Details

Time bar (total: 30.3s)

sample90.0ms

Algorithm
intervals
Results
56.0ms256×body80valid
12.0ms256×pre80true

simplify2.6s

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: 4.5b

localize41.0ms

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)))

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:
116.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
364.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
432.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
301.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series585.0ms

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)))
254.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
138.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.1s

Counts
492 → 492
Iterations
IterNodes
done5000
24622
11452
0614

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
819×times-frac
601×*-un-lft-identity
360×sqrt-prod
355×add-sqr-sqrt
349×add-cube-cbrt
126×distribute-lft-out
69×associate-/r*
53×associate-/r/
29×flip3-+ flip-+
27×div-inv
12×associate-/l*
10×add-cbrt-cube add-exp-log
6×associate-/l/
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rem-sqrt-square clear-num frac-2neg div-exp
2×sqrt-div
1×sqrt-pow1 pow1/2
Counts
4 → 489
Calls
4 calls:
131.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
391.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
277.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
298.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
401.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
112.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.9s

Counts
501 → 501
Iterations
IterNodes
done5000
23465
11257
0707

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
73×*-un-lft-identity
43×add-cube-cbrt sqrt-prod
27×associate-*r*
25×associate-*l*
23×add-exp-log
18×add-cbrt-cube
15×unswap-sqr
12×distribute-lft-out
8×pow1 div-exp
6×prod-exp
5×cbrt-undiv flip3-+ flip-+
4×expm1-log1p-u sqrt-div associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×associate-/r* div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 1-exp hypot-def associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 170
Calls
4 calls:
493.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))))
141.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
168.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
341.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))))
87.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
115.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.1s

Counts
182 → 182
Iterations
IterNodes
done5001
22436
1747
0239

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
0.5b
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (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))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
390×sqrt-prod
342×times-frac
340×add-sqr-sqrt
290×*-un-lft-identity
168×add-cube-cbrt
94×swap-sqr
53×distribute-lft-out
48×associate-*r* associate-*l*
25×unswap-sqr
18×add-cbrt-cube add-exp-log
16×sqrt-div
13×pow1
10×associate-/r/
8×flip3-+ flip-+
7×associate-/l*
6×associate-/r*
5×cbrt-undiv sqrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def associate-/l/
1×pow2 frac-times clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 359
Calls
4 calls:
239.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
686.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))))
131.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
126.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series417.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
144.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))))
62.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.3s

Counts
371 → 371
Iterations
IterNodes
done5004
22907
1987
0304

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.8b

regimes147.0ms

Accuracy

54% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch128.0ms

Steps
ItersRangePoint
9
7.775450676221288e+157
3.9765790759248505e+164
1.1044946435875943e+164

simplify14.0ms

Iterations
IterNodes
done36
136
027

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.3s8000×body80valid
294.0ms8000×pre80true