Details

Time bar (total: 19.8s)

sample60.0ms

Algorithm
intervals
Results
11.0ms37×body1280valid
11.0ms167×body80valid
6.0ms256×pre80true
6.0ms24×body640valid
3.0ms16×body320valid
2.0ms12×body160valid

simplify4.4s

Counts
1 → 1
Iterations
IterNodes
done5000
254885
244583
234303
223954
213572
203229
192829
182315
171985
161722
151474
141236
13995
12795
11669
10582
9467
8348
7290
6209
5124
469
350
233
120
010

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.7b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
104×*-un-lft-identity
50×times-frac
47×add-sqr-sqrt
34×distribute-lft-out
31×fma-def
25×add-cube-cbrt
11×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-cbrt-cube add-exp-log associate-/r/ add-log-exp
3×flip3-+ flip-+
2×expm1-log1p-u pow1 div-sub log1p-expm1-u div-inv associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- flip--
Counts
2 → 100
Calls
2 calls:
61.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
228.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series144.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts
106 → 106
Iterations
IterNodes
done5000
21160
1340
0128

prune554.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 19.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
2.7b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
182×*-un-lft-identity
91×times-frac
85×add-sqr-sqrt
80×add-cube-cbrt
63×prod-diff
60×distribute-lft-out
21×fma-neg
12×associate-/r/
10×associate-/r*
7×add-cbrt-cube add-exp-log
6×flip3-+ flip-+ div-inv associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 179
Calls
3 calls:
49.0ms
(/ beta (+ (+ alpha beta) 2.0))
50.0ms
(/ alpha (+ (+ alpha beta) 2.0))
225.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series266.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(/ beta (+ (+ alpha beta) 2.0))
75.0ms
(/ alpha (+ (+ alpha beta) 2.0))
106.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts
188 → 188
Iterations
IterNodes
done5013
21501
1513
0221

prune951.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.1b
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
2.7b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite466.0ms

Algorithm
rewrite-expression-head
Rules
209×*-un-lft-identity
108×times-frac
103×add-sqr-sqrt
91×add-cube-cbrt
69×distribute-lft-out
63×prod-diff
21×fma-neg associate-*r*
19×add-exp-log
14×associate-/r/
13×add-cbrt-cube
10×associate-/r*
7×pow1 flip3-+ flip-+ div-inv
6×associate-/l* add-log-exp
5×div-exp
4×expm1-log1p-u prod-exp log1p-expm1-u
3×cbrt-undiv associate-*l* unswap-sqr
2×rec-exp clear-num frac-2neg 1-exp cbrt-unprod difference-of-squares
1×sub-neg flip3-- diff-log pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip flip-- distribute-lft-out-- inv-pow
Counts
4 → 229
Calls
4 calls:
47.0ms
(/ 1 (+ (+ alpha beta) 2.0))
34.0ms
(/ alpha (+ (+ alpha beta) 2.0))
98.0ms
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
274.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series261.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1 (+ (+ alpha beta) 2.0))
72.0ms
(/ alpha (+ (+ alpha beta) 2.0))
54.0ms
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
86.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.0s

Counts
241 → 241
Iterations
IterNodes
done5002
21926
1637
0263

prune730.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize76.0ms

Local error

Found 4 expressions with local error:

2.7b
(fma (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (- 1.0))
4.7b
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
4.7b
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
4.7b
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
63×cbrt-prod
45×times-frac
31×add-sqr-sqrt add-cube-cbrt
27×distribute-lft-out
6×associate-/r/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
1×fma-udef
Counts
4 → 106
Calls
4 calls:
0.0ms
(fma (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (- 1.0))
27.0ms
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
18.0ms
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
14.0ms
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
519.0ms
(fma (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (- 1.0))
190.0ms
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
221.0ms
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
204.0ms
(cbrt (/ alpha (+ (+ alpha beta) 2.0)))

simplify2.7s

Counts
118 → 118
Iterations
IterNodes
done5000
34230
21073
1350
0156

prune790.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

regimes260.0ms

Accuracy

76.8% (2.8b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.4b

bsearch60.0ms

Steps
ItersRangePoint
7
22079.79486067198
654137.8667585424
644102.6150741008

simplify9.0ms

Iterations
IterNodes
done37
137
031

end0.0ms

sample1.4s

Algorithm
intervals
Results
403.0ms5877×body80valid
283.0ms838×body1280valid
222.0ms8000×pre80true
178.0ms711×body640valid
56.0ms388×body320valid
19.0ms186×body160valid