Details

Time bar (total: 8.7s)

sample38.0ms

Algorithm
intervals
Results
7.0ms187×body80valid
5.0ms25×body1280valid
5.0ms256×pre80true
4.0ms24×body640valid
2.0ms14×body320valid
0.0ms6×body160valid

simplify21.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite293.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
26×add-sqr-sqrt
25×times-frac
19×distribute-lft-out
14×add-cube-cbrt
6×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ associate-/l/
1×cbrt-undiv +-commutative associate-+l- flip3-- frac-2neg div-exp clear-num sum-log flip-- div-inv
Counts
2 → 65
Calls
2 calls:
68.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
222.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series147.0ms

Counts
2 → 6
Calls
2 calls:
72.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
75.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify73.0ms

Counts
71 → 71

prune181.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.1b
(/ beta (+ (+ alpha beta) 2.0))
1.5b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
61×add-sqr-sqrt
56×times-frac
36×add-cube-cbrt
24×distribute-lft-out
13×associate-/r* associate-/l* distribute-lft-out--
10×add-exp-log add-cbrt-cube difference-of-squares
6×add-log-exp
4×pow1 associate-/r/ associate-/l/
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
2×flip3-+ frac-sub flip-+
1×sub-neg diff-log div-sub
Counts
4 → 137
Calls
4 calls:
1.5s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
59.0ms
(/ alpha (+ (+ alpha beta) 2.0))
37.0ms
(/ beta (+ (+ alpha beta) 2.0))
324.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series391.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
83.0ms
(/ alpha (+ (+ alpha beta) 2.0))
70.0ms
(/ beta (+ (+ alpha beta) 2.0))
134.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify69.0ms

Counts
149 → 149

prune533.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b
(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b
(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.5b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite509.0ms

Algorithm
rewrite-expression-head
Rules
146×*-un-lft-identity
119×add-sqr-sqrt times-frac
81×sqrt-prod
68×add-cube-cbrt
42×distribute-lft-out
32×add-exp-log
30×associate-*r* associate-*l*
20×add-cbrt-cube
16×associate-/r*
15×unswap-sqr
11×div-exp
8×pow1 sqrt-div prod-exp associate-/r/
6×cbrt-undiv associate-/l* add-log-exp
4×flip3-+ cbrt-unprod flip-+ div-inv
3×rec-exp pow-flip 1-exp
2×frac-2neg clear-num difference-of-squares
1×frac-times sub-neg flip3-- sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- distribute-lft-out-- inv-pow
Counts
4 → 218
Calls
4 calls:
191.0ms
(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
52.0ms
(/ beta (sqrt (+ (+ alpha beta) 2.0)))
48.0ms
(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
205.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series373.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
97.0ms
(/ beta (sqrt (+ (+ alpha beta) 2.0)))
72.0ms
(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
119.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify95.0ms

Counts
230 → 230

prune824.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 1 (/ beta (+ (+ alpha beta) 2.0))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.1b
(/ beta (+ (+ alpha beta) 2.0))
1.5b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite730.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
31×times-frac
29×add-sqr-sqrt
24×add-cube-cbrt distribute-lft-out
11×add-log-exp
10×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 diff-log associate-/r/ distribute-lft-out--
3×sub-neg flip3-- flip--
2×cbrt-undiv frac-2neg flip3-+ associate-*r/ div-exp clear-num frac-sub flip-+ div-inv associate--r+ difference-of-squares
1×associate--r-
Counts
4 → 109
Calls
4 calls:
294.0ms
(- (* 1 (/ beta (+ (+ alpha beta) 2.0))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
69.0ms
(/ alpha (+ (+ alpha beta) 2.0))
65.0ms
(/ beta (+ (+ alpha beta) 2.0))
295.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series352.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (* 1 (/ beta (+ (+ alpha beta) 2.0))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
68.0ms
(/ alpha (+ (+ alpha beta) 2.0))
57.0ms
(/ beta (+ (+ alpha beta) 2.0))
123.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify40.0ms

Counts
121 → 121

prune385.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.2b

regimes134.0ms

Accuracy

77.4% (2.9b remaining)

Error of 5.8b against oracle of 3.0b and baseline of 15.7b

bsearch101.0ms

Steps
ItersRangePoint
10
0.0012078084232635357
319975762157.7142
1773850741.5207238

simplify104.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
294.0ms5847×body80valid
290.0ms849×body1280valid
171.0ms8000×pre80true
158.0ms710×body640valid
80.0ms402×body320valid
16.0ms192×body160valid