Details

Time bar (total: 46.3s)

sample1.1s

Algorithm
intervals
Results
1.0s3101×body80valid

simplify4.5s

Counts
1 → 1
Iterations
IterNodes
47429
31495
2392
195
031

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (+ (/ (/ 15/8 (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 1) (fabs x)) (+ (/ 3/4 (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))))))
0.3b
(* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
0.4b
(/ (/ 15/8 (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
129×pow1
84×add-cbrt-cube
83×add-exp-log
69×pow-prod-up
38×prod-exp cbrt-unprod
33×times-frac pow-plus
32×add-sqr-sqrt
28×*-un-lft-identity
23×associate-*l* add-cube-cbrt
22×cbrt-undiv div-exp
17×pow2 pow-sqr
16×pow-prod-down
13×sqrt-prod
8×frac-add
7×associate-/l*
6×associate-*r*
5×frac-times associate-*r/
4×flip3-+ pow3 flip-+ insert-posit16 div-inv add-log-exp
3×distribute-lft-out unswap-sqr
2×*-commutative
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 associate-*l/ associate-/l/
Counts
4 → 187
Calls
4 calls:
2.7s
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (+ (/ (/ 15/8 (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 1) (fabs x)) (+ (/ 3/4 (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))))))
86.0ms
(* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
47.0ms
(/ (/ 15/8 (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series539.0ms

Counts
4 → 10
Calls
4 calls:
434.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (+ (/ (/ 15/8 (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 1) (fabs x)) (+ (/ 3/4 (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))))))
41.0ms
(* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
64.0ms
(/ (/ 15/8 (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.2s

Counts
197 → 197
Iterations
IterNodes
24850
11073
0303

prune3.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
0.2b
(/ 15/8 (pow (fabs x) 7))
0.3b
(* (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7))) (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))))) (sqrt (/ 1 PI)))
0.3b
(/ 3/4 (pow (fabs x) 5))

rewrite814.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
46×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×frac-add
27×add-exp-log
24×unpow-prod-down
23×associate-*r/
22×add-cbrt-cube
16×associate-*r*
15×associate-/r*
14×flip3-+ flip-+
13×sqrt-prod
12×sqrt-div
11×frac-times associate-*l/
9×pow1 div-exp associate-/l*
8×sqr-pow
6×prod-exp cbrt-unprod
5×cbrt-undiv
4×insert-posit16 div-inv add-log-exp
3×clear-num frac-2neg pow-prod-down
2×pow-to-exp pow-exp
1×associate-*l* *-commutative
Counts
4 → 171
Calls
4 calls:
25.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
5.0ms
(/ 15/8 (pow (fabs x) 7))
768.0ms
(* (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7))) (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))))) (sqrt (/ 1 PI)))
10.0ms
(/ 3/4 (pow (fabs x) 5))

series668.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
80.0ms
(/ 15/8 (pow (fabs x) 7))
477.0ms
(* (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7))) (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))))) (sqrt (/ 1 PI)))
53.0ms
(/ 3/4 (pow (fabs x) 5))

simplify3.1s

Counts
183 → 183
Iterations
IterNodes
25335
11207
0427

prune3.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
0.3b
(* (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (/ (pow (fabs x) 7) 15/8))) (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))))) (sqrt (/ 1 PI)))
0.3b
(/ 3/4 (pow (fabs x) 5))
0.3b
(/ 1 (/ (pow (fabs x) 7) 15/8))

rewrite827.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
112×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×unpow-prod-down
44×add-exp-log
33×associate-/r*
30×frac-add
25×add-cbrt-cube
23×div-exp associate-*r/
16×associate-*r* sqr-pow
14×flip3-+ flip-+
13×sqrt-prod
12×sqrt-div
11×frac-times associate-*l/
10×pow1
9×associate-/l*
8×div-inv
7×cbrt-undiv
6×prod-exp cbrt-unprod
4×pow-to-exp rec-exp 1-exp pow-exp insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*l* associate-/r/ *-commutative pow-flip inv-pow
Counts
4 → 256
Calls
4 calls:
26.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
767.0ms
(* (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (/ (pow (fabs x) 7) 15/8))) (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))))) (sqrt (/ 1 PI)))
10.0ms
(/ 3/4 (pow (fabs x) 5))
15.0ms
(/ 1 (/ (pow (fabs x) 7) 15/8))

series643.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
461.0ms
(* (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (/ (pow (fabs x) 7) 15/8))) (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))))) (sqrt (/ 1 PI)))
60.0ms
(/ 3/4 (pow (fabs x) 5))
73.0ms
(/ 1 (/ (pow (fabs x) 7) 15/8))

simplify5.2s

Counts
268 → 268
Iterations
IterNodes
26413
11631
0572

prune5.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
0.2b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ 3/4 (pow (fabs x) 5))
0.3b
(* (sqrt (/ 1 PI)) (+ (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 3/4 (pow (fabs x) 5))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 1 (fabs x)))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
56×add-sqr-sqrt times-frac
47×add-cube-cbrt
30×frac-add
25×add-exp-log
24×unpow-prod-down
19×add-cbrt-cube
16×associate-*l* sqrt-prod
15×associate-/r*
14×flip3-+ flip-+
13×distribute-lft-out
12×sqrt-div
11×frac-times associate-*r/
9×div-exp associate-*r* associate-/l*
8×sqr-pow
6×pow1 div-inv
5×cbrt-undiv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg
2×pow-to-exp pow-exp
1×distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ *-commutative
Counts
4 → 182
Calls
4 calls:
28.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
12.0ms
(/ 15/8 (pow (fabs x) 7))
10.0ms
(/ 3/4 (pow (fabs x) 5))
978.0ms
(* (sqrt (/ 1 PI)) (+ (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 3/4 (pow (fabs x) 5))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 1 (fabs x)))))

series947.0ms

Counts
4 → 12
Calls
4 calls:
419.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
76.0ms
(/ 15/8 (pow (fabs x) 7))
64.0ms
(/ 3/4 (pow (fabs x) 5))
387.0ms
(* (sqrt (/ 1 PI)) (+ (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 3/4 (pow (fabs x) 5))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 1 (fabs x)))))

simplify2.6s

Counts
194 → 194
Iterations
IterNodes
25502
11200
0402

prune3.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes326.0ms

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
233
133
025

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.9s7389×body80valid