Details

Time bar (total: 7.6m)

sample58.0ms

Algorithm
intervals
Results
34.0ms256×body80valid
10.0ms256×pre80true

simplify118.0ms

Calls
1 calls:
Slowest
118.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize50.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ (+ 1.0 (+ beta alpha)) 2)

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
531×times-frac
256×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
69×associate-/l*
46×associate-/r/
25×flip3-+ flip-+
23×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
9×associate-/r*
4×pow1 insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Calls
4 calls:
Slowest
51.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
38.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
15.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
8.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series260.0ms

Calls
4 calls:
Slowest
116.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
78.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
54.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
12.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.7m

Calls
523 calls:
Slowest
992.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
902.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) 1)
795.0ms
(/ (/ (* (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
778.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
619.0ms
(/ (/ (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize8.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.0b
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
177×times-frac
103×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
71×associate-/r*
28×add-exp-log
25×associate-/r/
16×div-inv
14×div-exp
13×add-cbrt-cube
11×flip3-+ flip-+ associate-/l*
6×rec-exp
5×pow1 cbrt-undiv associate-/l/
4×clear-num frac-2neg insert-posit16 add-log-exp
1×pow-flip inv-pow
Calls
4 calls:
Slowest
15.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
11.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
9.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
4.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))

series332.0ms

Calls
4 calls:
Slowest
107.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
92.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
81.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
52.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify45.9s

Calls
250 calls:
Slowest
934.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
866.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
746.0ms
(/ (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
741.0ms
(+ (pow 2 3) (pow (+ beta alpha) 3))
707.0ms
(/ (* (* (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))) (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)))

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(* (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (/ 1 (+ (+ 1.0 (+ beta alpha)) 2)))
0.0b
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.0b
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
95×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
68×associate-/r*
39×add-exp-log
22×associate-/r/
13×rec-exp add-cbrt-cube div-exp div-inv
11×flip3-+ flip-+
9×pow1
8×prod-exp
6×associate-*r* associate-/l*
5×associate-*l*
4×cbrt-undiv insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg pow-prod-down pow-flip inv-pow
1×frac-times associate-*l/ associate-*r/ un-div-inv *-commutative cbrt-unprod
Calls
4 calls:
Slowest
34.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
22.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
15.0ms
(* (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (/ 1 (+ (+ 1.0 (+ beta alpha)) 2)))
8.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))

series319.0ms

Calls
4 calls:
Slowest
88.0ms
(* (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (/ 1 (+ (+ 1.0 (+ beta alpha)) 2)))
86.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
82.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
64.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify40.6s

Calls
234 calls:
Slowest
915.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
832.0ms
(/ (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
637.0ms
(/ (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))))
532.0ms
(/ (sqrt (+ 2 (+ beta alpha))) (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 2 (+ beta alpha)))))
525.0ms
(/ (* (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))

prune2.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.6b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
0.6b
(/ 1 (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
0.1b
(* (/ 1 (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
1557×times-frac
703×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
312×associate-*r* sqrt-prod
114×associate-/r/
58×flip3-+ flip-+
57×div-inv
54×associate-/l*
44×add-exp-log
29×add-cbrt-cube
19×div-exp
15×associate-/r*
13×cbrt-undiv
8×sqrt-div prod-exp
7×pow1
6×associate-*l*
5×rec-exp
4×cbrt-unprod insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l/
2×pow-flip
1×frac-times pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative inv-pow
Calls
4 calls:
Slowest
38.0ms
(* (/ 1 (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))
36.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
19.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
7.0ms
(/ 1 (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

series316.0ms

Calls
4 calls:
Slowest
102.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
93.0ms
(* (/ 1 (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))
74.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
47.0ms
(/ 1 (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

simplify4.0m

Calls
1061 calls:
Slowest
923.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
921.0ms
(/ (/ (/ 1 (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
657.0ms
(/ (/ (* (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (* (sqrt (+ (+ 1.0 (+ beta alpha)) 2)) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))
638.0ms
(/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) (sqrt (+ 2 (+ beta alpha)))) (sqrt (* (cbrt (+ (+ 1.0 (+ beta alpha)) 2)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))))
637.0ms
(/ (/ (* (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) (sqrt (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))

prune11.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

68% (1.1b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.5b

bsearch151.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.3s8000×body80valid
704.0ms8000×pre80true