Details

Time bar (total: 40.3s)

sample1.7s

Algorithm
intervals
Results
1.6s3611×body80valid

simplify6.4s

Counts
1 → 1

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
422×add-exp-log
324×pow1
270×times-frac
219×div-exp
176×pow-div
153×add-sqr-sqrt prod-exp
139×add-cbrt-cube
122×*-un-lft-identity
113×pow-prod-up
112×add-cube-cbrt
88×pow-flip inv-pow
63×cbrt-undiv
53×pow-sqr
49×pow-plus
45×cbrt-unprod
41×pow2
39×sqrt-prod
36×rec-exp 1-exp
22×associate-/r*
19×swap-sqr
17×associate-*r* associate-*l*
16×unswap-sqr
15×div-inv
13×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
1×frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*l/ associate-*r/ associate-/r/ *-commutative fma-udef
Counts
4 → 418
Calls
4 calls:
Slowest
81.0ms
(* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))))
21.0ms
(/ (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (/ 3/4 (fabs x)) (fabs x))) (fma (* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (/ 15/8 (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
2.0ms
(sqrt PI)
0.0ms
(fma (* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (/ 15/8 (fabs x)) (/ 1 (fabs x)))

series612.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
431.0ms
(/ (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (/ 3/4 (fabs x)) (fabs x))) (fma (* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (/ 15/8 (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
125.0ms
(fma (* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (/ 15/8 (fabs x)) (/ 1 (fabs x)))
56.0ms
(* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))))
0.0ms
(sqrt PI)

simplify1.4s

Counts
428 → 428

prune6.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize78.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (sqrt (/ 1 PI)))
0.3b
(/ 15/8 (pow (fabs x) 7))
0.2b
(/ 3/4 (pow (fabs x) 5))
0.2b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
56×add-sqr-sqrt
53×times-frac
46×add-cube-cbrt
30×frac-add
25×pow1
24×unpow-prod-down
21×add-exp-log
19×associate-*r*
16×sqrt-prod
15×add-cbrt-cube
14×associate-/r* flip3-+ flip-+
13×distribute-lft-out
12×sqrt-div
11×frac-times associate-*l/
10×associate-*l*
8×sqr-pow
6×pow-plus div-exp pow-prod-up associate-/l*
5×div-inv unswap-sqr
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×pow2 pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp pow-sqr *-commutative
1×pow3 associate-*r/
Counts
4 → 193
Calls
4 calls:
Slowest
1.1s
(* (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (sqrt (/ 1 PI)))
19.0ms
(* (* (fabs x) (fabs x)) (fabs x))
9.0ms
(/ 3/4 (pow (fabs x) 5))
9.0ms
(/ 15/8 (pow (fabs x) 7))

series607.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
428.0ms
(* (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (sqrt (/ 1 PI)))
96.0ms
(/ 15/8 (pow (fabs x) 7))
48.0ms
(/ 3/4 (pow (fabs x) 5))
35.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify2.3s

Counts
205 → 205

prune3.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
190×times-frac
111×add-sqr-sqrt
110×*-un-lft-identity add-cube-cbrt
39×sqrt-prod
35×add-exp-log
30×associate-/r*
23×add-cbrt-cube
19×pow1 associate-/l*
18×div-exp
12×unpow-prod-down
10×cbrt-undiv
9×div-inv
8×pow-div
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u pow-flip inv-pow add-log-exp sqr-pow
3×clear-num frac-2neg
2×pow2 rec-exp pow-plus 1-exp pow-sqr pow-prod-up cbrt-unprod
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp associate-/r/ associate-/l/
Counts
4 → 234
Calls
4 calls:
Slowest
28.0ms
(/ (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (/ 3/4 (fabs x)) (fabs x))) (+ (/ 1 (fabs x)) (/ 15/8 (pow (fabs x) 7)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
10.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
5.0ms
(/ 15/8 (pow (fabs x) 7))
2.0ms
(sqrt PI)

series561.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
444.0ms
(/ (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (/ 3/4 (fabs x)) (fabs x))) (+ (/ 1 (fabs x)) (/ 15/8 (pow (fabs x) 7)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
76.0ms
(/ 15/8 (pow (fabs x) 7))
41.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify1.8s

Counts
244 → 244

prune4.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
0.3b
(/ 15/8 (pow (fabs x) 7))
0.2b
(/ 3/4 (pow (fabs x) 5))
0.2b
(* (fabs x) (* (fabs x) (fabs x)))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
42×times-frac
39×add-sqr-sqrt
38×add-cube-cbrt
24×unpow-prod-down
23×pow1 add-exp-log
18×add-cbrt-cube frac-add
14×associate-/r*
9×associate-*l/ distribute-lft-out
8×sqrt-div associate-*r* sqr-pow
7×frac-times associate-*r/
6×flip3-+ div-exp pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
5×pow-prod-up
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp *-commutative
1×pow2 distribute-rgt-in distribute-lft-in pow-plus cube-unmult pow-sqr unswap-sqr
Counts
4 → 165
Calls
4 calls:
Slowest
2.3s
(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
27.0ms
(* (fabs x) (* (fabs x) (fabs x)))
10.0ms
(/ 3/4 (pow (fabs x) 5))
9.0ms
(/ 15/8 (pow (fabs x) 7))

series632.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
429.0ms
(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 1 (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))
87.0ms
(/ 15/8 (pow (fabs x) 7))
66.0ms
(/ 3/4 (pow (fabs x) 5))
49.0ms
(* (fabs x) (* (fabs x) (fabs x)))

simplify2.4s

Counts
177 → 177

prune3.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

regimes226.0ms

bsearch5.0ms

end0.0ms