Details

Time bar (total: 30.9s)

sample71.0ms

Algorithm
intervals
Results
20.0ms194×body80valid
16.0ms30×body1280valid
11.0ms256×pre80true
6.0ms14×body640valid
5.0ms16×body320valid
0.0ms2×body160valid

simplify104.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
104.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize23.0ms

Local error

Found 2 expressions with local error:

0.8b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite172.0ms

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-cbrt-cube add-exp-log add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Counts
2 → 67
Calls
2 calls:
Slowest
120.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
49.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series156.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
86.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
70.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify3.3s

Counts
74 → 73
Calls
74 calls:
Slowest
234.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
221.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
191.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
188.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
182.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune685.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (/ 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))

rewrite601.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
34×add-sqr-sqrt
32×times-frac
24×add-cube-cbrt distribute-lft-out
11×add-log-exp
10×associate-/r*
8×add-cbrt-cube add-exp-log
6×associate-/l*
4×pow1 diff-log associate-/r/ insert-posit16 distribute-lft-out-- difference-of-squares
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp frac-sub flip-+ div-inv associate--r+
1×associate--r-
Counts
4 → 115
Calls
4 calls:
Slowest
390.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
149.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
37.0ms
(/ alpha (+ (+ alpha beta) 2.0))
22.0ms
(/ beta (+ (+ alpha beta) 2.0))

series388.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
98.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
78.0ms
(/ alpha (+ (+ alpha beta) 2.0))
76.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify5.9s

Counts
114 → 127
Calls
114 calls:
Slowest
329.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
270.0ms
(* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
270.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
243.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
239.0ms
(/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.1b
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
0.0b
(/ 1 (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite302.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
48×times-frac
46×add-sqr-sqrt
34×add-cube-cbrt
33×distribute-lft-out
21×associate-*r*
19×add-exp-log
13×add-cbrt-cube
10×associate-/r*
7×pow1
6×associate-/r/ associate-/l* add-log-exp
5×div-exp
4×prod-exp insert-posit16
3×cbrt-undiv flip3-+ associate-*l* flip-+ div-inv unswap-sqr
2×rec-exp clear-num frac-2neg 1-exp cbrt-unprod difference-of-squares
1×sub-neg flip3-- diff-log pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip flip-- distribute-lft-out-- inv-pow
Counts
4 → 141
Calls
4 calls:
Slowest
170.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
68.0ms
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
38.0ms
(/ alpha (+ (+ alpha beta) 2.0))
22.0ms
(/ 1 (+ (+ alpha beta) 2.0))

series283.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
79.0ms
(/ alpha (+ (+ alpha beta) 2.0))
50.0ms
(* beta (/ 1 (+ (+ alpha beta) 2.0)))
40.0ms
(/ 1 (+ (+ alpha beta) 2.0))

simplify6.3s

Counts
140 → 153
Calls
140 calls:
Slowest
570.0ms
(* (* (* beta beta) beta) (* (* (/ 1 (+ (+ alpha beta) 2.0)) (/ 1 (+ (+ alpha beta) 2.0))) (/ 1 (+ (+ alpha beta) 2.0))))
387.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
329.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
265.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
249.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize51.0ms

Local error

Found 4 expressions with local error:

7.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
0.8b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
63×cbrt-prod
46×times-frac
36×add-sqr-sqrt
31×add-cube-cbrt
27×distribute-lft-out
6×associate-/r/ add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 109
Calls
4 calls:
Slowest
183.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
24.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
20.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series740.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
225.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
207.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
196.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
112.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify4.8s

Counts
84 → 121
Calls
84 calls:
Slowest
287.0ms
(- (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))))
272.0ms
(- (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))))
267.0ms
(- (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))))
210.0ms
(cbrt (/ beta (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0))))
201.0ms
(- (+ (* 0.8888888888888888 (/ 1 (pow beta 2))) 1) (* 0.6666666666666666 (/ 1 beta)))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

regimes276.0ms

Accuracy

99.3% (0.1b remaining)

Error of 2.9b against oracle of 2.8b and baseline of 15.7b

bsearch6.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
609.0ms5853×body80valid
413.0ms848×body1280valid
292.0ms8000×pre80true
254.0ms675×body640valid
155.0ms387×body320valid
44.0ms237×body160valid