Details

Time bar (total: 22.6s)

sample1.4s

Algorithm
intervals
Results
1.3s3804×body80valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: done (2.3s)

IterNodesCost
031103
190103
240165
3202351
done500149

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.2b
(pow (/ 1.0 (fabs x)) 6)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
13×add-exp-log cube-prod
9×pow-unpow
8×pow1
7×add-cbrt-cube
6×pow-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×rem-cube-cbrt
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3
Counts
4 → 123
Calls
4 calls:
14.0ms
(pow (/ 1.0 (fabs x)) 3)
7.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
14.0ms
(pow (/ 1.0 (fabs x)) 6)

series185.0ms

Counts
4 → 10
Calls
4 calls:
36.0ms
(pow (/ 1.0 (fabs x)) 3)
59.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
90.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify1.6s

Counts
133 → 133
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02081438
15311292
217371182
done50001175

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
37×times-frac
36×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
15×add-exp-log
13×cube-prod associate-*l*
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×expm1-log1p-u pow-exp log1p-expm1-u div-inv add-log-exp
3×div-exp associate-*r* sqrt-prod
2×cbrt-undiv frac-times pow-to-exp pow-pow flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr sqr-pow
1×cube-div distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down associate-*l/ *-commutative
Counts
4 → 133
Calls
4 calls:
72.0ms
(* (/ 1.0 (fabs x)) (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1)))
7.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
3.0ms
(sqrt PI)

series323.0ms

Counts
4 → 10
Calls
4 calls:
217.0ms
(* (/ 1.0 (fabs x)) (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1)))
55.0ms
(pow (/ 1.0 (fabs x)) 3)
50.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.3s

Counts
143 → 143
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02302594
17172399
229902167
done50022161

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
26×unpow-prod-down
13×cube-prod
10×add-exp-log
8×pow1
7×add-cbrt-cube
6×pow-unpow sqrt-prod
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×div-inv
2×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-exp rem-cube-cbrt sqr-pow
1×cbrt-undiv cube-div cube-mult unpow3
Counts
4 → 108
Calls
4 calls:
7.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series140.0ms

Counts
4 → 8
Calls
4 calls:
61.0ms
(pow (/ 1.0 (fabs x)) 3)
79.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.3s

Counts
116 → 116
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01451091
1385970
21108886
done5000880

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* 1.0 (fma (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6)) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1))) (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
85×times-frac
55×add-sqr-sqrt
54×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
22×associate-/r*
21×sqrt-prod
20×add-exp-log
19×add-cbrt-cube
13×cube-prod
8×div-exp
7×pow1 cbrt-undiv
6×pow-unpow div-inv
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
2×pow-to-exp pow-pow prod-exp cbrt-unprod rem-cube-cbrt sqr-pow
1×cube-div cube-mult rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 unpow3 clear-num associate-/r/ associate-/l*
Counts
4 → 159
Calls
4 calls:
41.0ms
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* 1.0 (fma (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6)) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1))) (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
14.0ms
(pow (/ 1.0 (fabs x)) 3)
15.0ms
(pow (/ 1.0 (fabs x)) 4)
16.0ms
(sqrt PI)

series740.0ms

Counts
4 → 10
Calls
4 calls:
628.0ms
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* 1.0 (fma (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6)) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1))) (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
38.0ms
(pow (/ 1.0 (fabs x)) 3)
73.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.0s

Counts
169 → 169
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03135190
18044878
227284317
done50004315

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes162.0ms

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample5.0s

Algorithm
intervals
Results
4.7s17116×body80valid