Details

Time bar (total: 53.9s)

sample823.0ms

Algorithm
intervals
Results
701.0ms3661×body80valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5001
31913
2396
190
031

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
1.0b
(sqrt PI)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
158×add-cbrt-cube add-exp-log
130×pow1
86×add-sqr-sqrt
80×times-frac
73×prod-exp cbrt-unprod
61×*-un-lft-identity add-cube-cbrt
48×cbrt-undiv div-exp
38×pow-prod-up
27×swap-sqr associate-*r* associate-*l*
25×pow-prod-down
24×pow-sqr
20×pow-plus
19×frac-times
15×pow2
13×associate-*l/ associate-*r/
9×unswap-sqr
8×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 275
Calls
4 calls:
26.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
17.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
65.0ms
(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
1.0ms
(sqrt PI)

series105.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
45.0ms
(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
0.0ms
(sqrt PI)

simplify2.9s

Counts
285 → 285
Iterations
IterNodes
done5000
22266
1704
0236

prune1.9s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.4b

localize94.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (/ 1.0 (fabs x)) (fma (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ (/ 1.0 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (/ 15.0 8.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 3.0 4.0)))) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 163
Calls
4 calls:
1.0ms
(fma (/ 1.0 (fabs x)) (fma (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ (/ 1.0 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (/ 15.0 8.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 3.0 4.0)))) (/ 1.0 (fabs x)))
34.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)

series380.0ms

Counts
4 → 10
Calls
4 calls:
285.0ms
(fma (/ 1.0 (fabs x)) (fma (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (* (/ (/ 1.0 (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (/ 15.0 8.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 3.0 4.0)))) (/ 1.0 (fabs x)))
47.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
48.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify2.2s

Counts
173 → 173
Iterations
IterNodes
done5001
21576
1504
0178

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
0.3b
(/ 1.875 (pow (fabs x) 7))
0.4b
(/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))
1.0b
(sqrt PI)

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
72×times-frac
58×add-sqr-sqrt *-un-lft-identity
49×add-cube-cbrt
26×add-exp-log
23×add-cbrt-cube
22×associate-*l*
18×frac-add
16×associate-/l*
13×sqrt-prod
12×unpow-prod-down
10×div-exp
8×cbrt-undiv associate-/r*
7×frac-times pow1 associate-*r/
6×flip3-+ associate-*r* flip-+ distribute-lft-out
5×div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp sqr-pow
3×unswap-sqr
2×clear-num frac-2neg
1×distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ pow-exp *-commutative associate-/l/
Counts
4 → 173
Calls
4 calls:
4.0s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
6.0ms
(/ 1.875 (pow (fabs x) 7))
10.0ms
(/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series709.0ms

Counts
4 → 10
Calls
4 calls:
542.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
104.0ms
(/ 1.875 (pow (fabs x) 7))
62.0ms
(/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify1.9s

Counts
183 → 183
Iterations
IterNodes
done5000
11124
0379

prune1.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 0.75 (pow (fabs x) 5))
0.3b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ (sqrt 1.875) (/ (pow (fabs x) 7) (sqrt 1.875))) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
0.4b
(/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))
1.0b
(sqrt PI)

rewrite22.7s

Algorithm
rewrite-expression-head
Rules
72×times-frac
58×add-sqr-sqrt *-un-lft-identity
49×add-cube-cbrt
26×add-exp-log
23×add-cbrt-cube
22×associate-*l*
18×frac-add
16×associate-/l*
13×sqrt-prod
12×unpow-prod-down
10×div-exp
8×cbrt-undiv associate-/r*
7×frac-times pow1 associate-*r/
6×flip3-+ associate-*r* flip-+ distribute-lft-out
5×div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp sqr-pow
3×unswap-sqr
2×clear-num frac-2neg
1×distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ pow-exp *-commutative associate-/l/
Counts
4 → 173
Calls
4 calls:
10.0ms
(/ 0.75 (pow (fabs x) 5))
22.6s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ (sqrt 1.875) (/ (pow (fabs x) 7) (sqrt 1.875))) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
10.0ms
(/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)

series815.0ms

Counts
4 → 10
Calls
4 calls:
74.0ms
(/ 0.75 (pow (fabs x) 5))
680.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (/ (sqrt 1.875) (/ (pow (fabs x) 7) (sqrt 1.875))) (/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))))
60.0ms
(/ (/ 0.5 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify2.6s

Counts
183 → 183
Iterations
IterNodes
done5001
11159
0389

prune1.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes313.0ms

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done30
130
025

end0.0ms

sample4.5s

Algorithm
intervals
Results
4.1s15801×body80valid