Details

Time bar (total: 25.1s)

sample86.0ms

Algorithm
intervals
Results
43.0ms256×body80valid
21.0ms256×pre80true

simplify2.9s

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.3b

localize39.0ms

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))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

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:
105.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
291.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
520.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
305.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series557.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
189.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
214.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
129.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.6s

Counts
492 → 492
Iterations
IterNodes
done5000
24622
11452
0614

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b
(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1)))
1.8b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1))))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite999.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
54×times-frac
34×add-sqr-sqrt
32×add-cube-cbrt
22×associate-/l*
20×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
14×associate-/r/
13×add-log-exp
12×distribute-lft-out
8×frac-times
7×cbrt-undiv div-exp
6×pow1 sum-log
4×expm1-log1p-u associate-/r* associate-*l* associate-*l/ associate-*r/ insert-posit16 log1p-expm1-u div-inv
3×fma-def associate-*r* prod-exp cbrt-unprod associate-/l/
2×clear-num frac-2neg
1×distribute-rgt-in +-commutative associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 158
Calls
4 calls:
89.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
336.0ms
(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1)))
366.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1))))
205.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
31.0ms
(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1)))
195.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1))))
114.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.2s

Counts
170 → 170
Iterations
IterNodes
done5000
23770
1799
0259

prune851.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (* (* 2 1) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
0.0b
(* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
1.8b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (* (* 2 1) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
144×times-frac
116×*-un-lft-identity
76×add-sqr-sqrt
74×add-cube-cbrt
55×flip3-+ flip-+
42×associate-*r/
32×frac-add
30×associate-/r/
22×associate-/l*
21×distribute-lft-out
20×frac-times distribute-rgt-out
13×add-cbrt-cube add-exp-log
10×associate-*l/
7×associate-/r* div-inv
6×pow1 add-log-exp
4×expm1-log1p-u cbrt-undiv div-exp associate-*r* associate-*l* insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in associate-/l/
2×associate-+l+ associate-+r+ clear-num frac-2neg
1×+-commutative sum-log fma-def pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 237
Calls
4 calls:
157.0ms
(+ (* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (* (* 2 1) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
292.0ms
(* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
391.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (* (* 2 1) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
322.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (* (* 2 1) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
34.0ms
(* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
239.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (* (+ alpha beta) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (* (* 2 1) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
105.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.8s

Counts
249 → 249
Iterations
IterNodes
done5003
11403
0437

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 2 (+ alpha beta)) 1.0)
0.0b
(/ (+ alpha (- beta 2)) (+ 2 (+ alpha beta)))
0.1b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma (+ alpha beta) (+ alpha beta) -4)) (+ (+ 2 (+ alpha beta)) 1.0))
16.5b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma (+ alpha beta) (+ alpha beta) -4))

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
376×*-un-lft-identity
217×times-frac
166×distribute-lft-out
99×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
14×associate-/r*
13×add-cbrt-cube add-exp-log add-log-exp
10×div-inv
6×sum-log distribute-lft-out--
5×cbrt-undiv fma-def flip3-+ div-exp flip-+ associate-/l/
4×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
1×+-commutative associate-+l+ associate-+r- div-sub
Counts
4 → 254
Calls
4 calls:
127.0ms
(+ (+ 2 (+ alpha beta)) 1.0)
71.0ms
(/ (+ alpha (- beta 2)) (+ 2 (+ alpha beta)))
84.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma (+ alpha beta) (+ alpha beta) -4)) (+ (+ 2 (+ alpha beta)) 1.0))
21.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma (+ alpha beta) (+ alpha beta) -4))

series464.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ 2 (+ alpha beta)) 1.0)
40.0ms
(/ (+ alpha (- beta 2)) (+ 2 (+ alpha beta)))
207.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma (+ alpha beta) (+ alpha beta) -4)) (+ (+ 2 (+ alpha beta)) 1.0))
193.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma (+ alpha beta) (+ alpha beta) -4))

simplify1.7s

Counts
266 → 266
Iterations
IterNodes
done5004
22295
1741
0305

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

regimes95.0ms

Accuracy

51.5% (1.5b remaining)

Error of 2.8b against oracle of 1.3b and baseline of 4.3b

bsearch158.0ms

Steps
ItersRangePoint
10
1.972616410681917e+143
1.347314599677347e+159
1.3353325288374214e+154

simplify8.0ms

Iterations
IterNodes
done37
137
025

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.7s8000×body80valid
323.0ms8000×pre80true