Details

Time bar (total: 14.6s)

sample358.0ms

Algorithm
intervals
Results
284.0ms3772×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: done (1.2s)

IterNodesCost
031103
190103
238466
3186154
done500051

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(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)

rewrite23.0ms

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:
6.0ms
(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)

series107.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(pow (/ 1.0 (fabs x)) 3)
35.0ms
(pow (/ 1.0 (fabs x)) 4)
39.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify894.0ms

Counts
125 → 125
Iterations

Useful iterations: done (890.0ms)

IterNodesCost
01591392
14301254
213571152
done50001140

prune541.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

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)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite80.0ms

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:
62.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series169.0ms

Counts
4 → 10
Calls
4 calls:
95.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
38.0ms
(pow (/ 1.0 (fabs x)) 3)
36.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify1.5s

Counts
133 → 133
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02051930
15591750
221441568
done50011565

prune636.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (pow 1.0 2) (/ 1.0 (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)

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
28×add-sqr-sqrt
27×prod-exp
22×add-cube-cbrt *-un-lft-identity
19×times-frac
18×add-cbrt-cube
16×associate-*r*
14×associate-*r/
13×unpow-prod-down
11×div-exp
10×pow1
9×frac-times pow-exp
8×pow-to-exp
7×cbrt-unprod
6×frac-add
5×associate-*l/
4×flip3-+ associate-*l* flip-+ add-log-exp
3×pow-unpow sqrt-prod
2×cbrt-undiv pow-prod-down *-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow1/2 sqr-pow
Counts
4 → 119
Calls
4 calls:
71.0ms
(* (* (pow 1.0 2) (/ 1.0 (pow (fabs x) 3))) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
63.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series282.0ms

Counts
4 → 10
Calls
4 calls:
151.0ms
(* (* (pow 1.0 2) (/ 1.0 (pow (fabs x) 3))) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
92.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
39.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.0s

Counts
129 → 129
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02862891
18472638
239792253
done50022252

prune709.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow (fabs x) 3) (* 2.0 (pow (fabs x) 4)))
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)

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
30×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
23×prod-exp
19×times-frac
16×unpow-prod-down
15×associate-*l*
14×associate-*r* add-cbrt-cube
9×pow-exp
8×pow1 pow-to-exp
5×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 → 112
Calls
4 calls:
25.0ms
(* (pow (fabs x) 3) (* 2.0 (pow (fabs x) 4)))
60.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series199.0ms

Counts
4 → 10
Calls
4 calls:
71.0ms
(* (pow (fabs x) 3) (* 2.0 (pow (fabs x) 4)))
92.0ms
(* (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4)) 1) (/ 1.0 (fabs x)))
35.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify1.2s

Counts
122 → 122
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02321921
15801760
223711544
done50011539

prune595.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes200.0ms

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03960
15558
done5558

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.9s38769×body80valid