Details

Time bar (total: 1.4m)

sample1.4s

Algorithm
intervals
Results
1.3s3575×body80valid

simplify738.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
737.0ms
(* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
182×add-exp-log
140×times-frac
110×add-cbrt-cube
103×pow1
90×div-exp
64×pow-div
57×add-sqr-sqrt
55×prod-exp
50×cbrt-undiv
48×*-un-lft-identity
45×add-cube-cbrt
31×cbrt-unprod
30×associate-/l*
21×associate-*l*
16×pow2 pow-plus pow-sqr pow-prod-up pow-flip inv-pow
11×div-inv
8×rec-exp 1-exp
5×unswap-sqr
4×associate-*r* insert-posit16 add-log-exp
3×sqrt-prod
2×frac-times clear-num associate-/r* frac-2neg flip3-+ associate-*r/ flip-+ associate-/l/
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative distribute-lft-out
Counts
4 → 245
Calls
4 calls:
Slowest
89.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
35.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
20.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series223.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
116.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
68.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
38.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify37.9s

Counts
278 → 255
Calls
278 calls:
Slowest
1.5s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.3s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.2s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.2s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.1s
(* (/ (* (* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))

prune3.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize93.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(/ 15/8 (* (fabs x) (fabs x)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
30×add-sqr-sqrt
26×*-un-lft-identity add-exp-log
24×add-cube-cbrt
23×add-cbrt-cube
16×associate-/l*
8×cbrt-undiv div-exp
7×associate-*l*
6×prod-exp
5×pow1
4×unpow-prod-down associate-*r* cbrt-unprod insert-posit16 div-inv add-log-exp
3×sqrt-prod unswap-sqr
2×clear-num associate-/r* frac-2neg associate-*r/ sqr-pow
1×distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 pow-exp *-commutative flip-+ distribute-lft-out associate-/l/
Counts
4 → 114
Calls
4 calls:
Slowest
48.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
13.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
9.0ms
(/ 15/8 (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series183.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
125.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
34.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
24.0ms
(/ 15/8 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify8.3s

Counts
97 → 124
Calls
97 calls:
Slowest
537.0ms
(* (pow (fabs x) (/ -5 2)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
517.0ms
(* (pow (sqrt (fabs x)) -5) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
465.0ms
(* (pow (sqrt (fabs x)) -5) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
464.0ms
(* (pow (fabs x) (/ -5 2)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
419.0ms
(* (/ 15/8 (* (fabs x) (fabs x))) (pow (fabs x) -5))

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(/ 15/8 (* (fabs x) (fabs x)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
30×add-sqr-sqrt
26×*-un-lft-identity add-exp-log
24×add-cube-cbrt
23×add-cbrt-cube
16×associate-/l*
8×cbrt-undiv div-exp
7×associate-*l*
6×prod-exp
5×pow1
4×unpow-prod-down associate-*r* cbrt-unprod insert-posit16 div-inv add-log-exp
3×sqrt-prod unswap-sqr
2×clear-num associate-/r* frac-2neg associate-*r/ sqr-pow
1×distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 pow-exp *-commutative flip-+ distribute-lft-out associate-/l/
Counts
4 → 114
Calls
4 calls:
Slowest
62.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
14.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
10.0ms
(sqrt PI)
6.0ms
(/ 15/8 (* (fabs x) (fabs x)))

series195.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
111.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
60.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
24.0ms
(/ 15/8 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify8.6s

Counts
97 → 124
Calls
97 calls:
Slowest
553.0ms
(* (pow (fabs x) (/ -5 2)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
541.0ms
(* (pow (fabs x) (/ -5 2)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
539.0ms
(* (pow (sqrt (fabs x)) -5) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
447.0ms
(* (pow (sqrt (fabs x)) -5) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
434.0ms
(* (pow (fabs x) -5) (/ 15/8 (* (fabs x) (fabs x))))

prune2.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
0.3b
(/ 15/8 (* (fabs x) (fabs x)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
55×*-un-lft-identity
40×add-sqr-sqrt
39×add-cube-cbrt
26×add-exp-log
23×add-cbrt-cube
20×associate-/l*
15×unpow-prod-down
11×div-exp
9×cbrt-undiv associate-/r*
8×distribute-lft-out
5×pow1 div-inv sqr-pow
4×insert-posit16 add-log-exp
3×clear-num frac-2neg prod-exp sqrt-prod cbrt-unprod associate-/l/
1×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+
Counts
4 → 139
Calls
4 calls:
Slowest
55.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
18.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
12.0ms
(/ 15/8 (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series190.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
113.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
51.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
26.0ms
(/ 15/8 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify16.1s

Counts
144 → 149
Calls
144 calls:
Slowest
415.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x))))
364.0ms
(- (log (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (log (pow (fabs x) 5)))
306.0ms
(/ (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (pow (fabs x) (/ 5 2)))
303.0ms
(/ (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (* (cbrt (pow (fabs x) 5)) (cbrt (pow (fabs x) 5))))
291.0ms
(/ (* (* 15/8 15/8) 15/8) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))

prune2.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes351.0ms

bsearch4.0ms

end0.0ms