Details

Time bar (total: 29.6s)

sample56.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
9.0ms256×pre80true

simplify2.5s

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.8b

localize49.0ms

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))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-cbrt-cube add-exp-log
13×add-log-exp
10×cbrt-undiv associate-/r* div-exp
6×sum-log
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg
1×+-commutative associate-+l+
Counts
4 → 480
Calls
4 calls:
123.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
419.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
686.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
496.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
168.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
218.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
110.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.8s

Counts
492 → 492
Iterations
IterNodes
done5000
24622
11452
0614

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.6b

localize40.0ms

Local error

Found 3 expressions with local error:

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) 3.0))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
954×times-frac
827×*-un-lft-identity
382×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
62×associate-/r/
32×flip3-+ flip-+
31×div-inv
19×add-cbrt-cube add-exp-log
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
Counts
3 → 520
Calls
3 calls:
415.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
535.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) 3.0))
370.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series491.0ms

Counts
3 → 9
Calls
3 calls:
162.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
205.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) 3.0))
124.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.8s

Counts
529 → 529
Iterations
IterNodes
done5001
24159
11384
0589

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ alpha beta) 3.0))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite984.0ms

Algorithm
rewrite-expression-head
Rules
129×times-frac
126×*-un-lft-identity
74×add-sqr-sqrt add-cube-cbrt
28×distribute-lft-out
25×associate-/l*
14×associate-/r/
13×add-cbrt-cube add-exp-log
11×associate-/r*
8×flip3-+ flip-+
7×div-inv
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-/l/
2×expm1-udef
1×expm1-log1p div-sub
Counts
4 → 186
Calls
4 calls:
0.0ms
(expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
487.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
64.0ms
(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ alpha beta) 3.0))
427.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
409.0ms
(expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
184.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
364.0ms
(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ alpha beta) 3.0))
99.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.3s

Counts
198 → 198
Iterations
IterNodes
done5004
22548
1731
0294

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1))))))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1))))
0.1b
(/ (expm1 (log1p (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1)))))) (+ (+ alpha beta) 3.0))
4.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
55×add-sqr-sqrt times-frac
38×add-cube-cbrt
30×add-exp-log
20×add-cbrt-cube
19×distribute-lft-out
18×associate-*l*
15×associate-*r*
10×div-exp
8×associate-/r* prod-exp associate-/r/
7×associate-/l*
6×pow1 cbrt-undiv unswap-sqr
5×flip3-+ flip-+
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×rec-exp clear-num frac-2neg 1-exp expm1-udef associate-/l/
1×frac-times expm1-log1p div-sub pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative
Counts
4 → 158
Calls
4 calls:
0.0ms
(expm1 (log1p (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1))))))
630.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1))))
39.0ms
(/ (expm1 (log1p (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1)))))) (+ (+ alpha beta) 3.0))
402.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series1.5s

Counts
4 → 12
Calls
4 calls:
799.0ms
(expm1 (log1p (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1))))))
182.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1))))
413.0ms
(/ (expm1 (log1p (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (/ 1 (+ (+ alpha beta) (* 2 1)))))) (+ (+ alpha beta) 3.0))
115.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.1s

Counts
170 → 170
Iterations
IterNodes
done5073
22963
1750
0263

prune986.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.6b

regimes140.0ms

Accuracy

53.7% (1.1b remaining)

Error of 2.2b against oracle of 1.2b and baseline of 3.5b

bsearch62.0ms

Steps
ItersRangePoint
4
3.989259968505067e+165
5.908223814084248e+165
5.248579992166405e+165

simplify12.0ms

Iterations
IterNodes
done41
141
030

end0.0ms

sample1.3s

Algorithm
intervals
Results
813.0ms8000×body80valid
306.0ms8000×pre80true