Details

Time bar (total: 21.5s)

sample1.6s

Algorithm
intervals
Results
1.4s3804×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: done (1.7s)

IterNodesCost
031103
190103
238466
3186154
done500051

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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×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 → 115
Calls
4 calls:
7.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series165.0ms

Counts
4 → 10
Calls
4 calls:
42.0ms
(pow (/ 1.0 (fabs x)) 3)
54.0ms
(pow (/ 1.0 (fabs x)) 4)
69.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify1.3s

Counts
125 → 125
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01591392
14301254
213571152
done50001140

prune817.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

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-*r*
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×pow-exp div-inv add-log-exp
3×div-exp associate-*l* sqrt-prod
2×cbrt-undiv frac-times pow-to-exp pow-pow flip3-+ associate-*l/ prod-exp cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr sqr-pow
1×cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down *-commutative
Counts
4 → 123
Calls
4 calls:
105.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
14.0ms
(pow (/ 1.0 (fabs x)) 3)
13.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series259.0ms

Counts
4 → 10
Calls
4 calls:
154.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
57.0ms
(pow (/ 1.0 (fabs x)) 3)
47.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify1.9s

Counts
133 → 133
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02051930
15591750
221441568
done50011565

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (pow 1.0 3) (pow (fabs x) 3)) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
0.4b
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
179×times-frac
151×associate-*l*
143×add-sqr-sqrt
95×add-cube-cbrt *-un-lft-identity
93×unpow-prod-down
80×cube-prod
35×add-exp-log
33×sqr-pow
24×cube-mult unpow3
19×unswap-sqr
16×associate-*r*
14×add-cbrt-cube
12×prod-exp
11×div-exp
10×pow1
9×frac-times
8×associate-*r/ pow-exp
7×pow-to-exp
6×frac-add
5×associate-*l/
4×flip3-+ cbrt-unprod flip-+ add-log-exp
3×pow-unpow sqrt-prod div-inv
2×cbrt-undiv pow-prod-down *-commutative
1×distribute-rgt-in rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 279
Calls
4 calls:
110.0ms
(* (/ (pow 1.0 3) (pow (fabs x) 3)) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
70.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
15.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series382.0ms

Counts
4 → 10
Calls
4 calls:
186.0ms
(* (/ (pow 1.0 3) (pow (fabs x) 3)) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
142.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
54.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify754.0ms

Counts
289 → 289
Iterations

Useful iterations: done (742.0ms)

IterNodesCost
04187020
112636567
done50016217

prune2.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (pow (fabs x) 3) (* 2.0 (* (pow (fabs x) 4) 8.0)))
0.4b
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
55×add-exp-log
38×prod-exp
30×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
19×times-frac
18×add-cbrt-cube
16×unpow-prod-down
15×associate-*l*
14×associate-*r*
10×pow-exp
9×pow-to-exp
8×pow1 cbrt-unprod
4×add-log-exp
3×pow-unpow cube-prod sqrt-prod
2×frac-times flip3-+ div-exp associate-*l/ *-commutative flip-+ div-inv unswap-sqr sqr-pow
1×cbrt-undiv cube-mult rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down
Counts
4 → 116
Calls
4 calls:
70.0ms
(* (pow (fabs x) 3) (* 2.0 (* (pow (fabs x) 4) 8.0)))
107.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
12.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series266.0ms

Counts
4 → 10
Calls
4 calls:
102.0ms
(* (pow (fabs x) 3) (* 2.0 (* (pow (fabs x) 4) 8.0)))
120.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
43.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.0s

Counts
126 → 126
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02412070
16001890
224741698
done50001693

prune948.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

regimes184.0ms

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03855
15355
done5355

end0.0ms

sample5.2s

Algorithm
intervals
Results
4.8s17116×body80valid