Details

Time bar (total: 18.5s)

sample321.0ms

Algorithm
intervals
Results
256.0ms3124×body80valid

simplify64.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
09061
138958
2211536
3500136
done500136

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt times-frac
63×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down cube-prod
22×add-exp-log add-cbrt-cube
14×pow1
13×swap-sqr associate-*r* associate-*l*
8×div-inv
6×cbrt-undiv pow-unpow div-exp
4×pow-exp prod-exp cbrt-unprod add-log-exp rem-cube-cbrt unswap-sqr
3×sqrt-prod
2×cube-div cube-mult pow-to-exp pow-pow unpow3 sqr-pow
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up
Counts
4 → 172
Calls
4 calls:
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
8.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series96.0ms

Counts
4 → 10
Calls
4 calls:
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify123.0ms

Counts
182 → 182
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
05841144
13655959
25003912
done5003912

prune668.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
98×times-frac
76×add-cube-cbrt *-un-lft-identity
31×add-exp-log add-cbrt-cube
26×swap-sqr associate-*r* associate-*l*
20×pow1
13×unpow-prod-down cube-prod
10×div-inv
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod unswap-sqr
4×add-log-exp
3×pow-unpow sqrt-prod
2×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ pow-exp pow-sqr *-commutative pow-prod-up rem-cube-cbrt
1×cube-div cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 sqr-pow
Counts
4 → 193
Calls
4 calls:
22.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series87.0ms

Counts
4 → 10
Calls
4 calls:
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify107.0ms

Counts
203 → 203
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
05351295
133211109
25001969
done5001969

prune885.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (+ (+ (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite5.6s

Algorithm
rewrite-expression-head
Rules
216×frac-add
181×associate-*l/
154×frac-times
116×times-frac
87×add-sqr-sqrt
83×associate-/l/
74×add-cube-cbrt *-un-lft-identity
64×associate-*r/
31×add-cbrt-cube
29×add-exp-log
22×associate-/r*
21×sqrt-prod
13×pow1 unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
11×cbrt-undiv div-exp
10×flip3-+ flip-+
9×div-inv
6×prod-exp cbrt-unprod
4×add-log-exp unswap-sqr
3×pow-unpow
2×pow-exp rem-cube-cbrt
1×cube-div pow2 cube-mult pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow-plus pow1/2 unpow3 pow-prod-down clear-num associate-/r/ pow-sqr *-commutative pow-prod-up associate-/l* sqr-pow
Counts
4 → 273
Calls
4 calls:
5.6s
(/ (* (+ (+ (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
21.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series711.0ms

Counts
4 → 10
Calls
4 calls:
652.0ms
(/ (* (+ (+ (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ (* (* 1.0 1.0) 1.0) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
25.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify93.0ms

Counts
283 → 283
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
022476406
150015835
done50015835

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (sqrt 1.0) 2) (pow (fabs x) 5))
0.3b
(* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7)))
0.3b
(* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))
0.5b
(* (sqrt (/ 1 PI)) (* (exp (pow (fabs x) 2)) (+ (+ (+ (* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3))))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
270×times-frac
256×unpow-prod-down
222×add-sqr-sqrt
163×associate-*r*
150×add-cube-cbrt *-un-lft-identity
85×sqrt-prod
72×sqr-pow
66×add-exp-log
64×associate-*r/
36×frac-add
32×unswap-sqr
28×unpow2
27×div-exp
23×prod-exp
22×associate-*l*
21×add-cbrt-cube
18×pow-to-exp pow-exp
13×pow1 sqrt-div
12×frac-times
11×associate-/l*
10×flip3-+ un-div-inv flip-+
7×associate-/r* cbrt-unprod
5×pow-prod-down
4×distribute-rgt-in distribute-lft-in div-inv add-log-exp
3×cbrt-undiv *-commutative
1×frac-2neg associate-*l/ clear-num
Counts
4 → 419
Calls
4 calls:
15.0ms
(/ (pow (sqrt 1.0) 2) (pow (fabs x) 5))
42.0ms
(* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7)))
43.0ms
(* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))
1.0s
(* (sqrt (/ 1 PI)) (* (exp (pow (fabs x) 2)) (+ (+ (+ (* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3))))))

series984.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (pow (sqrt 1.0) 2) (pow (fabs x) 5))
147.0ms
(* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7)))
140.0ms
(* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))
591.0ms
(* (sqrt (/ 1 PI)) (* (exp (pow (fabs x) 2)) (+ (+ (+ (* 1.875 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 7))) (/ 1.0 (fabs x))) (* 0.75 (/ (pow (sqrt 1.0) 2) (pow (fabs x) 5)))) (* 0.5 (/ 1 (pow (fabs x) 3))))))

simplify94.0ms

Counts
431 → 431
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
017946534
150015830
done50015830

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes368.0ms

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04529
14529
done4529

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.7s33658×body80valid