Details

Time bar (total: 35.2s)

sample1.4s

Algorithm
intervals
Results
1.3s3101×body80valid

simplify5.1s

Counts
1 → 1
Iterations
IterNodes
47662
31577
2409
195
031

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
590×pow1
324×pow-div
216×pow-plus pow-prod-up
204×add-exp-log
114×add-cbrt-cube
94×div-exp
81×pow-flip inv-pow
79×times-frac
75×prod-exp
72×pow2 pow-sqr
49×cbrt-undiv
39×cbrt-unprod
37×add-sqr-sqrt
36×*-un-lft-identity pow3 add-cube-cbrt
20×associate-/l*
15×sqrt-prod
9×rec-exp 1-exp
7×associate-/r*
6×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef associate-/l/
Counts
4 → 340
Calls
4 calls:
62.0ms
(/ (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
5.0ms
(/ (fma (/ (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
0.0ms
(fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series543.0ms

Counts
4 → 10
Calls
4 calls:
90.0ms
(/ (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
350.0ms
(/ (fma (/ (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
102.0ms
(fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify4.8s

Counts
350 → 350
Iterations
IterNodes
38754
21980
1822
0365

prune5.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (fabs x)) 3/4)
0.3b
(/ (fma (pow (fabs x) -7) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
0.4b
(fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
29×*-un-lft-identity times-frac
28×add-cube-cbrt
15×add-exp-log sqrt-prod
13×associate-*l*
11×add-cbrt-cube
7×pow1
6×associate-/r*
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×div-exp associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv cbrt-unprod div-inv
1×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 107
Calls
4 calls:
29.0ms
(* (/ 1 (fabs x)) 3/4)
7.0ms
(/ (fma (pow (fabs x) -7) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
0.0ms
(fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series454.0ms

Counts
4 → 10
Calls
4 calls:
6.0ms
(* (/ 1 (fabs x)) 3/4)
366.0ms
(/ (fma (pow (fabs x) -7) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
82.0ms
(fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify1.3s

Counts
117 → 117
Iterations
IterNodes
32723
2909
1367
0187

prune2.6s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×times-frac
51×*-un-lft-identity
45×add-cube-cbrt
24×unpow-prod-down
16×associate-*r* add-exp-log sqrt-prod
14×associate-/r*
10×add-cbrt-cube
8×sqr-pow
6×pow1 div-exp associate-/l*
5×sqrt-div associate-*l*
4×expm1-log1p-u frac-times flip3-+ associate-*l/ frac-add flip-+ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×div-inv distribute-lft-out
2×pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp
1×pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod fma-udef
Counts
4 → 155
Calls
4 calls:
7.0ms
(/ 15/8 (pow (fabs x) 7))
230.0ms
(* (+ (/ 3/4 (pow (fabs x) 5)) (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 15/8 (pow (fabs x) 7)))) (sqrt (/ 1 PI)))
8.0ms
(/ 3/4 (pow (fabs x) 5))
0.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))

series663.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ 15/8 (pow (fabs x) 7))
432.0ms
(* (+ (/ 3/4 (pow (fabs x) 5)) (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 15/8 (pow (fabs x) 7)))) (sqrt (/ 1 PI)))
81.0ms
(/ 3/4 (pow (fabs x) 5))
70.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))

simplify1.5s

Counts
167 → 167
Iterations
IterNodes
22484
1656
0307

prune3.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))) (cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))))
0.5b
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))
0.5b
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))
0.5b
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
17.0ms
(* (cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))) (cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))))
1.0ms
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))
10.0ms
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))
1.0ms
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))

series943.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(* (cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))) (cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))))
265.0ms
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))
231.0ms
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))
203.0ms
(cbrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))))

simplify1.2s

Counts
97 → 97
Iterations
IterNodes
42113
3660
2271
1130
064

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes252.0ms

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
238
138
030

end0.0ms

sample3.2s

Algorithm
intervals
Results
3.1s7389×body80valid