Details

Time bar (total: 1.3m)

sample75.0ms

Algorithm
intervals
Results
43.0ms256×body80valid
11.0ms256×pre80true

simplify638.0ms

Counts
1 → 1
Iterations
IterNodes
done2001
42001
3641
2119
136
015

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
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))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+l+
Counts
4 → 467
Calls
4 calls:
37.0ms
(+ (+ alpha beta) (* beta alpha))
286.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
436.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
271.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (+ alpha beta) (* beta alpha))
172.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
173.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
123.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts
479 → 479
Iterations
IterNodes
done2009
22009
11457
0608

prune5.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* beta alpha) (+ alpha beta))
0.0b
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
4.8b
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+r+
Counts
4 → 467
Calls
4 calls:
27.0ms
(+ (* beta alpha) (+ alpha beta))
347.0ms
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
467.0ms
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
272.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (* beta alpha) (+ alpha beta))
205.0ms
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
253.0ms
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
135.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.5s

Counts
479 → 479
Iterations
IterNodes
done2004
22004
11462
0607

prune5.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))))
0.5b
(/ 1 (sqrt (+ (+ alpha beta) (* 2 1))))
2.6b
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
3.4b
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

rewrite796.0ms

Algorithm
rewrite-expression-head
Rules
8286×times-frac
4237×*-un-lft-identity
3275×add-sqr-sqrt add-cube-cbrt
1839×sqrt-prod
481×distribute-lft-out
381×associate-/r/
354×sqrt-div
204×div-inv
179×flip3-+ flip-+
137×associate-/r*
54×add-exp-log
36×div-exp
34×add-cbrt-cube associate-/l*
20×cbrt-undiv
6×pow1
5×associate-/l/
4×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
3×pow-flip
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 2670
Calls
4 calls:
174.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))))
34.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2 1))))
217.0ms
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
240.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

series627.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))))
87.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2 1))))
243.0ms
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))))
113.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

simplify3.6s

Counts
2682 → 2682
Iterations
IterNodes
done2712
02712

prune45.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.5b
(* (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))))
4.8b
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.8b
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
160×*-un-lft-identity
141×times-frac
110×add-sqr-sqrt
98×sqrt-prod
82×add-cube-cbrt
36×distribute-lft-out
29×swap-sqr
24×associate-/r/
21×associate-*r* associate-*l*
19×pow1 add-cbrt-cube add-exp-log
17×associate-/l*
14×flip3-+ flip-+
12×div-inv
10×associate-/r*
9×unswap-sqr
8×sqrt-pow1 pow1/2
7×cbrt-undiv div-exp
5×pow-prod-up associate-/l/
4×sqrt-div insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down pow-sqr
2×prod-exp cbrt-unprod
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod associate-*l/ associate-*r/ *-commutative
Counts
4 → 250
Calls
4 calls:
324.0ms
(/ (/ (* (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
502.0ms
(* (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))))
200.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))
223.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ (/ (* (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
141.0ms
(* (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))))
112.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))
146.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.2s

Counts
262 → 262
Iterations
IterNodes
done2003
22003
1801
0323

prune3.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.6b

regimes135.0ms

Accuracy

53.8% (1.2b remaining)

Error of 2.5b against oracle of 1.3b and baseline of 3.9b

bsearch171.0ms

Steps
ItersRangePoint
8
1.3095755543340861e+200
9.078109045320583e+202
8.004231800207308e+201

simplify22.0ms

Iterations
IterNodes
done61
161
041

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.8s8000×body80valid
314.0ms8000×pre80true