Details

Time bar (total: 4.8m)

sample49.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
8.0ms256×pre80true

simplify132.0ms

Calls
1 calls:
Slowest
132.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize57.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (+ 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
(+ (* alpha beta) (+ beta alpha))

rewrite147.0ms

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*
6×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+r+ sum-log
Calls
4 calls:
Slowest
58.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
39.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
30.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
6.0ms
(+ (* alpha beta) (+ beta alpha))

series287.0ms

Calls
4 calls:
Slowest
119.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
87.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
65.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
16.0ms
(+ (* alpha beta) (+ beta alpha))

simplify1.8m

Calls
524 calls:
Slowest
940.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
707.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
658.0ms
(/ (/ (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
653.0ms
(/ (/ (* (* (+ 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)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
634.0ms
(/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) (sqrt (+ 2 (+ beta alpha))))

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize8.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
0.1b
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
0.0b
(/ 1 (+ 2 (+ beta alpha)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
33×add-exp-log
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×times-frac
20×add-cbrt-cube
15×associate-*l*
10×div-exp associate-/r/
9×associate-/r*
8×prod-exp
7×pow1
6×cbrt-undiv flip3-+ associate-*r* flip-+ associate-/l/
5×rec-exp div-inv
4×cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×clear-num frac-2neg
2×frac-times associate-*l/ associate-*r/ un-div-inv
1×pow-prod-down *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
30.0ms
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
17.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
11.0ms
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
1.0ms
(/ 1 (+ 2 (+ beta alpha)))

series233.0ms

Calls
4 calls:
Slowest
88.0ms
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
69.0ms
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
49.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
27.0ms
(/ 1 (+ 2 (+ beta alpha)))

simplify17.2s

Calls
103 calls:
Slowest
875.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
863.0ms
(* (/ (* (* (+ 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)))) (* (* (/ 1 (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (/ 1 (+ 2 (+ beta alpha)))))
859.0ms
(/ (* (* (* (/ (+ 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)))) (* (* (/ 1 (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (/ 1 (+ 2 (+ beta alpha))))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)))
794.0ms
(/ (* (* (* (/ (+ 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 (+ 2 (+ beta alpha))))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)))
570.0ms
(/ (* (* (+ 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))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize30.0ms

Local error

Found 4 expressions with local error:

4.0b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
4.0b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.5b
(/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
0.5b
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
618×times-frac
321×sqrt-prod
316×add-sqr-sqrt
314×*-un-lft-identity add-cube-cbrt
58×div-inv
54×associate-/l*
32×associate-/r/
22×sqrt-div
18×flip3-+ flip-+
14×add-cbrt-cube add-exp-log
12×associate-/r*
6×cbrt-undiv div-exp
4×pow1 insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg pow1/2 associate-/l/
Calls
4 calls:
Slowest
20.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
14.0ms
(/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
7.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
5.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series284.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
90.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
48.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
41.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify2.1m

Calls
750 calls:
Slowest
963.0ms
(sqrt (+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3)))
912.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) (sqrt (+ (pow 2 3) (pow (+ beta alpha) 3)))) 1)
903.0ms
(sqrt (+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3)))
575.0ms
(/ (/ (sqrt (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1)) (cbrt (sqrt (+ 2 (+ beta alpha))))) (sqrt (cbrt (+ (+ 1.0 (+ beta alpha)) 2))))
534.0ms
(/ (/ (sqrt (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

prune7.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.6b

localize8.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.2b
(* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) 1) (/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
0.1b
(/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ 1 (+ 2 (+ beta alpha)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
35×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
24×associate-*r*
22×associate-/r/
19×add-exp-log
13×add-cbrt-cube
12×flip3-+ flip-+ div-inv
9×associate-/r* associate-/l*
7×pow1
5×div-exp
4×associate-*l* insert-posit16 add-log-exp
3×cbrt-undiv rec-exp clear-num frac-2neg prod-exp associate-/l/
2×cbrt-unprod
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
41.0ms
(* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) 1) (/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
17.0ms
(/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
15.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.0ms
(/ 1 (+ 2 (+ beta alpha)))

series216.0ms

Calls
4 calls:
Slowest
91.0ms
(* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) 1) (/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))
62.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
45.0ms
(/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
18.0ms
(/ 1 (+ 2 (+ beta alpha)))

simplify22.7s

Calls
132 calls:
Slowest
976.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
674.0ms
(* (* (* (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) 1) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) 1)) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) 1)) (/ (* (* (/ 1 (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (/ 1 (+ 2 (+ beta alpha)))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2))))
558.0ms
(/ (- 2 (+ beta alpha)) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))
513.0ms
(/ 1 (+ (pow 2 3) (pow (+ beta alpha) 3)))
511.0ms
(sqrt (/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2)))

prune1.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.6b

regimes158.0ms

Accuracy

58.4% (1.0b remaining)

Error of 2.1b against oracle of 1.1b and baseline of 3.5b

bsearch114.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.3s8000×body80valid
346.0ms8000×pre80true