Details

Time bar (total: 28.6s)

sample57.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
7.0ms256×pre80true

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5000
43214
3509
2114
133
014

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
6×add-log-exp
4×expm1-log1p-u pow1 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg flip3-+ flip-+
2×associate-/r/
1×+-commutative associate-+r+ sum-log fma-udef
Counts
4 → 422
Calls
4 calls:
4.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
22.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
44.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
25.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series682.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
262.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
243.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
155.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify3.4s

Counts
434 → 434
Iterations
IterNodes
done5001
22978
11172
0516

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
111×*-un-lft-identity
71×add-sqr-sqrt add-cube-cbrt
23×associate-/l*
20×distribute-lft-out
13×add-cbrt-cube add-exp-log
10×associate-/r*
7×div-inv
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-/l/
2×flip3-+ associate-/r/ flip-+
1×log1p-udef log1p-expm1
Counts
4 → 165
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
20.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
17.0ms
(/ (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
29.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series1.0s

Counts
4 → 12
Calls
4 calls:
307.0ms
(log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
245.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
324.0ms
(/ (log1p (expm1 (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
149.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.7s

Counts
177 → 177
Iterations
IterNodes
done5004
21742
1585
0256

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.7b

localize93.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
2.4b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
2.4b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
2.4b
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
17×*-un-lft-identity
12×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt
9×flip3-+ add-exp-log flip-+
8×associate-/l/
7×add-cbrt-cube
6×associate-/r* times-frac sqrt-prod
4×expm1-log1p-u frac-times pow1 log1p-expm1-u add-log-exp
3×pow1/3 distribute-lft-out
2×cbrt-undiv div-exp associate-*l/ associate-*r/
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 85
Calls
4 calls:
20.0ms
(/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
3.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series701.0ms

Counts
4 → 12
Calls
4 calls:
423.0ms
(/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
113.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
90.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
74.0ms
(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify2.7s

Counts
97 → 97
Iterations
IterNodes
done5000
34553
21348
1505
0193

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
0.7b
(* (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
1.1b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
1.8b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
2068×times-frac
1414×*-un-lft-identity
892×add-sqr-sqrt
884×add-cube-cbrt
718×sqrt-prod
265×distribute-lft-out
120×associate-/l*
39×div-inv
22×add-cbrt-cube add-exp-log
16×associate-/r*
10×cbrt-undiv div-exp
8×pow1
7×associate-*l*
6×associate-*r*
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp unswap-sqr associate-/l/
3×clear-num frac-2neg flip3-+ pow-prod-down flip-+
2×sqrt-pow1 pow1/2 associate-*l/ associate-/r/
1×sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 949
Calls
4 calls:
82.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
37.0ms
(* (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
23.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
21.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
380.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
122.0ms
(* (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
297.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
168.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

simplify2.5s

Counts
961 → 961
Iterations
IterNodes
done5000
12057
0900

prune4.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.7b

regimes164.0ms

Accuracy

54.9% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.5b

bsearch99.0ms

Steps
ItersRangePoint
6
1.886212634237049e+212
1.1632245709592838e+213
1.1495110216775583e+213

simplify9.0ms

Iterations
IterNodes
done48
148
037

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s8000×body80valid
184.0ms8000×pre80true