Details

Time bar (total: 2.5m)

sample1.6s

Algorithm
intervals
Results
1.5s3358×body80valid

simplify775.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
775.0ms
(* (* (/ 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))))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize90.0ms

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))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.4b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.4b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
131×add-exp-log
110×times-frac
81×add-cbrt-cube
60×div-exp
55×add-sqr-sqrt
46×*-un-lft-identity
43×add-cube-cbrt
42×prod-exp
34×cbrt-undiv
26×associate-/l*
24×cbrt-unprod
21×pow1 associate-*l*
div-inv
pow-div
rec-exp 1-exp
unswap-sqr
associate-*r* insert-posit16 pow-flip inv-pow add-log-exp
sqrt-prod
pow2 frac-times clear-num associate-/r* frac-2neg flip3-+ pow-plus associate-*r/ pow-sqr pow-prod-up flip-+ associate-/l/
distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative distribute-lft-out
Counts
4 → 197
Calls
4 calls:
Slowest
92.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
19.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
19.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series215.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
124.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
56.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
35.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify32.8s

Counts
200 → 207
Calls
200 calls:
Slowest
1.4s
(* (/ (/ (* (* (/ 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))))))
1.4s
(* (/ (/ (* (* (/ 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))))))
1.4s
(* (/ (/ (* (* (/ 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))))))

prune3.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
0.4b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(* (/ (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))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
79×times-frac
75×*-un-lft-identity
60×add-sqr-sqrt
51×add-cube-cbrt
25×add-exp-log
23×add-cbrt-cube
22×associate-*l*
17×associate-/l*
15×unpow-prod-down
14×distribute-lft-out
13×sqrt-prod
10×div-exp
cbrt-undiv associate-/r* frac-add
pow1 associate-*r* div-inv
frac-times flip3-+ associate-*r/ flip-+ sqr-pow
prod-exp cbrt-unprod insert-posit16 add-log-exp
unswap-sqr associate-/l/
clear-num frac-2neg
distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ pow-exp *-commutative
Counts
4 → 176
Calls
4 calls:
Slowest
1.1s
(* (/ (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))))
59.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
20.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series626.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
451.0ms
(* (/ (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))))
119.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
56.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify33.5s

Counts
188 → 186
Calls
188 calls:
Slowest
1.4s
(* (/ (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))) (* (* (sqrt PI) (sqrt PI)) (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))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))))
1.0s
(* (* (* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (/ (exp (* (fabs x) (fabs x))) (sqrt PI))) (/ (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))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))))
711.0ms
(* (exp (* (fabs x) (fabs x))) (+ (* (+ (pow (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) 3) (pow (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5)) 3)) (fabs x)) (* (+ (* (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))) (- (* (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5)) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (* (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))))) 1)))
515.0ms
(* (sqrt (/ (exp (* (fabs x) (fabs x))) (sqrt PI))) (sqrt (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))))
514.0ms
(* (cbrt (/ (exp (* (fabs x) (fabs x))) (sqrt PI))) (cbrt (/ (exp (* (fabs x) (fabs x))) (sqrt PI))))

prune3.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
45×times-frac
39×add-sqr-sqrt add-cube-cbrt
27×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube
18×frac-add
15×associate-/r*
11×distribute-lft-out
pow1 div-exp associate-*l/ associate-/l*
sqrt-div associate-*r* sqr-pow
frac-times associate-*r/
flip3-+ prod-exp cbrt-unprod flip-+
cbrt-undiv div-inv
insert-posit16 add-log-exp
clear-num frac-2neg pow-prod-down
pow-to-exp pow-exp
distribute-rgt-in distribute-lft-in associate-*l* *-commutative
Counts
4 → 157
Calls
4 calls:
Slowest
1.7s
(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
28.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
10.0ms
(/ 3/4 (pow (fabs x) 5))
10.0ms
(/ 15/8 (pow (fabs x) 7))

series723.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
526.0ms
(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
82.0ms
(/ 3/4 (pow (fabs x) 5))
75.0ms
(/ 15/8 (pow (fabs x) 7))
39.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify29.9s

Counts
176 → 169
Calls
176 calls:
Slowest
2.0s
(* (* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))) (* (* (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
1.8s
(* (* (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))) (* (* (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
827.0ms
(* (pow (fabs x) 7) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (pow (fabs x) 5)) (fabs x)))
777.0ms
(/ (* (* 3/4 3/4) 3/4) (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5)))
622.0ms
(* (sqrt PI) (* (pow (fabs x) 7) (* (- (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (fabs x))))

prune3.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
45×times-frac
39×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
36×frac-add
31×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube associate-*r/
15×associate-/r*
14×associate-*l/
13×sqrt-div
12×frac-times div-exp
10×flip3-+ un-div-inv flip-+
pow1 associate-/l*
sqr-pow
prod-exp cbrt-unprod
cbrt-undiv
pow-to-exp pow-exp insert-posit16 add-log-exp
rec-exp clear-num frac-2neg 1-exp associate-*r* pow-prod-down div-inv
distribute-rgt-in distribute-lft-in associate-*l* *-commutative pow-flip inv-pow
Counts
4 → 170
Calls
4 calls:
Slowest
1.6s
(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
29.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
7.0ms
(/ 3/4 (pow (fabs x) 5))
6.0ms
(/ 1 (pow (fabs x) 7))

series619.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
445.0ms
(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
74.0ms
(/ 1 (pow (fabs x) 7))
63.0ms
(/ 3/4 (pow (fabs x) 5))
37.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify33.9s

Counts
190 → 182
Calls
190 calls:
Slowest
1.7s
(* (* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))) (* (* (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))) (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
1.6s
(* (* (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))) (* (* (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))) (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
1.1s
(* (pow (fabs x) 7) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (pow (fabs x) 5)) (fabs x)))
727.0ms
(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7))
713.0ms
(* (sqrt PI) (+ (* (* 15/8 (/ 1 (pow (fabs x) 7))) (* 15/8 (/ 1 (pow (fabs x) 7)))) (- (* (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (* (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))))

prune3.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes238.0ms

bsearch5.0ms

end0.0ms