Details

Time bar (total: 1.8m)

sample1.2s

Algorithm
intervals
Results
1.1s3245×body80valid

simplify717.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
716.0ms
(* (* (/ 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: 0.7b

localize57.0ms

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 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))

rewrite198.0ms

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
126.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
39.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
22.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series254.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
148.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
57.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
49.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify37.0s

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 1) 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))) (* (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))))))
1.3s
(* (/ (/ (* (* (/ 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)) (* (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))))))

prune3.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite493.0ms

Algorithm
rewrite-expression-head
Rules
51×times-frac
50×add-sqr-sqrt
41×*-un-lft-identity
36×add-cube-cbrt
29×associate-*l*
25×add-exp-log
23×add-cbrt-cube
13×sqrt-prod associate-/l*
12×frac-add associate-*r/
9×associate-*r*
7×pow1 cbrt-undiv flip3-+ div-exp prod-exp flip-+
6×frac-times unswap-sqr
5×cbrt-unprod div-inv
4×unpow-prod-down insert-posit16 add-log-exp
3×distribute-lft-out
2×distribute-rgt-in distribute-lft-in *-commutative sqr-pow
1×pow-to-exp rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ pow-exp associate-/l/
Counts
4 → 151
Calls
4 calls:
Slowest
401.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x))))
65.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
22.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series723.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
535.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x))))
141.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
47.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify23.8s

Counts
142 → 161
Calls
142 calls:
Slowest
1.5s
(* (/ (* (* (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))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x)))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 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))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x)))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x)))))
887.0ms
(* (pow (fabs x) (/ -5 2)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
647.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (/ 1 (fabs x)))
633.0ms
(* (exp (* (fabs x) (fabs x))) (+ (* (- (* (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))) (* (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))) (fabs x)) (* (- (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) 1)))

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize91.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
56×add-sqr-sqrt times-frac
47×add-cube-cbrt
25×add-exp-log
24×unpow-prod-down
19×add-cbrt-cube
18×frac-add
16×associate-*l* sqrt-prod
15×associate-/r*
11×distribute-lft-out
9×div-exp associate-/l*
8×sqrt-div associate-*r* sqr-pow
7×frac-times associate-*r/
6×pow1 flip3-+ flip-+ 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 → 173
Calls
4 calls:
Slowest
2.0s
(* (sqrt (/ 1 PI)) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
38.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
10.0ms
(/ 15/8 (pow (fabs x) 7))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series621.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
458.0ms
(* (sqrt (/ 1 PI)) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
69.0ms
(/ 15/8 (pow (fabs x) 7))
60.0ms
(/ 3/4 (pow (fabs x) 5))
34.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify29.2s

Counts
195 → 185
Calls
195 calls:
Slowest
1.4s
(* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (+ (/ 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))))))
722.0ms
(* (pow (fabs x) 7) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (pow (fabs x) 5)) (fabs x)))
690.0ms
(* (sqrt PI) (* (pow (fabs x) 7) (* (- (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (fabs x))))
574.0ms
(* (sqrt 1) (+ (* 15/8 (+ (* (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5)))) (- (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))) (* (pow (fabs x) 7) (+ (pow (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) 3) (pow (/ 1 (fabs x)) 3)))))
532.0ms
(* (sqrt PI) (+ (* (/ 15/8 (pow (fabs x) 7)) (/ 15/8 (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 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))))

prune3.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (sqrt (fabs x)) 5)
1.0b
(pow (sqrt (fabs x)) 5)
1.0b
(cbrt 3/4)
1.0b
(cbrt 3/4)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt unpow-prod-down *-un-lft-identity add-cube-cbrt
8×pow1
6×cbrt-prod pow-unpow pow-pow add-exp-log sqrt-prod
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-to-exp sqrt-pow1 pow1/2 pow1/3 pow-exp sqrt-pow2 sqr-pow
Counts
4 → 72
Calls
4 calls:
Slowest
3.0ms
(pow (sqrt (fabs x)) 5)
3.0ms
(pow (sqrt (fabs x)) 5)
1.0ms
(cbrt 3/4)
1.0ms
(cbrt 3/4)

series132.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
73.0ms
(pow (sqrt (fabs x)) 5)
59.0ms
(pow (sqrt (fabs x)) 5)
0.0ms
(cbrt 3/4)
0.0ms
(cbrt 3/4)

simplify1.9s

Counts
42 → 80
Calls
42 calls:
Slowest
267.0ms
(pow (sqrt (* (cbrt (fabs x)) (cbrt (fabs x)))) 5)
257.0ms
(pow (sqrt (* (cbrt (fabs x)) (cbrt (fabs x)))) 5)
220.0ms
(/ (* (cbrt 3/4) (cbrt 3/4)) (pow (sqrt (fabs x)) 5))
216.0ms
(pow (* (cbrt (sqrt (fabs x))) (cbrt (sqrt (fabs x)))) 5)
199.0ms
(pow (* (cbrt (sqrt (fabs x))) (cbrt (sqrt (fabs x)))) 5)

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes238.0ms

bsearch10.0ms

end0.0ms