Details

Time bar (total: 26.9s)

sample49.0ms

Algorithm
intervals
Results
18.0ms184×body80valid
7.0ms256×pre80true
6.0ms26×body640valid
6.0ms21×body1280valid
3.0ms18×body320valid
1.0ms7×body160valid

simplify158.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
158.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite157.0ms

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
121.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
35.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series134.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
85.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
49.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.2s

Counts
74 → 73
Calls
74 calls:
Slowest
254.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
230.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
168.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
163.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
150.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune667.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ 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))

rewrite575.0ms

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
373.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
137.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
42.0ms
(/ beta (+ (+ alpha beta) 2.0))
21.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series363.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
96.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
80.0ms
(/ beta (+ (+ alpha beta) 2.0))
64.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify6.2s

Counts
114 → 127
Calls
114 calls:
Slowest
361.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
311.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
304.0ms
(- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))
294.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
276.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize58.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×cbrt-prod
12×add-sqr-sqrt
9×distribute-lft-out
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
Slowest
120.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
19.0ms
(cbrt (+ (+ alpha beta) 2.0))
13.0ms
(cbrt (+ (+ alpha beta) 2.0))
10.0ms
(cbrt (+ (+ alpha beta) 2.0))

series550.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(cbrt (+ (+ alpha beta) 2.0))
143.0ms
(cbrt (+ (+ alpha beta) 2.0))
130.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
128.0ms
(cbrt (+ (+ alpha beta) 2.0))

simplify4.0s

Counts
39 → 76
Calls
39 calls:
Slowest
234.0ms
(+ (pow 2.0 1/3) (+ (* 0.16666666666666666 (* (pow 2.0 1/3) beta)) (* 1/3 (* (pow 0.25 1/3) alpha))))
233.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
225.0ms
(cbrt (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
222.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
218.0ms
(- (+ (* 0.6666666666666666 (/ (exp (* 1/3 (- (log -1) (log (/ -1 alpha))))) alpha)) (exp (* 1/3 (- (log -1) (log (/ -1 alpha)))))) (* 0.4444444444444444 (/ (exp (* 1/3 (- (log -1) (log (/ -1 alpha))))) (pow alpha 2))))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize73.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite468.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×*-un-lft-identity
10×add-log-exp
6×difference-of-squares
5×cbrt-prod add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out distribute-lft-out--
2×cbrt-div
1×flip3-+ pow1/3 flip-+
Counts
4 → 64
Calls
4 calls:
Slowest
170.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
145.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
143.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.0ms
(cbrt (+ (+ alpha beta) 2.0))

series462.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
127.0ms
(cbrt (+ (+ alpha beta) 2.0))
112.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
92.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.3s

Counts
37 → 76
Calls
37 calls:
Slowest
254.0ms
(- (+ (* 0.6666666666666666 (/ (exp (* 1/3 (- (log -1) (log (/ -1 alpha))))) alpha)) (exp (* 1/3 (- (log -1) (log (/ -1 alpha)))))) (* 0.4444444444444444 (/ (exp (* 1/3 (- (log -1) (log (/ -1 alpha))))) (pow alpha 2))))
241.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
232.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
208.0ms
(+ (pow 2.0 1/3) (+ (* 0.16666666666666666 (* (pow 2.0 1/3) beta)) (* 1/3 (* (pow 0.25 1/3) alpha))))
191.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes223.0ms

Accuracy

98.9% (0.1b remaining)

Error of 3.0b against oracle of 2.9b and baseline of 15.4b

bsearch6.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
698.0ms8000×pre80true
597.0ms5907×body80valid
449.0ms792×body1280valid
277.0ms727×body640valid
128.0ms388×body320valid
30.0ms186×body160valid