Details

Time bar (total: 40.9s)

sample746.0ms

Algorithm
intervals
Results
627.0ms3208×body80valid

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
done5000
31575
2409
195
031

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize116.0ms

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)

rewrite52.0ms

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:
13.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
18.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
13.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series80.0ms

Counts
4 → 10
Calls
4 calls:
22.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
23.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
34.0ms
(* (/ 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

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(/ (/ 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))))
1.0b
(sqrt PI)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
48×add-exp-log
34×add-sqr-sqrt
33×pow1 *-un-lft-identity add-cube-cbrt
28×add-cbrt-cube
26×associate-/l*
24×div-exp
16×pow-div
12×cbrt-undiv
8×prod-exp pow-flip inv-pow
6×div-inv
4×pow2 expm1-log1p-u rec-exp pow-plus 1-exp pow-sqr pow-prod-up cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num associate-/r* frac-2neg associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 149
Calls
4 calls:
18.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
18.0ms
(/ (/ 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))))
2.0ms
(sqrt PI)

series308.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
48.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
223.0ms
(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))))
0.0ms
(sqrt PI)

simplify1.7s

Counts
159 → 159
Iterations
IterNodes
done5001
21006
1359
0170

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(* (/ (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)))))
0.4b
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
41×times-frac
40×*-un-lft-identity
35×add-cube-cbrt
22×associate-*l*
13×add-exp-log sqrt-prod
12×unpow-prod-down
11×add-cbrt-cube
7×pow1 associate-/r*
5×associate-*r*
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×distribute-lft-out associate-/l* unswap-sqr
2×frac-times cbrt-undiv flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ div-inv
1×distribute-rgt-in pow-to-exp rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ pow-exp *-commutative fma-udef
Counts
4 → 128
Calls
4 calls:
10.0ms
(/ 15/8 (pow (fabs x) 7))
271.0ms
(* (/ (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
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series609.0ms

Counts
4 → 10
Calls
4 calls:
88.0ms
(/ 15/8 (pow (fabs x) 7))
454.0ms
(* (/ (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)))))
67.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify2.7s

Counts
138 → 138
Iterations
IterNodes
done5008
23024
1649
0231

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 3/4 (pow (fabs x) 5))
0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(* (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (sqrt (/ 1 PI)))
0.3b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
68×add-sqr-sqrt
65×*-un-lft-identity
59×add-cube-cbrt
38×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube
20×pow1
19×associate-/l*
18×div-exp
16×associate-*r* sqrt-prod
15×associate-/r*
8×cbrt-undiv pow-div sqr-pow
6×div-inv
5×sqrt-div associate-*l* prod-exp
4×expm1-log1p-u frac-times flip3-+ associate-*l/ frac-add flip-+ insert-posit16 log1p-expm1-u pow-flip inv-pow add-log-exp unswap-sqr
3×clear-num frac-2neg cbrt-unprod distribute-lft-out
2×pow2 pow-to-exp rec-exp pow-plus 1-exp pow-exp pow-sqr pow-prod-up
1×pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
4 → 205
Calls
4 calls:
10.0ms
(/ 3/4 (pow (fabs x) 5))
10.0ms
(/ 15/8 (pow (fabs x) 7))
204.0ms
(* (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (sqrt (/ 1 PI)))
10.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))

series553.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 3/4 (pow (fabs x) 5))
78.0ms
(/ 15/8 (pow (fabs x) 7))
365.0ms
(* (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))) (sqrt (/ 1 PI)))
58.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))

simplify2.5s

Counts
217 → 217
Iterations
IterNodes
done5001
23334
1905
0397

prune1.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

regimes257.0ms

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done30
130
024

end0.0ms

sample16.8s

Algorithm
intervals
Results
16.0s62856×body80valid