Details

Time bar (total: 3.9m)

sample1.2s

Algorithm
intervals
Results
1.1s2898×body80valid

simplify671.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
671.0ms
(* (* (/ 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))))))

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.4b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.4b
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
115×pow1
111×add-exp-log
72×pow-div
69×add-cbrt-cube
60×div-exp
50×add-sqr-sqrt
49×*-un-lft-identity add-cube-cbrt
43×associate-/l*
34×cbrt-undiv
23×prod-exp
20×pow-flip inv-pow
18×pow2 pow-plus pow-sqr pow-prod-up
13×cbrt-unprod
11×div-inv
6×rec-exp 1-exp
4×insert-posit16 add-log-exp
3×clear-num associate-/r* frac-2neg sqrt-prod associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 227
Calls
4 calls:
Slowest
24.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
12.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
10.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series150.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
64.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
45.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
40.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify15.8s

Counts
270 → 237
Calls
270 calls:
Slowest
657.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
467.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
407.0ms
(/ (/ (/ (sqrt 1) (sqrt (fabs x))) (fabs x)) (fabs x))
394.0ms
(/ (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
378.0ms
(/ (/ (* (* (/ 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))))

prune3.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite477.0ms

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
407.0ms
(* (/ (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))))
56.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
10.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series632.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
464.0ms
(* (/ (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))))
120.0ms
(* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
48.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify23.7s

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)))))
941.0ms
(* (* (* (/ (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)))))
863.0ms
(* (exp (* (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 (fabs x))))
644.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (/ 1 (fabs x)))
630.0ms
(* (sqrt PI) (* (+ (* (/ (/ 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)))))) (* (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (pow (fabs x) -5) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))))) (fabs x)))

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
40×add-sqr-sqrt
39×*-un-lft-identity add-cube-cbrt
28×add-exp-log
24×unpow-prod-down
23×pow1
22×add-cbrt-cube
15×associate-/r*
9×div-exp associate-/l*
8×sqr-pow
6×pow-plus prod-exp pow-prod-up cbrt-unprod
5×cbrt-undiv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* pow-prod-down div-inv
2×pow2 pow-to-exp pow-exp pow-sqr
1×associate-*l* pow3 *-commutative unswap-sqr
Counts
4 → 145
Calls
4 calls:
Slowest
19.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
15.0ms
(* (* (fabs x) (fabs x)) (fabs x))
8.0ms
(/ 15/8 (pow (fabs x) 7))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series237.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(/ 15/8 (pow (fabs x) 7))
60.0ms
(/ 3/4 (pow (fabs x) 5))
59.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
37.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify12.3s

Counts
162 → 157
Calls
162 calls:
Slowest
472.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
396.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
395.0ms
(/ (* (* 3/4 3/4) 3/4) (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5)))
324.0ms
(/ (* (* 15/8 15/8) 15/8) (* (* (pow (fabs x) 7) (pow (fabs x) 7)) (pow (fabs x) 7)))
263.0ms
(/ (* (cbrt 3/4) (cbrt 3/4)) (* (cbrt (pow (fabs x) 5)) (cbrt (pow (fabs x) 5))))

prune2.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
594×times-frac
307×add-sqr-sqrt
306×*-un-lft-identity add-cube-cbrt
288×sqrt-prod
138×unpow-prod-down
54×associate-/r*
46×sqr-pow
33×add-exp-log
25×add-cbrt-cube
23×pow1
13×div-exp
12×associate-/l*
10×div-inv
7×cbrt-undiv
6×pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* pow-prod-down
2×pow2 pow-to-exp pow-exp pow-sqr
1×associate-*l* pow3 associate-/r/ *-commutative unswap-sqr
Counts
4 → 445
Calls
4 calls:
Slowest
27.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
16.0ms
(* (* (fabs x) (fabs x)) (fabs x))
14.0ms
(/ (sqrt 15/8) (/ (pow (fabs x) 7) (sqrt 15/8)))
10.0ms
(/ 3/4 (pow (fabs x) 5))

series304.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(/ (sqrt 15/8) (/ (pow (fabs x) 7) (sqrt 15/8)))
48.0ms
(/ 3/4 (pow (fabs x) 5))
36.0ms
(* (* (fabs x) (fabs x)) (fabs x))
33.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify2.7m

Counts
717 → 457
Calls
717 calls:
Slowest
1.1s
(/ (sqrt (* (cbrt 15/8) (cbrt 15/8))) (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) (sqrt 1)))
1.0s
(/ (sqrt (sqrt 15/8)) (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) (sqrt 1)))
991.0ms
(/ (sqrt (sqrt 15/8)) (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) (sqrt 1)))
948.0ms
(/ (sqrt (* (cbrt 15/8) (cbrt 15/8))) (/ (pow (fabs x) (/ 7 2)) (sqrt 1)))
934.0ms
(/ (sqrt (sqrt 15/8)) (/ (pow (fabs x) (/ 7 2)) (sqrt 1)))

prune9.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes251.0ms

bsearch6.0ms

end0.0ms