Details

Time bar (total: 34.7s)

sample42.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
7.0ms256×pre80true

simplify476.0ms

Counts
1 → 1
Iterations
IterNodes
done2006
3680
2123
136
015

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.3b

localize45.0ms

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

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
Counts
3 → 459
Calls
3 calls:
329.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
395.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
323.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series541.0ms

Counts
3 → 9
Calls
3 calls:
181.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
235.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
125.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.0s

Counts
468 → 468
Iterations
IterNodes
done2002
11399
0588

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

localize46.0ms

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

rewrite750.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
113×*-un-lft-identity
73×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
20×distribute-lft-out
14×associate-/r/
13×add-cbrt-cube add-exp-log
10×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 → 182
Calls
4 calls:
0.0ms
(expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
319.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
131.0ms
(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
294.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series1.2s

Counts
4 → 12
Calls
4 calls:
320.0ms
(expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
185.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
609.0ms
(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
93.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify568.0ms

Counts
194 → 194
Iterations
IterNodes
done2001
1736
0294

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
0.3b
(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1494×times-frac
1264×sqrt-prod
987×*-un-lft-identity
975×add-sqr-sqrt
617×add-cube-cbrt
238×swap-sqr
161×distribute-lft-out
132×associate-*r* associate-*l*
84×associate-/r/
49×unswap-sqr
44×flip3-+ flip-+
42×div-inv
29×associate-/l*
22×add-cbrt-cube add-exp-log
12×associate-/r*
11×pow1 sqrt-div
7×cbrt-undiv div-exp
5×sqrt-undiv associate-/l/
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 828
Calls
4 calls:
175.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
570.0ms
(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))))
202.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
270.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series639.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
170.0ms
(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))))
106.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
121.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.2s

Counts
840 → 840
Iterations
IterNodes
done2000
0676

prune4.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
0.5b
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
3898×times-frac
2274×*-un-lft-identity
1614×add-sqr-sqrt
1608×add-cube-cbrt
1358×sqrt-prod
604×cbrt-prod
333×distribute-lft-out
298×associate-/l*
86×associate-/r/
64×sqrt-div
47×flip3-+ flip-+
46×add-exp-log
42×div-inv
28×div-exp
25×add-cbrt-cube
18×cbrt-undiv
14×cbrt-div
8×associate-/r*
6×pow1
5×prod-exp
4×expm1-log1p-u frac-times 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-unprod
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*l/ associate-*r/ hypot-def associate-/l/
Counts
4 → 1604
Calls
4 calls:
334.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
360.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
152.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
122.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
499.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
695.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
77.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify3.3s

Counts
1616 → 1616
Iterations
IterNodes
done2000
01788

prune10.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 2.2b

regimes164.0ms

Accuracy

57% (1.0b remaining)

Error of 2.4b against oracle of 1.4b and baseline of 3.7b

bsearch168.0ms

Steps
ItersRangePoint
9
6.099793177335316e+189
4.7434130209651403e+198
1.1138260050088568e+191

simplify6.0ms

Iterations
IterNodes
done41
141
030

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8000×body80valid
320.0ms8000×pre80true