Details

Time bar (total: 2.1m)

sample55.0ms

Algorithm
intervals
Results
12.0ms256×pre80true
12.0ms185×body80valid
8.0ms26×body1280valid
7.0ms24×body640valid
2.0ms11×body320valid
1.0ms10×body160valid

simplify103.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
103.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize20.0ms

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))

rewrite171.0ms

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
117.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
52.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series146.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
80.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
66.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify6.8s

Counts
101 → 73
Calls
101 calls:
Slowest
662.0ms
(* (* (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)) (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0))
386.0ms
(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
298.0ms
(* (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
210.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
200.0ms
(/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)))

prune660.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.9b

localize21.0ms

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))

rewrite664.0ms

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
374.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
199.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
45.0ms
(/ beta (+ (+ alpha beta) 2.0))
44.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series366.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
81.0ms
(/ alpha (+ (+ alpha beta) 2.0))
81.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
71.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify11.8s

Counts
169 → 127
Calls
169 calls:
Slowest
655.0ms
(* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
614.0ms
(* (* (- (/ 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)))
602.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
471.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
363.0ms
(+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize31.0ms

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)

rewrite176.0ms

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
134.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
19.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series791.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
227.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
225.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
225.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
114.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify10.2s

Counts
188 → 121
Calls
188 calls:
Slowest
518.0ms
(* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
364.0ms
(+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
333.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
306.0ms
(- (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))))
283.0ms
(cbrt (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0))))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize88.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))) (* 1.0 (* 1.0 1.0)))
0.1b
(* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))))
0.1b
(* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))
0.1b
(* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
388×*-un-lft-identity
216×times-frac
153×distribute-lft-out
136×add-sqr-sqrt
109×add-cube-cbrt
78×swap-sqr
69×add-cbrt-cube add-exp-log
63×associate-*l*
43×associate-*r*
32×pow1
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
18×associate-/r/
10×unswap-sqr
9×flip3-+ flip-+ div-inv
7×frac-times associate-*r/ pow-prod-up
6×add-log-exp
5×pow-prod-down associate-*l/
4×insert-posit16
3×pow2 pow-plus cube-unmult pow-sqr *-commutative
1×difference-cubes sub-neg flip3-- diff-log flip--
Counts
4 → 301
Calls
4 calls:
Slowest
131.0ms
(- (* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))) (* 1.0 (* 1.0 1.0)))
118.0ms
(* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))
113.0ms
(* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))
104.0ms
(* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(- (* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))) (* 1.0 (* 1.0 1.0)))
113.0ms
(* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))))
86.0ms
(* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))
82.0ms
(* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))

simplify1.4m

Counts
403 → 313
Calls
403 calls:
Slowest
962.0ms
(* (* (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))) (/ alpha (+ 2.0 (+ alpha beta)))) (* (/ (* (* alpha alpha) alpha) (* (* (+ 2.0 (+ alpha beta)) (+ 2.0 (+ alpha beta))) (+ 2.0 (+ alpha beta)))) (/ (* (* alpha alpha) alpha) (* (* (+ 2.0 (+ alpha beta)) (+ 2.0 (+ alpha beta))) (+ 2.0 (+ alpha beta))))))
774.0ms
(* (* (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))) (/ alpha (+ 2.0 (+ alpha beta)))) (* (* (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))) (/ alpha (+ 2.0 (+ alpha beta)))) (* (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))) (/ alpha (+ 2.0 (+ alpha beta))))))
735.0ms
(- (* (* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta))))) (* (/ alpha (+ 2.0 (+ alpha beta))) (* (/ alpha (+ 2.0 (+ alpha beta))) (/ alpha (+ 2.0 (+ alpha beta)))))) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0))))
709.0ms
(* (/ alpha (+ 2.0 (+ alpha beta))) (/ (* (cbrt alpha) (cbrt alpha)) (sqrt (+ 2.0 (+ alpha beta)))))
694.0ms
(* (/ (* (* alpha alpha) alpha) (* (* (+ 2.0 (+ alpha beta)) (+ 2.0 (+ alpha beta))) (+ 2.0 (+ alpha beta)))) (* (/ (* (* alpha alpha) alpha) (* (* (+ 2.0 (+ alpha beta)) (+ 2.0 (+ alpha beta))) (+ 2.0 (+ alpha beta)))) (/ (* (* alpha alpha) alpha) (* (* (+ 2.0 (+ alpha beta)) (+ 2.0 (+ alpha beta))) (+ 2.0 (+ alpha beta))))))

prune5.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

regimes130.0ms

Accuracy

78.2% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 16.4b

bsearch104.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
755.0ms8000×pre80true
584.0ms5746×body80valid
453.0ms862×body1280valid
298.0ms739×body640valid
112.0ms443×body320valid
34.0ms210×body160valid