Details

Time bar (total: 25.6s)

sample882.0ms

Algorithm
intervals
Results
798.0ms3611×body80valid

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5000
31575
2409
195
031

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize95.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b
(sqrt PI)

rewrite150.0ms

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:
42.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
49.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
47.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms
(sqrt PI)

series71.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
22.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
23.0ms
(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify4.2s

Counts
320 → 320
Iterations
IterNodes
done5000
34141
21252
1490
0168

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
48×add-exp-log
34×add-sqr-sqrt
33×pow1 *-un-lft-identity add-cube-cbrt
28×add-cbrt-cube
26×associate-/l*
24×div-exp
16×pow-div
12×cbrt-undiv
8×prod-exp pow-flip inv-pow
6×div-inv
4×pow2 expm1-log1p-u rec-exp pow-plus 1-exp pow-sqr pow-prod-up cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num associate-/r* frac-2neg associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 149
Calls
4 calls:
28.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
20.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))
2.0ms
(sqrt PI)

series416.0ms

Counts
4 → 10
Calls
4 calls:
57.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
63.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
295.0ms
(fma (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma 15/8 (/ 1 (* (fabs x) (fabs x))) 3/4) (fma 1/2 (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ 1 (fabs x))))
0.0ms
(sqrt PI)

simplify1.6s

Counts
159 → 159
Iterations
IterNodes
done5001
21006
1359
0170

prune918.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite778.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
41×times-frac
40×*-un-lft-identity
35×add-cube-cbrt
22×associate-*l*
13×add-exp-log sqrt-prod
12×unpow-prod-down
11×add-cbrt-cube
7×pow1 associate-/r*
5×associate-*r*
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×distribute-lft-out associate-/l* unswap-sqr
2×frac-times cbrt-undiv flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ div-inv
1×distribute-rgt-in pow-to-exp rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ pow-exp *-commutative fma-udef
Counts
4 → 128
Calls
4 calls:
9.0ms
(/ 15/8 (pow (fabs x) 7))
764.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7)))))
0.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms
(sqrt PI)

series650.0ms

Counts
4 → 10
Calls
4 calls:
79.0ms
(/ 15/8 (pow (fabs x) 7))
504.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 7)))))
66.0ms
(fma (/ 1/2 (* (fabs x) (fabs x))) (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms
(sqrt PI)

simplify2.8s

Counts
138 → 138
Iterations
IterNodes
done5008
23024
1649
0231

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
1.0b
(sqrt (* (cbrt PI) (cbrt PI)))
1.0b
(* (cbrt PI) (cbrt PI))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×pow1
22×*-un-lft-identity add-cube-cbrt
19×cbrt-prod pow1/3
18×sqrt-pow1
12×times-frac
11×pow-flip
10×add-exp-log
6×add-cbrt-cube swap-sqr associate-*r* associate-*l* pow-prod-down pow-sqr pow-prod-up
5×sqrt-prod
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow2 pow-plus associate-/l*
2×pow1/2 div-exp
1×cbrt-undiv rem-sqrt-square rec-exp clear-num frac-2neg 1-exp prod-exp *-commutative cbrt-unprod div-inv inv-pow
Counts
4 → 127
Calls
4 calls:
1.0ms
(cbrt PI)
22.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
15.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
22.0ms
(* (cbrt PI) (cbrt PI))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
0.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
0.0ms
(* (cbrt PI) (cbrt PI))

simplify2.7s

Counts
131 → 131
Iterations
IterNodes
done5020
43262
31134
2486
1258
0138

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes276.0ms

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done28
128
023

end0.0ms

sample2.2s

Algorithm
intervals
Results
2.1s7407×body80valid