Details

Time bar (total: 36.2s)

sample850.0ms

Algorithm
intervals
Results
747.0ms3661×body80valid

simplify2.7s

Counts
1 → 1
Iterations
IterNodes
done5000
32139
2384
190
031

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize94.0ms

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)

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
120×times-frac
89×*-un-lft-identity add-cube-cbrt
40×add-cbrt-cube add-exp-log
39×swap-sqr associate-*r* associate-*l*
26×pow1
12×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×add-log-exp
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 214
Calls
4 calls:
36.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
42.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)

series101.0ms

Counts
4 → 10
Calls
4 calls:
29.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify2.9s

Counts
224 → 224
Iterations
IterNodes
done5000
23353
1462
0143

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.5b

localize110.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))))))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)

rewrite814.0ms

Algorithm
rewrite-expression-head
Rules
395×frac-times
291×associate-*r/
268×frac-add
137×associate-*l/
93×add-sqr-sqrt
89×times-frac
68×*-un-lft-identity add-cube-cbrt
60×add-cbrt-cube add-exp-log
39×associate-*l*
27×associate-*r*
26×swap-sqr
24×pow1 prod-exp cbrt-unprod
20×flip3-+ flip-+
16×cbrt-undiv div-exp
9×div-inv
8×unswap-sqr
5×pow-prod-down
4×distribute-rgt-in distribute-lft-in add-log-exp
3×*-commutative sqrt-prod
2×pow2 pow-plus pow-sqr pow-prod-up
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 358
Calls
4 calls:
720.0ms
(* (/ 1.0 (fabs x)) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))))))
20.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)

series319.0ms

Counts
4 → 10
Calls
4 calls:
250.0ms
(* (/ 1.0 (fabs x)) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))))))
36.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify3.6s

Counts
368 → 368
Iterations
IterNodes
done5002
13431
0786

prune3.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize121.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 3.0 (* (fabs x) (fabs x)))
0.3b
(* (* (fabs x) (fabs x)) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))))
0.4b
(/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* (* (fabs x) (fabs x)) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))))))
1.0b
(sqrt PI)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
300×add-cbrt-cube add-exp-log
212×prod-exp cbrt-unprod
55×pow1
38×pow-prod-down
36×cbrt-undiv div-exp
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×associate-*l* associate-*r/ add-log-exp
3×sqrt-prod
2×associate-*r* *-commutative associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-+ times-frac pow1/2 flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 159
Calls
4 calls:
26.0ms
(* 3.0 (* (fabs x) (fabs x)))
410.0ms
(* (* (fabs x) (fabs x)) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))))
1.4s
(/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* (* (fabs x) (fabs x)) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))))))
1.0ms
(sqrt PI)

series378.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* 3.0 (* (fabs x) (fabs x)))
79.0ms
(* (* (fabs x) (fabs x)) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))))
266.0ms
(/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* (* (fabs x) (fabs x)) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))))))
0.0ms
(sqrt PI)

simplify2.9s

Counts
169 → 169
Iterations
IterNodes
done5001
11238
0290

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (sqrt PI)) (+ (/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* 8.0 (pow (fabs x) 5)))) (/ 1.0 (fabs x))))
0.3b
(* 3.0 (* (fabs x) (fabs x)))
0.4b
(/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* 8.0 (pow (fabs x) 5))))
1.0b
(sqrt PI)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
50×add-cbrt-cube
41×prod-exp
30×add-sqr-sqrt
25×associate-*l*
23×cbrt-unprod
22×*-un-lft-identity
21×times-frac
20×add-cube-cbrt
16×div-exp
13×sqrt-prod
12×pow1
10×cbrt-undiv
7×associate-*r/
5×associate-*r*
4×pow-prod-down add-log-exp unswap-sqr
3×frac-times pow-to-exp flip3-+ pow-exp flip-+
2×frac-add *-commutative div-inv associate-/l/
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 associate-*l/ distribute-lft-out associate-/l*
Counts
4 → 122
Calls
4 calls:
1.3s
(* (/ 1.0 (sqrt PI)) (+ (/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* 8.0 (pow (fabs x) 5)))) (/ 1.0 (fabs x))))
21.0ms
(* 3.0 (* (fabs x) (fabs x)))
338.0ms
(/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* 8.0 (pow (fabs x) 5))))
1.0ms
(sqrt PI)

series851.0ms

Counts
4 → 10
Calls
4 calls:
550.0ms
(* (/ 1.0 (sqrt PI)) (+ (/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* 8.0 (pow (fabs x) 5)))) (/ 1.0 (fabs x))))
34.0ms
(* 3.0 (* (fabs x) (fabs x)))
266.0ms
(/ (* 1.0 (* 1.0 (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0))))))))) (* (fabs x) (* 8.0 (pow (fabs x) 5))))
0.0ms
(sqrt PI)

simplify2.9s

Counts
132 → 132
Iterations
IterNodes
done5000
11033
0282

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes451.0ms

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done36
136
027

end0.0ms

sample4.6s

Algorithm
intervals
Results
4.2s15801×body80valid