow-exp fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ *-commutative
Counts
4 → 162
Calls
4 calls:
10.0ms
(/ 3/4 (pow (fabs x) 5))
10.0ms
(/ 15/8 (pow (fabs x) 7))
22.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
11.0ms
(* (sqrt (/ 1 PI)) (fma (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7))) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (exp (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))

series729.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 3/4 (pow (fabs x) 5))
63.0ms
(/ 15/8 (pow (fabs x) 7))
33.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
564.0ms
(* (sqrt (/ 1 PI)) (fma (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7))) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (exp (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))

simplify1.8s

Counts
174 → 174
Iterations
IterNodes
done5001
21754
1599
0314

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (pow (fabs x) 5))
1.0b
(cbrt 3/4)
1.0b
(cbrt 3/4)
1.0b
(cbrt 3/4)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-prod
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×unpow-prod-down
1×sqr-pow
Counts
4 → 60
Calls
4 calls:
1.0ms
(cbrt (pow (fabs x) 5))
1.0ms
(cbrt 3/4)
1.0ms
(cbrt 3/4)
1.0ms
(cbrt 3/4)

series240.0ms

Counts
4 → 6
Calls
4 calls:
240.0ms
(cbrt (pow (fabs x) 5))
0.0ms
(cbrt 3/4)
0.0ms
(cbrt 3/4)
0.0ms
(cbrt 3/4)

simplify2.1s

Counts
66 → 66
Iterations
IterNodes
done5012
42273
3625
2252
1120
072

prune612.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes255.0ms

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done35
135
028

end0.0ms

sample5.7s

Algorithm
intervals
Results
5.5s12976×body80valid