Details

Time bar (total: 2.8m)

sample67.0ms

Algorithm
intervals
Results
22.0ms185×body80valid
11.0ms26×body1280valid
9.0ms256×pre80true
7.0ms24×body640valid
3.0ms11×body320valid
2.0ms10×body160valid

simplify129.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
129.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize19.0ms

Local error

Found 2 expressions with local error:

2.4b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite158.0ms

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
110.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
45.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series186.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
102.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
84.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify7.7s

Counts
105 → 108
Calls
105 calls:
Slowest
722.0ms
(* (* (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)) (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))
432.0ms
(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
311.0ms
(* (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
279.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
274.0ms
(+ (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0))) (- (* 1.0 1.0) (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.8b

localize41.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ 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))

rewrite812.0ms

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
520.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
220.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
35.0ms
(/ alpha (+ (+ alpha beta) 2.0))
22.0ms
(/ beta (+ (+ alpha beta) 2.0))

series329.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
79.0ms
(/ beta (+ (+ alpha beta) 2.0))
73.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
70.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify1.6m

Counts
660 → 429
Calls
660 calls:
Slowest
707.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) 1) (/ (cbrt beta) (+ (+ alpha beta) 2.0)) (- (* (- (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))
657.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
648.0ms
(* (* (- (/ 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)))
638.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
591.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (fma (/ 1 (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ alpha (cbrt (+ (+ alpha beta) 2.0))) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0))))))

prune4.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize38.0ms

Local error

Found 4 expressions with local error:

6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
2.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite211.0ms

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 insert-posit16 log1p-expm1-u
3×cbrt-div pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 201
Calls
4 calls:
Slowest
168.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
13.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series741.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
233.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
206.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
176.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
126.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify21.3s

Counts
343 → 213
Calls
343 calls:
Slowest
637.0ms
(* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
464.0ms
(+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
351.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
350.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
334.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize53.0ms

Local error

Found 4 expressions with local error:

10.7b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.6b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite810.0ms

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
414.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
212.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
156.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
23.0ms
(/ beta (+ (+ alpha beta) 2.0))

series440.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
136.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
88.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
52.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify25.4s

Counts
306 → 203
Calls
306 calls:
Slowest
800.0ms
(* (* (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)))))
610.0ms
(* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
523.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
501.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
490.0ms
(+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

regimes169.0ms

Accuracy

78.5% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 16.7b

bsearch118.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
848.0ms862×body1280valid
624.0ms5746×body80valid
403.0ms8000×pre80true
302.0ms739×body640valid
154.0ms443×body320valid
36.0ms210×body160valid