Details

Time bar (total: 34.4s)

sample1.4s

Algorithm
intervals
Results
1.3s3623×body80valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done2009
42009
31575
2409
195
031

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize105.0ms

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)

rewrite64.0ms

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:
24.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
14.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
14.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series95.0ms

Counts
4 → 10
Calls
4 calls:
29.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
31.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
35.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify1.9s

Counts
320 → 320
Iterations
IterNodes
done2011
32011
21252
1490
0168

prune6.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

localize87.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
584×add-exp-log
312×div-exp
221×prod-exp
124×add-cbrt-cube
114×times-frac
93×add-sqr-sqrt
76×*-un-lft-identity
74×rec-exp 1-exp
68×add-cube-cbrt
56×associate-*l*
53×pow1
52×cbrt-undiv
43×cbrt-unprod
21×pow-prod-up
20×pow-flip inv-pow
16×pow-div
15×swap-sqr
14×associate-*r*
10×div-inv
9×unswap-sqr
6×frac-times pow-prod-down associate-*r/
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr sqrt-prod
2×*-commutative
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 un-div-inv fma-udef
Counts
4 → 323
Calls
4 calls:
75.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
0.0ms
(fma (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) 15/8) (+ (fma (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 1/2 (* 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (/ 1 (fabs x))))
14.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series372.0ms

Counts
4 → 10
Calls
4 calls:
73.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
265.0ms
(fma (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) 15/8) (+ (fma (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 1/2 (* 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (/ 1 (fabs x))))
32.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify1.4s

Counts
333 → 333
Iterations
IterNodes
done2005
22005
11297
0454

prune5.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.2b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite729.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
62×times-frac
60×add-sqr-sqrt
51×add-cube-cbrt
30×frac-add
24×unpow-prod-down
22×associate-*l*
18×add-exp-log
14×associate-/r* flip3-+ flip-+
13×add-cbrt-cube sqrt-prod distribute-lft-out
11×frac-times associate-*r/
9×associate-*r*
8×sqr-pow
7×pow1 div-exp
6×associate-/l*
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv unswap-sqr
2×pow-to-exp clear-num frac-2neg pow-exp prod-exp cbrt-unprod
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
4 → 187
Calls
4 calls:
709.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7)))))
9.0ms
(/ 3/4 (pow (fabs x) 5))
5.0ms
(/ 15/8 (pow (fabs x) 7))
1.0ms
(sqrt PI)

series585.0ms

Counts
4 → 10
Calls
4 calls:
443.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7)))))
60.0ms
(/ 3/4 (pow (fabs x) 5))
81.0ms
(/ 15/8 (pow (fabs x) 7))
0.0ms
(sqrt PI)

simplify1.6s

Counts
197 → 197
Iterations
IterNodes
done2003
22003
11263
0385

prune3.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 3/4 (pow (fabs x) 5))
0.3b
(/ 15/8 (pow (fabs x) 7))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
40×add-sqr-sqrt
38×*-un-lft-identity add-cube-cbrt
24×unpow-prod-down
14×associate-/r* add-exp-log
8×add-cbrt-cube sqr-pow
6×pow1 div-exp sqrt-prod associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-exp div-inv
Counts
4 → 128
Calls
4 calls:
10.0ms
(/ 3/4 (pow (fabs x) 5))
10.0ms
(/ 15/8 (pow (fabs x) 7))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series150.0ms

Counts
4 → 8
Calls
4 calls:
55.0ms
(/ 3/4 (pow (fabs x) 5))
96.0ms
(/ 15/8 (pow (fabs x) 7))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify944.0ms

Counts
136 → 136
Iterations
IterNodes
done2004
32004
2852
1317
0187

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes251.0ms

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done33
133
026

end0.0ms

sample4.5s

Algorithm
intervals
Results
4.3s9605×body80valid