Details

Time bar (total: 3.2m)

sample59.0ms

Algorithm
intervals
Results
14.0ms181×body80valid
9.0ms256×pre80true
9.0ms32×body640valid
7.0ms22×body1280valid
3.0ms13×body320valid
1.0ms8×body160valid

simplify170.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
170.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize38.0ms

Local error

Found 3 expressions with local error:

2.2b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.0b
(+ (+ alpha beta) 2.0)

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
50×times-frac
49×add-sqr-sqrt
38×distribute-lft-out
35×fma-def
27×add-cube-cbrt
11×distribute-lft-out-- difference-of-squares
10×add-log-exp
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×sum-log flip3-+ associate-/r/ flip-+
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×+-commutative div-sub div-inv associate-/l/
1×cbrt-undiv associate-+l+ clear-num frac-2neg flip3-- div-exp associate-+l- flip--
Counts
3 → 124
Calls
3 calls:
Slowest
123.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
36.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
19.0ms
(+ (+ alpha beta) 2.0)

series187.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
92.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
72.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
23.0ms
(+ (+ alpha beta) 2.0)

simplify9.2s

Counts
127 → 133
Calls
127 calls:
Slowest
704.0ms
(* (* (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)) (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))
489.0ms
(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
295.0ms
(* (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
246.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
229.0ms
(+ (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0))) (- (* 1.0 1.0) (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.8b

localize39.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))

rewrite829.0ms

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
513.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
232.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
36.0ms
(/ alpha (+ (+ alpha beta) 2.0))
22.0ms
(/ beta (+ (+ alpha beta) 2.0))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
91.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
74.0ms
(/ beta (+ (+ alpha beta) 2.0))
64.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify1.7m

Counts
660 → 429
Calls
660 calls:
Slowest
684.0ms
(fma (/ (sqrt beta) (sqrt (+ (+ alpha beta) 2.0))) (/ (sqrt beta) (sqrt (+ (+ alpha beta) 2.0))) (- (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
661.0ms
(fma (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))) (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0))) (- (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 1)))
652.0ms
(* (* (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
597.0ms
(fma (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))) (- (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))
563.0ms
(fma (/ 1 (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ alpha (cbrt (+ (+ alpha beta) 2.0))) (- (* 1.0 1)))

prune4.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize40.0ms

Local error

Found 4 expressions with local error:

9.1b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b
(- (/ 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
(/ alpha (+ (+ alpha beta) 2.0))

rewrite857.0ms

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
349.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
240.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
214.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
46.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series455.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
95.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
94.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
70.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify25.6s

Counts
306 → 203
Calls
306 calls:
Slowest
712.0ms
(* (* (exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))) (exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
628.0ms
(log (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
604.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
552.0ms
(* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
527.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize50.0ms

Local error

Found 4 expressions with local error:

9.1b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.1b
(pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
167×*-un-lft-identity
90×add-sqr-sqrt
78×times-frac
75×add-cube-cbrt
63×prod-diff
48×distribute-lft-out
21×fma-neg
14×log-prod
10×associate-/r/
8×log-div add-exp-log
7×pow1 unpow-prod-up distribute-lft-out--
6×add-cbrt-cube add-log-exp difference-of-squares
5×associate-/r* flip3-+ flip3-- flip-+ div-inv flip--
4×expm1-log1p-u pow-unpow frac-sub insert-posit16 log1p-expm1-u pow-sub
3×unpow-prod-down associate-/l*
2×pow-exp log-pow
1×pow-to-exp cbrt-undiv e-exp-1 clear-num sub-neg pow-pow frac-2neg diff-log div-exp rem-log-exp sqr-pow
Counts
4 → 198
Calls
4 calls:
Slowest
291.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
265.0ms
(pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
200.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
36.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series601.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
181.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
123.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
87.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify37.4s

Counts
318 → 210
Calls
318 calls:
Slowest
670.0ms
(pow E (* (cbrt (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (cbrt (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
603.0ms
(* (* (pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))) (pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
556.0ms
(exp (pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
551.0ms
(* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
538.0ms
(pow E (log (sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

regimes304.0ms

Accuracy

99.1% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 16.2b

bsearch7.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s5792×body80valid
404.0ms8000×pre80true
402.0ms874×body1280valid
288.0ms730×body640valid
101.0ms402×body320valid
35.0ms202×body160valid