Details

Time bar (total: 29.9s)

sample1.7s

Algorithm
intervals
Results
1.6s3412×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done2009
42009
31575
2409
195
031

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize100.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
144×times-frac
124×add-exp-log
113×*-un-lft-identity
89×add-cube-cbrt
50×pow1
48×div-exp prod-exp
45×swap-sqr
40×add-cbrt-cube
39×associate-*r* associate-*l*
27×unswap-sqr
24×rec-exp 1-exp pow-flip inv-pow
18×div-inv
15×pow-prod-up
12×cbrt-undiv cbrt-unprod
9×pow-prod-down pow-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow2 frac-times pow-plus associate-*l/ associate-*r/ un-div-inv *-commutative sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 310
Calls
4 calls:
22.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
30.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
25.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series86.0ms

Counts
4 → 10
Calls
4 calls:
36.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
22.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
28.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify1.4s

Counts
320 → 320
Iterations
IterNodes
done2011
32011
21252
1490
0168

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
0.4b
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
1124×add-exp-log
608×div-exp
426×prod-exp
232×add-cbrt-cube
180×times-frac
140×rec-exp 1-exp
128×add-sqr-sqrt
111×*-un-lft-identity
103×add-cube-cbrt
100×cbrt-undiv
99×associate-*l*
86×pow1
82×cbrt-unprod
37×pow-prod-up
32×pow-flip inv-pow pow-div
15×swap-sqr associate-*r*
14×div-inv
11×frac-times associate-*r/
9×pow-prod-down unswap-sqr
7×associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr *-commutative sqrt-prod
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 un-div-inv
Counts
4 → 510
Calls
4 calls:
61.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
88.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
15.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series152.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
45.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
46.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify1.9s

Counts
520 → 520
Iterations
IterNodes
done2000
22000
11274
0431

prune2.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.2b

localize109.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (pow (fabs x) -5) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) 15/8) (+ (fma (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 1/2 (* 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (/ 1 (fabs x))))
0.4b
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
0.6b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
584×add-exp-log
312×div-exp
221×prod-exp
124×add-cbrt-cube
114×times-frac
93×add-sqr-sqrt
76×*-un-lft-identity
74×rec-exp 1-exp
68×add-cube-cbrt
56×associate-*l*
53×pow1
52×cbrt-undiv
43×cbrt-unprod
21×pow-prod-up
20×pow-flip inv-pow
16×pow-div
15×swap-sqr
14×associate-*r*
10×div-inv
9×unswap-sqr
6×frac-times pow-prod-down associate-*r/
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr sqrt-prod
2×*-commutative
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 un-div-inv fma-udef
Counts
4 → 323
Calls
4 calls:
0.0ms
(fma (pow (fabs x) -5) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) 15/8) (+ (fma (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 1/2 (* 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (/ 1 (fabs x))))
82.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
29.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series336.0ms

Counts
4 → 10
Calls
4 calls:
252.0ms
(fma (pow (fabs x) -5) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) 15/8) (+ (fma (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 1/2 (* 3/4 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (/ 1 (fabs x))))
63.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ 1 (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
21.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify1.8s

Counts
333 → 333
Iterations
IterNodes
done2001
22001
11342
0456

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (fabs x) (fabs x)) (fabs x))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))))
1.0b
(sqrt PI)

rewrite759.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
32×add-sqr-sqrt
30×frac-add
26×pow1
23×times-frac add-cbrt-cube associate-*l*
22×add-exp-log add-cube-cbrt
14×flip3-+ flip-+
13×sqrt-prod distribute-lft-out
12×associate-*r*
11×frac-times associate-*r/
8×prod-exp cbrt-unprod
6×pow-plus pow-prod-up
4×expm1-log1p-u cbrt-undiv div-exp pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
3×associate-/l*
2×pow2 pow-sqr *-commutative
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow3 associate-*l/
Counts
4 → 148
Calls
4 calls:
22.0ms
(* (* (fabs x) (fabs x)) (fabs x))
26.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
707.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))))
2.0ms
(sqrt PI)

series554.0ms

Counts
4 → 10
Calls
4 calls:
40.0ms
(* (* (fabs x) (fabs x)) (fabs x))
52.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
461.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))))
0.0ms
(sqrt PI)

simplify1.3s

Counts
158 → 158
Iterations
IterNodes
done2000
22000
11170
0296

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes299.0ms

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done33
133
025

end0.0ms

sample10.1s

Algorithm
intervals
Results
9.7s23668×body80valid