Details

Time bar (total: 36.2s)

sample860.0ms

Algorithm
intervals
Results
733.0ms3566×body80valid

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: done (4.7s)

IterNodesCost
031103
1234103
done500061

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (/ 1.0 (fabs x)) 3)
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)
1.2b
(pow (/ 1.0 (fabs x)) (* 2 3))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
43×add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
39×unpow-prod-down
26×cube-prod
13×add-exp-log
10×add-cbrt-cube
8×pow1
7×pow-unpow
6×pow-exp
5×div-inv
4×add-log-exp rem-cube-cbrt
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×cbrt-undiv cube-div cube-mult unpow3
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 131
Calls
4 calls:
12.0ms
(pow (/ 1.0 (fabs x)) 3)
9.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)
7.0ms
(pow (/ 1.0 (fabs x)) (* 2 3))

series171.0ms

Counts
4 → 10
Calls
4 calls:
67.0ms
(pow (/ 1.0 (fabs x)) 3)
38.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)
65.0ms
(pow (/ 1.0 (fabs x)) (* 2 3))

simplify925.0ms

Counts
141 → 141
Iterations

Useful iterations: done (920.0ms)

IterNodesCost
01581696
done50001506

prune982.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow (/ 1.0 (fabs x)) 3)) (fabs x)) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6)))))
0.8b
(pow (/ 1.0 (fabs x)) 3)
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite309.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
46×times-frac
43×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down cube-prod
15×add-exp-log add-cbrt-cube
13×associate-*l*
9×pow1
7×frac-times associate-*r/
6×pow-unpow frac-add
5×div-inv
4×pow-exp add-log-exp rem-cube-cbrt
3×cbrt-undiv div-exp associate-*r* associate-*l/ sqrt-prod
2×cube-div cube-mult pow-to-exp pow-pow flip3-+ unpow3 prod-exp cbrt-unprod flip-+ unswap-sqr sqr-pow
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 149
Calls
4 calls:
271.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow (/ 1.0 (fabs x)) 3)) (fabs x)) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6)))))
7.0ms
(pow (/ 1.0 (fabs x)) 3)
16.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series370.0ms

Counts
4 → 10
Calls
4 calls:
258.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow (/ 1.0 (fabs x)) 3)) (fabs x)) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6)))))
63.0ms
(pow (/ 1.0 (fabs x)) 3)
49.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.4s

Counts
159 → 159
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02073139
done50002963

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize92.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (+ (* 1.0 (/ (+ (* 1.875 (/ 1 (pow (fabs x) 6))) (* 0.75 (/ 1 (pow (fabs x) 4)))) (fabs x))) (+ (/ 1.0 (fabs x)) (/ (* 1.0 (pow (/ 1.0 (fabs x)) 3)) 2.0))) (* 1.0 (exp (* (fabs x) (fabs x))))) (sqrt PI))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
51×times-frac
42×*-un-lft-identity
39×add-cube-cbrt
35×add-exp-log
25×associate-*r*
24×unpow-prod-down
21×add-cbrt-cube
13×cube-prod prod-exp
10×div-exp
9×sqrt-prod
8×pow1
7×unswap-sqr
6×associate-/r* sqr-pow
5×cbrt-undiv associate-*l/ pow-exp cbrt-unprod associate-/l/
4×pow-to-exp associate-*r/ frac-add div-inv add-log-exp
3×rec-exp pow-unpow 1-exp associate-*l*
2×flip3-+ flip-+ rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 pow-prod-down clear-num un-div-inv *-commutative associate-/l*
Counts
4 → 151
Calls
4 calls:
190.0ms
(/ (* (+ (* 1.0 (/ (+ (* 1.875 (/ 1 (pow (fabs x) 6))) (* 0.75 (/ 1 (pow (fabs x) 4)))) (fabs x))) (+ (/ 1.0 (fabs x)) (/ (* 1.0 (pow (/ 1.0 (fabs x)) 3)) 2.0))) (* 1.0 (exp (* (fabs x) (fabs x))))) (sqrt PI))
23.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
10.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series724.0ms

Counts
4 → 10
Calls
4 calls:
609.0ms
(/ (* (+ (* 1.0 (/ (+ (* 1.875 (/ 1 (pow (fabs x) 6))) (* 0.75 (/ 1 (pow (fabs x) 4)))) (fabs x))) (+ (/ 1.0 (fabs x)) (/ (* 1.0 (pow (/ 1.0 (fabs x)) 3)) 2.0))) (* 1.0 (exp (* (fabs x) (fabs x))))) (sqrt PI))
57.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
57.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify857.0ms

Counts
161 → 161
Iterations

Useful iterations: done (849.0ms)

IterNodesCost
03183630
done50003225

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (pow (fabs x) 7))
0.2b
(* (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (/ 0.75 (pow (fabs x) 5)) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (sqrt (/ 1 PI)))
0.3b
(/ 1 (pow (fabs x) 3))
0.3b
(/ 0.75 (pow (fabs x) 5))

rewrite812.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
79×add-sqr-sqrt
72×frac-add
71×*-un-lft-identity
70×add-cube-cbrt
36×unpow-prod-down
33×associate-*r/
32×un-div-inv
29×add-exp-log
26×associate-/r*
19×sqrt-div
18×frac-times associate-*l/
16×associate-*r* sqrt-prod
15×div-exp
12×cube-prod add-cbrt-cube sqr-pow
10×flip3-+ flip-+
9×associate-/l*
7×pow-to-exp pow-exp
6×pow1 rec-exp 1-exp
4×cube-mult unpow3 div-inv add-log-exp unswap-sqr
3×cbrt-undiv frac-2neg associate-*l* clear-num
2×pow-flip inv-pow
1×pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 242
Calls
4 calls:
17.0ms
(/ 1 (pow (fabs x) 7))
733.0ms
(* (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (/ 0.75 (pow (fabs x) 5)) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (sqrt (/ 1 PI)))
19.0ms
(/ 1 (pow (fabs x) 3))
17.0ms
(/ 0.75 (pow (fabs x) 5))

series712.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ 1 (pow (fabs x) 7))
494.0ms
(* (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (/ 0.75 (pow (fabs x) 5)) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (sqrt (/ 1 PI)))
52.0ms
(/ 1 (pow (fabs x) 3))
65.0ms
(/ 0.75 (pow (fabs x) 5))

simplify1.2s

Counts
254 → 254
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04517210
done50015927

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes315.0ms

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03040
13940
done3940

end0.0ms

sample17.3s

Algorithm
intervals
Results
15.7s57200×body80valid