Details

Time bar (total: 30.0s)

sample1.4s

Algorithm
intervals
Results
1.3s3599×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5001
2518
195
031

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x))))
1.0b
(sqrt PI)

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
1478×add-exp-log
865×prod-exp
576×div-exp
288×rec-exp 1-exp
258×pow1
158×add-cbrt-cube
150×pow-prod-up
128×pow-flip inv-pow
110×add-sqr-sqrt
96×times-frac
77×*-un-lft-identity
73×cbrt-unprod
68×pow-sqr
61×add-cube-cbrt
53×pow-prod-down
48×cbrt-undiv
31×swap-sqr
28×frac-times
27×associate-*r* associate-*l*
20×pow-plus
19×unswap-sqr
16×associate-*l/ associate-*r/
15×pow2
12×un-div-inv div-inv
4×insert-posit16 add-log-exp
3×*-commutative sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 656
Calls
4 calls:
22.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
24.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
68.0ms
(* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x))))
2.0ms
(sqrt PI)

series109.0ms

Counts
4 → 10
Calls
4 calls:
20.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
27.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
62.0ms
(* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x))))
0.0ms
(sqrt PI)

simplify2.0s

Counts
666 → 666
Iterations
IterNodes
done5001
12710
0562

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* (pow (fabs x) -4) (* (/ (* (/ 1 (fabs x)) (/ 1 (fabs x))) (fabs x)) 15/8)) (+ (/ 1 (fabs x)) (* (/ (* (/ 1 (fabs x)) (/ 1 (fabs x))) (fabs x)) (+ 1/2 (* (/ 1 (fabs x)) (* (/ 1 (fabs x)) 3/4)))))))
0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite708.0ms

Algorithm
rewrite-expression-head
Rules
132×add-sqr-sqrt
116×times-frac
91×*-un-lft-identity
88×add-exp-log
75×add-cube-cbrt
48×associate-*l*
37×pow1
34×prod-exp
33×add-cbrt-cube div-exp
30×swap-sqr
29×associate-*r* associate-*r/
24×frac-add
21×unswap-sqr
19×associate-*l/
16×rec-exp 1-exp pow-flip inv-pow
15×frac-times
13×sqrt-prod div-inv
10×pow-prod-up cbrt-unprod
9×cbrt-undiv
8×flip3-+ flip-+
7×pow-prod-down
6×pow-sqr
4×insert-posit16 add-log-exp
3×*-commutative
2×pow2 pow-plus un-div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 269
Calls
4 calls:
652.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* (pow (fabs x) -4) (* (/ (* (/ 1 (fabs x)) (/ 1 (fabs x))) (fabs x)) 15/8)) (+ (/ 1 (fabs x)) (* (/ (* (/ 1 (fabs x)) (/ 1 (fabs x))) (fabs x)) (+ 1/2 (* (/ 1 (fabs x)) (* (/ 1 (fabs x)) 3/4)))))))
16.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
28.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series548.0ms

Counts
4 → 10
Calls
4 calls:
501.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (* (pow (fabs x) -4) (* (/ (* (/ 1 (fabs x)) (/ 1 (fabs x))) (fabs x)) 15/8)) (+ (/ 1 (fabs x)) (* (/ (* (/ 1 (fabs x)) (/ 1 (fabs x))) (fabs x)) (+ 1/2 (* (/ 1 (fabs x)) (* (/ 1 (fabs x)) 3/4)))))))
26.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
21.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify2.4s

Counts
279 → 279
Iterations
IterNodes
done5000
11452
0354

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
0.3b
(* (fabs x) (* (fabs x) (fabs x)))
0.3b
(/ 3/4 (pow (fabs x) 5))
0.5b
(* (sqrt (/ 1 PI)) (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 1 (fabs x)) (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 3/4 (pow (fabs x) 5)))) (/ 15/8 (pow (fabs x) 7)))))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
33×times-frac
32×add-sqr-sqrt
31×*-un-lft-identity add-cube-cbrt
27×add-exp-log
25×add-cbrt-cube
23×pow1
21×associate-*r/
19×associate-*l*
18×frac-add
13×sqrt-prod
12×unpow-prod-down
9×prod-exp cbrt-unprod
8×associate-/r* sqrt-div
7×frac-times
6×flip3-+ div-exp pow-prod-down flip-+ associate-/l*
5×pow-prod-up
4×distribute-rgt-in cbrt-undiv distribute-lft-in insert-posit16 add-log-exp sqr-pow
3×div-inv
2×clear-num frac-2neg associate-*r* *-commutative
1×pow2 pow-to-exp pow-plus cube-unmult associate-*l/ pow-exp pow-sqr unswap-sqr
Counts
4 → 146
Calls
4 calls:
14.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
19.0ms
(* (fabs x) (* (fabs x) (fabs x)))
10.0ms
(/ 3/4 (pow (fabs x) 5))
1.9s
(* (sqrt (/ 1 PI)) (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 1 (fabs x)) (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 3/4 (pow (fabs x) 5)))) (/ 15/8 (pow (fabs x) 7)))))

series690.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
27.0ms
(* (fabs x) (* (fabs x) (fabs x)))
81.0ms
(/ 3/4 (pow (fabs x) 5))
522.0ms
(* (sqrt (/ 1 PI)) (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 1 (fabs x)) (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 3/4 (pow (fabs x) 5)))) (/ 15/8 (pow (fabs x) 7)))))

simplify2.1s

Counts
158 → 158
Iterations
IterNodes
done5000
11023
0344

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
0.3b
(* (fabs x) (* (fabs x) (fabs x)))
0.3b
(/ 3/4 (pow (fabs x) 5))
0.4b
(* (+ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (sqrt (/ 1 PI)))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
42×add-sqr-sqrt
35×times-frac
32×add-cube-cbrt
25×add-exp-log
22×add-cbrt-cube
20×pow1
18×frac-add
17×associate-*r*
16×sqrt-prod
12×unpow-prod-down
10×associate-*l*
9×distribute-lft-out
8×associate-/r* sqrt-div
7×frac-times associate-*l/ prod-exp cbrt-unprod
6×flip3-+ div-exp flip-+ associate-/l*
5×pow-prod-up unswap-sqr
4×cbrt-undiv pow-prod-down insert-posit16 div-inv add-log-exp sqr-pow
2×clear-num frac-2neg *-commutative
1×pow2 pow-to-exp pow-plus cube-unmult pow-exp associate-*r/ pow-sqr
Counts
4 → 149
Calls
4 calls:
24.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
29.0ms
(* (fabs x) (* (fabs x) (fabs x)))
10.0ms
(/ 3/4 (pow (fabs x) 5))
2.1s
(* (+ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (sqrt (/ 1 PI)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
38.0ms
(* (fabs x) (* (fabs x) (fabs x)))
64.0ms
(/ 3/4 (pow (fabs x) 5))
422.0ms
(* (+ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (sqrt (/ 1 PI)))

simplify3.5s

Counts
161 → 161
Iterations
IterNodes
done5000
24565
1801
0324

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes304.0ms

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done33
133
025

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.7s8934×body80valid