Details

Time bar (total: 1.3m)

sample1.2s

Algorithm
intervals
Results
1.1s3379×body80valid

simplify719.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
719.0ms
(* (* (/ 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))))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

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
46.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
21.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
21.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series147.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
60.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
48.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
39.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify15.8s

Counts
270 → 237
Calls
270 calls:
Slowest
627.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
516.0ms
(- (- (log (/ 1 (fabs x))) (+ (log (fabs x)) (log (fabs x)))) (+ (log (fabs x)) (log (fabs x))))
482.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
400.0ms
(/ (/ (* (* (/ 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))))
364.0ms
(/ (/ (* (* 1 1) 1) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))

prune3.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
61×times-frac
52×add-sqr-sqrt
41×*-un-lft-identity add-exp-log
36×add-cube-cbrt
26×add-cbrt-cube
25×associate-*l*
16×associate-/l*
14×div-exp
13×prod-exp
11×unpow-prod-down
9×cbrt-undiv
7×pow1 unswap-sqr
5×cbrt-unprod div-inv sqr-pow
4×associate-*r* insert-posit16 add-log-exp
3×pow-to-exp rec-exp 1-exp pow-exp sqrt-prod
2×frac-times clear-num associate-/r* frac-2neg flip3-+ associate-*r/ flip-+
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative distribute-lft-out associate-/l/
Counts
4 → 148
Calls
4 calls:
Slowest
78.0ms
(* (/ 1 (pow (fabs x) 5)) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
19.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
6.0ms
(/ 15/8 (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series232.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
150.0ms
(* (/ 1 (pow (fabs x) 5)) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
46.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
35.0ms
(/ 15/8 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify16.8s

Counts
136 → 158
Calls
136 calls:
Slowest
561.0ms
(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 5))
532.0ms
(* (/ (sqrt 1) (pow (sqrt (fabs x)) 5)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
491.0ms
(* (/ (sqrt 1) (pow (sqrt (fabs x)) 5)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
483.0ms
(* (/ 1 (pow (sqrt (fabs x)) 5)) (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
453.0ms
(* (* (* (/ 1 (pow (fabs x) 5)) (/ 1 (pow (fabs x) 5))) (/ 1 (pow (fabs x) 5))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))

prune2.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

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
58.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
19.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
12.0ms
(/ 15/8 (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series205.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
131.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
46.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
28.0ms
(/ 15/8 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify16.0s

Counts
144 → 149
Calls
144 calls:
Slowest
327.0ms
(* (/ (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))))
314.0ms
(/ (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 5))
304.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (cbrt (fabs x)) 5))
304.0ms
(/ (* (cbrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (cbrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 5))
304.0ms
(/ (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (pow (sqrt (fabs x)) 5))

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
59×times-frac
54×*-un-lft-identity
40×add-sqr-sqrt
38×add-cube-cbrt
21×add-exp-log
18×add-cbrt-cube
17×associate-/l*
15×unpow-prod-down
9×div-exp
8×associate-/r* distribute-lft-out
7×cbrt-undiv
6×pow1 sqrt-prod
5×sqr-pow
4×insert-posit16 div-inv add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod
1×pow-to-exp flip3-+ pow-exp flip-+
Counts
4 → 131
Calls
4 calls:
Slowest
46.0ms
(/ (+ 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)
1.0ms
(sqrt PI)

series175.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
132.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
42.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify15.7s

Counts
131 → 139
Calls
131 calls:
Slowest
659.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (cbrt (pow (fabs x) 5)))
391.0ms
(- (log (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (log (pow (fabs x) 5)))
304.0ms
(/ (* (cbrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (cbrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (pow (sqrt (fabs x)) 5))
295.0ms
(/ (sqrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 5))
291.0ms
(/ (cbrt (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (pow (sqrt (fabs x)) 5))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes165.0ms

bsearch6.0ms

end0.0ms