Details

Time bar (total: 42.6s)

sample728.0ms

Algorithm
intervals
Results
650.0ms3458×body80valid

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5000
31575
2409
195
031

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.6b

localize88.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite166.0ms

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:
53.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
51.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
35.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
3.0ms
(sqrt PI)

series99.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
28.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
37.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify4.2s

Counts
320 → 320
Iterations
IterNodes
done5000
34141
21252
1490
0168

prune2.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize85.0ms

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)

rewrite89.0ms

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:
30.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
1.0ms
(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))))
48.0ms
(* (/ (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)

series752.0ms

Counts
4 → 10
Calls
4 calls:
54.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
242.0ms
(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))))
456.0ms
(* (/ (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)

simplify2.5s

Counts
145 → 145
Iterations
IterNodes
done5005
21828
1588
0239

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.3b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs x) (* (fabs x) (fabs x)))
0.3b
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
0.3b
(/ 15/8 (pow (fabs x) 7))
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))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
35×times-frac
33×*-un-lft-identity
32×add-cube-cbrt
25×add-exp-log
22×add-cbrt-cube
20×pow1
19×associate-*l*
16×sqrt-prod
12×unpow-prod-down
8×associate-/r*
7×prod-exp cbrt-unprod
6×div-exp associate-/l*
5×pow-prod-up unswap-sqr
4×expm1-log1p-u cbrt-undiv associate-*r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×div-inv
2×clear-num frac-2neg *-commutative fma-udef
1×pow2 distribute-rgt-in pow-to-exp distribute-lft-in pow-plus sqrt-div cube-unmult associate-*l/ pow-exp pow-sqr
Counts
4 → 141
Calls
4 calls:
40.0ms
(* (fabs x) (* (fabs x) (fabs x)))
28.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
8.0ms
(/ 15/8 (pow (fabs x) 7))
25.0ms
(* (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))))

series780.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (fabs x) (* (fabs x) (fabs x)))
50.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
103.0ms
(/ 15/8 (pow (fabs x) 7))
589.0ms
(* (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))))

simplify2.8s

Counts
153 → 153
Iterations
IterNodes
done5000
34709
21340
1494
0253

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×times-frac
46×*-un-lft-identity
45×add-cube-cbrt
24×unpow-prod-down
16×associate-*l* sqrt-prod
14×associate-/r*
10×add-cbrt-cube add-exp-log
8×sqr-pow
6×pow1 div-exp associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-*r* fma-udef div-inv
2×pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 147
Calls
4 calls:
14.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
1.0ms
(fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) 15/8 (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) 3/4 (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
20.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
22.0ms
(* (sqrt (/ 1 PI)) (fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) 15/8 (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) 3/4 (/ (exp (* (fabs x) (fabs x))) (fabs x))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
591.0ms
(fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) 15/8 (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) 3/4 (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
140.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
625.0ms
(* (sqrt (/ 1 PI)) (fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) 15/8 (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) 3/4 (/ (exp (* (fabs x) (fabs x))) (fabs x))))))

simplify2.9s

Counts
159 → 159
Iterations
IterNodes
done5000
34639
21448
1480
0257

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes263.0ms

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done30
130
024

end0.0ms

sample15.9s

Algorithm
intervals
Results
15.1s56504×body80valid