Details

Time bar (total: 3.6m)

sample64.0ms

Algorithm
intervals
Results
41.0ms256×body80valid
11.0ms256×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))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize26.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (+ 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)

rewrite129.0ms

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
40.0ms
(/ (/ (/ (+ 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)))
27.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
9.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series251.0ms

Calls
4 calls:
Slowest
101.0ms
(/ (/ (/ (+ 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)))
49.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
14.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.7m

Calls
523 calls:
Slowest
868.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
647.0ms
(/ (/ (* (* (+ 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))))
640.0ms
(/ (/ (- 2 (+ beta alpha)) (cbrt (+ 2 (+ beta alpha)))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
615.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (pow 2 3) (pow (+ beta alpha) 3)))
606.0ms
(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))

prune4.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.1b

localize13.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.1b
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.1b
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))
0.0b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
87×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
33×associate-/r/
29×associate-/l*
28×add-exp-log
25×div-inv
24×associate-/r*
14×div-exp
13×add-cbrt-cube
9×flip3-+ flip-+
6×rec-exp
5×pow1 cbrt-undiv
4×clear-num frac-2neg insert-posit16 add-log-exp associate-/l/
1×pow-flip inv-pow
Calls
4 calls:
Slowest
19.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
16.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
10.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))
3.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))

series283.0ms

Calls
4 calls:
Slowest
85.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
78.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))
71.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
48.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))

simplify49.5s

Calls
258 calls:
Slowest
658.0ms
(/ (* (* (/ (/ 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)))
636.0ms
(/ (/ (cbrt (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))) (+ 2 (+ beta alpha))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))
544.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))
517.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
500.0ms
(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (cbrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
5.5b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.3b
(* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))))
0.1b
(/ (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
51×times-frac
42×add-sqr-sqrt *-un-lft-identity add-cube-cbrt sqrt-prod
24×associate-*r* associate-*l*
16×associate-/r/
15×add-cbrt-cube add-exp-log
11×div-inv
9×pow1 associate-/r*
8×sqrt-div
7×flip3-+ flip-+ associate-/l* associate-/l/
4×cbrt-undiv pow1/2 div-exp insert-posit16 add-log-exp
3×clear-num frac-2neg
2×frac-times pow-prod-down associate-*l/ prod-exp associate-*r/ pow-prod-up cbrt-unprod
1×pow2 rem-square-sqrt pow-plus sqrt-unprod *-commutative
Calls
4 calls:
Slowest
28.0ms
(/ (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
13.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
10.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
9.0ms
(* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))))

series286.0ms

Calls
4 calls:
Slowest
100.0ms
(/ (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))) (+ (+ 1.0 (+ beta alpha)) 2))
76.0ms
(* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))))
60.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
49.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify25.8s

Calls
152 calls:
Slowest
737.0ms
(/ (* (* (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))) (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))))) (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 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)))
705.0ms
(sqrt (* (cbrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (cbrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))))
670.0ms
(/ (* (* (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))) (* (* (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha)))) (sqrt (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (+ 2 (+ beta alpha))))) (sqrt (/ (/ 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)))
560.0ms
(+ (pow 2 3) (pow (+ beta alpha) 3))
481.0ms
(+ (pow 2 3) (pow (+ beta alpha) 3))

prune2.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.3b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha))))
0.1b
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))
0.0b
(* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
23×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
19×associate-/r*
15×flip3-+ associate-/r/ flip-+
13×add-cbrt-cube
10×div-exp
8×frac-times associate-/l*
7×pow1
6×rec-exp div-inv
4×associate-*l/ prod-exp associate-*r/ insert-posit16 add-log-exp
3×cbrt-undiv clear-num frac-2neg associate-*r* associate-*l* associate-/l/
2×cbrt-unprod
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
24.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
20.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha))))
11.0ms
(* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))
6.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))

series234.0ms

Calls
4 calls:
Slowest
102.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha))))
64.0ms
(/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
49.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))
19.0ms
(* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))

simplify19.7s

Calls
110 calls:
Slowest
1.5s
(/ (* (* (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))) (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (+ (* alpha beta) (+ beta alpha)))))) (* (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))) (* (+ (+ 1.0 (+ beta alpha)) 2) (+ 2 (+ beta alpha)))))
924.0ms
(* (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
704.0ms
(* (+ (* (+ 1.0 (+ beta alpha)) (+ 1.0 (+ beta alpha))) (- (* 2 2) (* (+ 1.0 (+ beta alpha)) 2))) (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
503.0ms
(/ (* (* (+ 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)))))
443.0ms
(* (+ (* (+ 1.0 (+ beta alpha)) (+ 1.0 (+ beta alpha))) (- (* 2 2) (* (+ 1.0 (+ beta alpha)) 2))) (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

62% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 3.5b

bsearch61.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8000×body80valid
284.0ms8000×pre80true