Details

Time bar (total: 20.2s)

sample337.0ms

Algorithm
intervals
Results
276.0ms3513×body80valid

simplify818.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (166.0ms)

IterNodesCost
031103
190103
238165
3195451
done500151

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
120×times-frac
89×add-cube-cbrt *-un-lft-identity
40×add-exp-log add-cbrt-cube
39×swap-sqr associate-*r* associate-*l*
26×pow1
12×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ sqrt-prod pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 222
Calls
4 calls:
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms
(sqrt PI)

series70.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify771.0ms

Counts
232 → 232
Iterations

Useful iterations: done (765.0ms)

IterNodesCost
01503287
14242964
217002446
done50012437

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
52×times-frac
44×unpow-prod-down
43×add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
38×cube-prod
24×add-exp-log
16×add-cbrt-cube
13×pow-exp
9×pow-unpow
8×pow1 div-exp
7×rem-cube-cbrt
6×div-inv
5×pow-to-exp sqr-pow
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-div cube-mult pow-pow unpow3 prod-exp sqrt-prod
2×unpow2
1×rem-sqrt-square sqrt-pow1 pow1/2 cbrt-unprod
Counts
4 → 163
Calls
4 calls:
7.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series125.0ms

Counts
4 → 10
Calls
4 calls:
56.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
32.0ms
(pow (/ 1.0 (fabs x)) 3)
36.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.0s

Counts
173 → 173
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
01942107
15571874
223311527
done50011525

prune730.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (/ (pow (/ 1.0 (fabs x)) 3) (/ (fabs x) 1.0))) (/ (* 15.0 (/ 1.0 (pow (fabs x) 6))) 8.0)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
46×times-frac
43×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down cube-prod
15×add-exp-log add-cbrt-cube
13×associate-*l*
9×pow1
7×frac-times associate-*r/
6×pow-unpow frac-add
5×div-inv
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×cbrt-undiv div-exp associate-*r* associate-*l/ sqrt-prod
2×cube-div cube-mult pow-to-exp pow-pow flip3-+ unpow3 prod-exp cbrt-unprod flip-+ unswap-sqr sqr-pow
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 157
Calls
4 calls:
154.0ms
(* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (/ (pow (/ 1.0 (fabs x)) 3) (/ (fabs x) 1.0))) (/ (* 15.0 (/ 1.0 (pow (fabs x) 6))) 8.0)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series238.0ms

Counts
4 → 10
Calls
4 calls:
166.0ms
(* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (/ (pow (/ 1.0 (fabs x)) 3) (/ (fabs x) 1.0))) (/ (* 15.0 (/ 1.0 (pow (fabs x) 6))) 8.0)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.9s

Counts
167 → 167
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02133234
17513020
238802679
done50002629

prune808.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 0.75 (pow (fabs x) 4))
0.4b
(/ (* (* 1.0 (exp (pow (fabs x) 2))) (+ (/ (* (+ (/ 1.875 (pow (fabs x) 6)) (/ 0.75 (pow (fabs x) 4))) 1.0) (fabs x)) (fma (pow (/ 1.0 (fabs x)) 3) (/ 1.0 2.0) (/ 1.0 (fabs x))))) (sqrt PI))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
41×add-sqr-sqrt
40×add-cube-cbrt *-un-lft-identity
25×unpow-prod-down
20×add-exp-log
18×add-cbrt-cube
13×cube-prod associate-/r*
9×sqrt-prod
7×div-exp
6×pow1
5×cbrt-undiv sqr-pow
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×pow-unpow pow-exp prod-exp cbrt-unprod
2×pow-to-exp frac-2neg associate-*r/ clear-num associate-/l/ rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 unpow3 flip-+
Counts
4 → 143
Calls
4 calls:
4.0ms
(/ 0.75 (pow (fabs x) 4))
100.0ms
(/ (* (* 1.0 (exp (pow (fabs x) 2))) (+ (/ (* (+ (/ 1.875 (pow (fabs x) 6)) (/ 0.75 (pow (fabs x) 4))) 1.0) (fabs x)) (fma (pow (/ 1.0 (fabs x)) 3) (/ 1.0 2.0) (/ 1.0 (fabs x))))) (sqrt PI))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series466.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(/ 0.75 (pow (fabs x) 4))
396.0ms
(/ (* (* 1.0 (exp (pow (fabs x) 2))) (+ (/ (* (+ (/ 1.875 (pow (fabs x) 6)) (/ 0.75 (pow (fabs x) 4))) 1.0) (fabs x)) (fma (pow (/ 1.0 (fabs x)) 3) (/ 1.0 2.0) (/ 1.0 (fabs x))))) (sqrt PI))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.2s

Counts
153 → 153
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02763343
17193167
231162707
done50002706

prune612.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes300.0ms

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03249
13749
done3749

end0.0ms

sample9.2s

Algorithm
intervals
Results
7.9s103451×body80valid