Details

Time bar (total: 15.7s)

sample29.0ms

Algorithm
intervals
Results
6.0ms189×body80valid
4.0ms26×body1280valid
4.0ms256×pre80true
2.0ms20×body640valid
1.0ms15×body320valid
0.0ms6×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
12013
23413
35313
47413
516413
631813
766513
8153113
9469113
done500113

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite270.0ms

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:
40.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
221.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series193.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
109.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify840.0ms

Counts
106 → 106
Iterations

Useful iterations: done (836.0ms)

IterNodesCost
01281178
13401111
214311056
done50021055

prune521.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
2.6b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite324.0ms

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:
57.0ms
(/ alpha (+ (+ alpha beta) 2.0))
50.0ms
(/ beta (+ (+ alpha beta) 2.0))
205.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series242.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(/ alpha (+ (+ alpha beta) 2.0))
79.0ms
(/ beta (+ (+ alpha beta) 2.0))
103.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts
188 → 188
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02213563
15142878
218822543
done50012387

prune707.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize42.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.7b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.7b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.7b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite408.0ms

Algorithm
rewrite-expression-head
Rules
195×*-un-lft-identity
106×times-frac
93×add-sqr-sqrt
88×add-cube-cbrt
63×cbrt-prod prod-diff distribute-lft-out
21×fma-neg
14×associate-/r/
7×flip3-+ flip-+ div-inv
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×cbrt-div pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 197
Calls
4 calls:
345.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
25.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
14.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
15.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series693.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
209.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
182.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
205.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.1s

Counts
209 → 209
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02414333
15223622
215913227
done50013050

prune825.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize57.0ms

Local error

Found 4 expressions with local error:

7.7b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.7b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.7b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.1b
(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
84×cbrt-prod
60×times-frac
42×add-sqr-sqrt add-cube-cbrt
36×distribute-lft-out
25×log-pow
24×exp-prod
8×associate-/r/
5×pow1
4×expm1-log1p-u flip3-+ add-cbrt-cube add-exp-log flip-+ log1p-expm1-u div-inv add-log-exp
3×cbrt-div log-prod pow1/3
1×rem-log-exp
Counts
4 → 134
Calls
4 calls:
31.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
27.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
16.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
76.0ms
(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

series818.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
200.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
184.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
189.0ms
(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

simplify1.7s

Counts
146 → 146
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01672304
12992102
28001957
340261931
done50001927

prune944.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

regimes145.0ms

Accuracy

77% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.5b

bsearch116.0ms

Steps
ItersRangePoint
8
1.6797771833777472e+17
1.0218839581142054e+21
1.4037838382120008e+19

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03382
13782
done3782

end0.0ms

sample1.8s

Algorithm
intervals
Results
761.0ms5791×body80valid
290.0ms880×body1280valid
193.0ms8000×pre80true
172.0ms705×body640valid
56.0ms418×body320valid
18.0ms206×body160valid