Details

Time bar (total: 45.5s)

sample1.1s

Algorithm
intervals
Results
945.0ms3589×body80valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: done (2.1s)

IterNodesCost
031103
190103
238466
3214754
done500051

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize97.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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:
12.0ms
(pow (/ 1.0 (fabs x)) 3)
11.0ms
(pow (/ 1.0 (fabs x)) 4)
12.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series201.0ms

Counts
4 → 10
Calls
4 calls:
57.0ms
(pow (/ 1.0 (fabs x)) 3)
59.0ms
(pow (/ 1.0 (fabs x)) 4)
84.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.0s

Counts
125 → 125
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01591392
16051269
226301160
done50021148

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize105.0ms

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)
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite811.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
38×*-un-lft-identity
37×times-frac
36×add-cube-cbrt
26×unpow-prod-down
15×add-exp-log
13×cube-prod associate-*r*
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×associate-*l* pow-exp div-inv add-log-exp
3×div-exp 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 distribute-lft-out
Counts
4 → 124
Calls
4 calls:
775.0ms
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
12.0ms
(pow (/ 1.0 (fabs x)) 3)
15.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series289.0ms

Counts
4 → 10
Calls
4 calls:
171.0ms
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
56.0ms
(pow (/ 1.0 (fabs x)) 3)
62.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify4.3s

Counts
134 → 134
Iterations

Useful iterations: 2 (1.6s)

IterNodesCost
02051947
17641810
244301591
done50011591

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize106.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (pow (fabs x) 3)) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))
0.4b
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
59×times-frac
48×*-un-lft-identity
44×add-cube-cbrt associate-*l*
23×unpow-prod-down
22×add-exp-log
17×associate-*r*
14×add-cbrt-cube
10×pow1 cube-prod
7×unswap-sqr
6×prod-exp
5×frac-times div-exp sqr-pow
4×flip3-+ associate-*r/ cbrt-unprod flip-+ add-log-exp
3×cube-mult pow-unpow unpow3 associate-*l/ pow-exp sqrt-prod div-inv
2×cbrt-undiv pow-to-exp pow-prod-down frac-add *-commutative distribute-lft-out
1×distribute-rgt-in rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 151
Calls
4 calls:
179.0ms
(* (/ 1.0 (pow (fabs x) 3)) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))
1.4s
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
11.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series513.0ms

Counts
4 → 10
Calls
4 calls:
258.0ms
(* (/ 1.0 (pow (fabs x) 3)) (+ (/ 1.0 2.0) (/ (* 15.0 (/ 1.0 (pow (fabs x) 4))) 8.0)))
183.0ms
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
72.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify906.0ms

Counts
161 → 161
Iterations

Useful iterations: done (894.0ms)

IterNodesCost
02983381
110723251
done50012977

prune2.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize113.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0.5 (/ 1.875 (pow (fabs x) 4))) (pow (fabs x) 3))
0.4b
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity
67×times-frac
55×add-sqr-sqrt
49×add-cube-cbrt
28×unpow-prod-down
17×add-exp-log
15×cube-prod
14×distribute-lft-out
13×associate-*r*
12×associate-/r*
11×add-cbrt-cube
8×pow1
6×sqr-pow
5×cube-mult unpow3 div-exp
4×associate-*l* associate-/l* add-log-exp
3×pow-unpow flip3-+ pow-exp sqrt-prod flip-+ div-inv
2×cbrt-undiv frac-times pow-to-exp associate-*l/ prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 158
Calls
4 calls:
131.0ms
(/ (+ 0.5 (/ 1.875 (pow (fabs x) 4))) (pow (fabs x) 3))
971.0ms
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
13.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series445.0ms

Counts
4 → 10
Calls
4 calls:
197.0ms
(/ (+ 0.5 (/ 1.875 (pow (fabs x) 4))) (pow (fabs x) 3))
176.0ms
(* (+ (/ 3.0 (/ 4.0 (pow (/ 1.0 (fabs x)) 4))) 1) (/ 1.0 (fabs x)))
71.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify752.0ms

Counts
168 → 168
Iterations

Useful iterations: done (741.0ms)

IterNodesCost
02683319
17503064
done50002842

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

regimes604.0ms

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03454
14454
done4454

end0.0ms

sample21.6s

Algorithm
intervals
Results
19.5s57145×body80valid