Details

Time bar (total: 25.9s)

sample52.0ms

Algorithm
intervals
Results
13.0ms183×body80valid
9.0ms24×body1280valid
8.0ms256×pre80true
6.0ms26×body640valid
3.0ms17×body320valid
1.0ms6×body160valid

simplify628.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize32.0ms

Local error

Found 2 expressions with local error:

1.6b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite174.0ms

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 insert-posit16 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 → 102
Calls
2 calls:
Slowest
133.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
37.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series152.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
88.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
65.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify1.5s

Counts
108 → 108

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.2b

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))

rewrite769.0ms

Algorithm
rewrite-expression-head
Rules
512×*-un-lft-identity
328×add-sqr-sqrt
263×times-frac
252×prod-diff
213×add-cube-cbrt
150×distribute-lft-out
65×associate--r+
46×difference-of-squares
42×fma-neg
32×associate-/r/
25×distribute-lft-out--
16×flip3-+ flip-+ div-inv
11×add-log-exp
10×associate-/r*
8×add-cbrt-cube add-exp-log
6×associate-/l*
4×expm1-log1p-u pow1 diff-log insert-posit16 log1p-expm1-u
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg div-exp frac-sub
1×associate--r-
Counts
4 → 417
Calls
4 calls:
Slowest
511.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
169.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
46.0ms
(/ beta (+ (+ alpha beta) 2.0))
30.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series331.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
105.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
61.0ms
(/ beta (+ (+ alpha beta) 2.0))
56.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify1.4s

Counts
429 → 429

prune5.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize105.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0))
0.1b
(/ (- (* (fma (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))) (* 1.0 (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) beta) (* (- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0)) (+ 2.0 (+ beta alpha)))) (* (fma (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))) (* 1.0 (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) (+ 2.0 (+ beta alpha))))
0.1b
(* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))))
0.0b
(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
210×*-un-lft-identity
119×times-frac
81×distribute-lft-out
78×add-sqr-sqrt
63×add-cube-cbrt
62×add-cbrt-cube add-exp-log
42×associate-*l*
39×swap-sqr
25×pow1
23×prod-exp cbrt-unprod
22×associate-*r*
19×cbrt-undiv div-exp
12×associate-/r/
8×associate-*r/
6×frac-times flip3-+ pow-prod-up flip-+ div-inv add-log-exp unswap-sqr
4×expm1-log1p-u pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u
3×associate-/l*
2×pow2 pow-plus flip3-- cube-unmult pow-sqr *-commutative flip-- associate-/l/
1×difference-cubes clear-num associate-/r* sub-neg frac-2neg fma-neg diff-log div-sub prod-diff pow3
Counts
4 → 228
Calls
4 calls:
Slowest
160.0ms
(- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0))
149.0ms
(* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))))
122.0ms
(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
43.0ms
(/ (- (* (fma (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))) (* 1.0 (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) beta) (* (- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0)) (+ 2.0 (+ beta alpha)))) (* (fma (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))) (* 1.0 (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) (+ 2.0 (+ beta alpha))))

series955.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
609.0ms
(/ (- (* (fma (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))) (* 1.0 (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) beta) (* (- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0)) (+ 2.0 (+ beta alpha)))) (* (fma (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))) (* 1.0 (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) (+ 2.0 (+ beta alpha))))
140.0ms
(- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0))
106.0ms
(* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))))
100.0ms
(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))

simplify2.2s

Counts
240 → 240

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize36.0ms

Local error

Found 4 expressions with local error:

12.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.6b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite831.0ms

Algorithm
rewrite-expression-head
Rules
166×*-un-lft-identity
89×add-sqr-sqrt
78×times-frac
74×add-cube-cbrt
63×prod-diff
48×distribute-lft-out
21×fma-neg
14×log-prod
10×associate-/r/
8×log-div
7×exp-sum add-exp-log distribute-lft-out--
6×pow1 add-cbrt-cube add-log-exp difference-of-squares
5×associate-/r* flip3-+ flip3-- flip-+ div-inv flip--
4×expm1-log1p-u exp-prod exp-diff frac-sub insert-posit16 log1p-expm1-u
3×associate-/l*
2×log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp rem-log-exp rem-exp-log
Counts
4 → 191
Calls
4 calls:
Slowest
412.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
223.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
168.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
24.0ms
(/ beta (+ (+ alpha beta) 2.0))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
133.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
74.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify848.0ms

Counts
203 → 203

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes220.0ms

Accuracy

72.3% (3.5b remaining)

Error of 6.4b against oracle of 2.9b and baseline of 15.6b

bsearch104.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
725.0ms5872×body80valid
672.0ms718×body640valid
476.0ms811×body1280valid
286.0ms8000×pre80true
105.0ms404×body320valid
36.0ms195×body160valid