Details

Time bar (total: 7.3m)

sample59.0ms

Algorithm
intervals
Results
16.0ms193×body80valid
10.0ms25×body1280valid
9.0ms256×pre80true
8.0ms26×body640valid
2.0ms6×body320valid
1.0ms6×body160valid

simplify131.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
131.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize34.0ms

Local error

Found 2 expressions with local error:

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

rewrite180.0ms

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
139.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
38.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series164.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
88.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify5.0s

Counts
104 → 108
Calls
104 calls:
Slowest
297.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
285.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
250.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
237.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
230.0ms
(/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)))

prune939.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (/ 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))

rewrite778.0ms

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
466.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
236.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
39.0ms
(/ beta (+ (+ alpha beta) 2.0))
23.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series374.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
95.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
82.0ms
(/ alpha (+ (+ alpha beta) 2.0))
74.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify1.3m

Counts
593 → 429
Calls
593 calls:
Slowest
665.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) (sqrt (+ (+ alpha beta) 2.0))) (/ (cbrt beta) (sqrt (+ (+ alpha beta) 2.0))) (- (* (- (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))
556.0ms
(fma (- (- (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0))) (+ (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (* (- (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (/ (sqrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (sqrt 1.0))))
476.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) 1) (/ (cbrt beta) (+ (+ 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))))))
474.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) 1) (/ (cbrt beta) (+ (+ 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))))))
452.0ms
(fma (/ (sqrt beta) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (sqrt beta) (cbrt (+ (+ alpha beta) 2.0))) (- (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))

prune4.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize45.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.9b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.9b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
1.5b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite255.0ms

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
211.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
14.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series751.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
239.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
198.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
185.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
129.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify15.9s

Counts
229 → 213
Calls
229 calls:
Slowest
500.0ms
(fma (/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3))) (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0))) (- (* 1.0 1)))
360.0ms
(- (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))))
323.0ms
(- (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))))
295.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
295.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize74.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.9b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.9b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
1.5b
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite468.0ms

Algorithm
rewrite-expression-head
Rules
867×*-un-lft-identity
576×prod-diff
468×add-sqr-sqrt
443×times-frac
435×unpow-prod-down cube-prod
422×add-cube-cbrt
261×distribute-lft-out
71×sqr-pow
63×cbrt-prod
61×cube-mult unpow3
58×associate-/r/
48×fma-neg
29×flip3-+ flip-+ div-inv
24×difference-of-squares
6×add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-div pow1/3
1×difference-cubes sub-neg flip3-- diff-log flip--
Counts
4 → 768
Calls
4 calls:
Slowest
414.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
12.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series786.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
209.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
197.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
160.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify5.2m

Counts
1337 → 780
Calls
1337 calls:
Slowest
1.0s
(pow (/ alpha (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0))) 3)
951.0ms
(pow (/ alpha (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0))) 3)
929.0ms
(fma (pow (/ (sqrt alpha) 1) 3) (pow (/ (sqrt alpha) (+ (+ alpha beta) 2.0)) 3) (- (* 1.0 (* 1.0 1.0))))
897.0ms
(fma (/ alpha (+ (+ alpha beta) 2.0)) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (* (cbrt (pow 1.0 3)) (* (cbrt (pow 1.0 3)) (cbrt (pow 1.0 3))))))
891.0ms
(fma (pow (/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3))) 3) (pow (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0))) 3) (- (* (pow (cbrt 1.0) 3) (pow (* (cbrt 1.0) (cbrt 1.0)) 3))))

prune13.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

regimes137.0ms

Accuracy

75.4% (3.1b remaining)

Error of 6.0b against oracle of 2.9b and baseline of 15.7b

bsearch153.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
771.0ms865×body1280valid
644.0ms5852×body80valid
311.0ms715×body640valid
302.0ms8000×pre80true
114.0ms365×body320valid
67.0ms203×body160valid