Details

Time bar (total: 49.9s)

sample77.0ms

Algorithm
intervals
Results
44.0ms256×body80valid
12.0ms256×pre80true

simplify2.6s

Counts
1 → 1
Iterations
IterNodes
done5000
43944
3680
2123
136
015

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
4.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite6.5s

Algorithm
rewrite-expression-head
Rules
58398×*-un-lft-identity
38852×distribute-lft-out
23496×times-frac
7084×associate-*l*
5080×*-commutative
3666×add-sqr-sqrt add-cube-cbrt
888×associate-/l*
248×associate-/r/
162×associate-/l/
128×flip3-+ flip-+
124×div-inv
55×associate-/r*
20×add-cbrt-cube add-exp-log
13×add-log-exp
10×cbrt-undiv div-exp
9×fma-def
6×associate-+l+ clear-num sum-log frac-2neg
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×+-commutative
Counts
4 → 8905
Calls
4 calls:
193.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
1.1s
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
1.9s
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
612.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
172.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
199.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
137.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify5.2s

Counts
8917 → 8917
Iterations
IterNodes
done5001
12139
0870

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
866×*-un-lft-identity
524×distribute-lft-out
440×sqrt-prod
264×times-frac
112×add-sqr-sqrt
106×add-cube-cbrt
104×associate-*l*
48×*-commutative
24×associate-/r*
22×associate-/l*
12×sqrt-div
8×add-cbrt-cube add-exp-log
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
Counts
4 → 398
Calls
4 calls:
544.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
453.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
295.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
286.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series426.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
148.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
58.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
63.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.4s

Counts
410 → 410
Iterations
IterNodes
done5000
33787
2932
1362
0172

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))
0.2b
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
1910×*-un-lft-identity
1157×distribute-lft-out
571×sqrt-prod
518×associate-/l*
475×frac-times
276×add-sqr-sqrt
267×associate-/r*
263×associate-*l*
253×times-frac
224×add-cube-cbrt
105×associate-*r*
98×sqrt-div
94×associate-/l/
87×*-commutative
51×flip3-+ flip-+
48×clear-num
47×frac-2neg
25×associate-*r/
23×add-exp-log
19×associate-*l/
18×add-cbrt-cube
15×unswap-sqr
8×pow1 div-exp
6×prod-exp
5×cbrt-undiv
4×expm1-log1p-u associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 1-exp un-div-inv hypot-def
1×pow-prod-down
Counts
4 → 886
Calls
4 calls:
538.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))
2.4s
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))))
326.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
304.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series556.0ms

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1)))
118.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))))
56.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
80.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.2s

Counts
898 → 898
Iterations
IterNodes
done5000
11796
0516

prune2.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ (+ beta alpha) (+ 1.0 2)))
0.1b
(* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha)))))
0.8b
(/ 1 (* (* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ (+ beta alpha) (+ 1.0 2))))
4.4b
(/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite4.4s

Algorithm
rewrite-expression-head
Rules
996×frac-times
951×*-un-lft-identity
768×flip3-+ flip-+
406×distribute-lft-out
392×frac-add
356×associate-/r/
314×add-sqr-sqrt
310×times-frac
278×associate-/l*
239×add-cube-cbrt
237×associate-/r*
222×associate-*r/
220×associate-*l*
191×associate-*r*
126×associate-*l/
92×associate-/l/
62×clear-num
60×un-div-inv
54×add-exp-log
47×frac-2neg
37×unswap-sqr
34×add-cbrt-cube
22×prod-exp
17×pow1
14×div-exp
12×cbrt-unprod
11×*-commutative
8×cbrt-undiv div-inv
7×pow-prod-down
6×distribute-rgt-in +-commutative distribute-lft-in
4×expm1-log1p-u rec-exp associate-+l+ associate-+r+ 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-flip
1×inv-pow
Counts
4 → 1156
Calls
4 calls:
1.3s
(* (* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ (+ beta alpha) (+ 1.0 2)))
305.0ms
(* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha)))))
2.5s
(/ 1 (* (* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ (+ beta alpha) (+ 1.0 2))))
108.0ms
(/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))

series1.3s

Counts
4 → 12
Calls
4 calls:
330.0ms
(* (* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ (+ beta alpha) (+ 1.0 2)))
224.0ms
(* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha)))))
217.0ms
(/ 1 (* (* (+ (+ beta alpha) 2) (/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ (+ beta alpha) (+ 1.0 2))))
544.0ms
(/ (+ (+ beta alpha) 2) (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify2.2s

Counts
1168 → 1168
Iterations
IterNodes
done5000
01182

prune5.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes142.0ms

Accuracy

71.5% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.7b

bsearch90.0ms

Steps
ItersRangePoint
7
4.794504063855796e+156
7.775450676221288e+157
2.3403637264423054e+157

simplify14.0ms

Iterations
IterNodes
done43
143
030

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.3s8000×body80valid
340.0ms8000×pre80true