Details

Time bar (total: 3.4m)

sample92.0ms

Algorithm
intervals
Results
37.0ms198×body80valid
11.0ms256×pre80true
10.0ms17×body1280valid
9.0ms20×body640valid
4.0ms12×body320valid
2.0ms9×body160valid

simplify120.0ms

Calls
1 calls:
Slowest
120.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize34.0ms

Local error

Found 3 expressions with local error:

22.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.9b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
39×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
33×fma-def
20×associate-/r/
17×add-cbrt-cube add-exp-log
14×flip3-+ flip-+
10×div-inv associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp
6×associate-/r*
4×frac-times
3×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative
Calls
3 calls:
Slowest
152.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
55.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
29.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series556.0ms

Calls
3 calls:
Slowest
251.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
231.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
74.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify27.0s

Calls
139 calls:
Slowest
796.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
705.0ms
(/ (* (* (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
703.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
579.0ms
(* (+ (pow alpha 3) (pow beta 3)) (- (pow beta 3) (pow alpha 3)))
563.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize48.0ms

Local error

Found 4 expressions with local error:

1.9b
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
0.1b
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
0.1b
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×times-frac
20×add-cbrt-cube add-exp-log
13×associate-*r*
7×associate-/l/
6×pow1 cbrt-undiv associate-/r* flip3-+ div-exp flip-+
4×expm1-log1p-u frac-times associate-*l/ prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×associate-*l* div-inv
2×clear-num frac-2neg associate-*r/ associate-/r/
1×+-commutative fma-def flip3-- div-sub pow-prod-down *-commutative flip--
Calls
4 calls:
Slowest
11.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
7.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
7.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
4.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

series506.0ms

Calls
4 calls:
Slowest
210.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
176.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
63.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
56.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify11.8s

Calls
90 calls:
Slowest
880.0ms
(/ (* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
663.0ms
(/ (* (* (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
586.0ms
(/ (* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (/ (- beta alpha) (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
564.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))
545.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(+ (* 1 (/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))) 1.0)
0.3b
(/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))
0.1b
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
0.1b
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
18×add-cbrt-cube
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×times-frac
13×associate-/r* associate-*r*
11×associate-/r/
9×div-exp
8×flip3-+ flip-+
7×pow1
6×frac-times associate-*l/ prod-exp
5×cbrt-undiv
4×expm1-log1p-u rec-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
3×associate-*l* associate-*r/ associate-/l*
2×clear-num frac-2neg associate-/l/
1×+-commutative fma-def pow-prod-down *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
16.0ms
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))
13.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
10.0ms
(/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))
5.0ms
(+ (* 1 (/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))) 1.0)

series513.0ms

Calls
4 calls:
Slowest
220.0ms
(/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))
118.0ms
(+ (* 1 (/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))) 1.0)
116.0ms
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))
59.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))

simplify12.1s

Calls
75 calls:
Slowest
692.0ms
(/ (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))) (* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))))
665.0ms
(/ (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))) (* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (/ (- beta alpha) (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))
661.0ms
(* (+ (* beta beta) (- (* alpha alpha) (* beta alpha))) (fma 2 i (+ beta alpha)))
540.0ms
(/ (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))) (* (* (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))) (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))
473.0ms
(* (- beta alpha) (fma 2 i (+ beta alpha)))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize36.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 1 (/ (/ 1 (/ 1 (+ beta alpha))) (/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))) 1.0)
3.0b
(/ (/ 1 (/ 1 (+ beta alpha))) (/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))
0.2b
(/ 1 (/ 1 (+ beta alpha)))
0.1b
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
691×times-frac
302×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
77×div-inv
63×associate-/r*
56×associate-/r/
38×add-exp-log
21×div-exp
18×add-cbrt-cube
12×rec-exp
9×cbrt-undiv
8×associate-/l*
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u pow-flip add-log-exp
3×clear-num frac-2neg flip3-+ flip-+ associate-/l/
2×inv-pow
1×+-commutative fma-def remove-double-div
Calls
4 calls:
Slowest
24.0ms
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
18.0ms
(/ (/ 1 (/ 1 (+ beta alpha))) (/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))
11.0ms
(+ (* 1 (/ (/ 1 (/ 1 (+ beta alpha))) (/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))) 1.0)
2.0ms
(/ 1 (/ 1 (+ beta alpha)))

series457.0ms

Calls
4 calls:
Slowest
196.0ms
(/ (/ 1 (/ 1 (+ beta alpha))) (/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))
158.0ms
(+ (* 1 (/ (/ 1 (/ 1 (+ beta alpha))) (/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))))) 1.0)
85.0ms
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
18.0ms
(/ 1 (/ 1 (+ beta alpha)))

simplify2.3m

Calls
622 calls:
Slowest
934.0ms
(/ (/ 1 (/ 1 (+ beta alpha))) (/ (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (sqrt (- beta alpha)) (cbrt (fma 2 i (+ beta alpha))))))
736.0ms
(/ 1 (/ (* (cbrt (+ 2.0 (fma 2 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2 i (+ beta alpha))))) (- beta alpha)))
715.0ms
(/ (* (* (/ 1 (/ 1 (+ beta alpha))) (/ 1 (/ 1 (+ beta alpha)))) (/ 1 (/ 1 (+ beta alpha)))) (/ (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))) (* (* (/ (- beta alpha) (fma 2 i (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))))))
709.0ms
(/ (* (* (/ 1 (/ 1 (+ beta alpha))) (/ 1 (/ 1 (+ beta alpha)))) (/ 1 (/ 1 (+ beta alpha)))) (/ (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))))
648.0ms
(/ (/ 1 1) (/ 1 (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (fma 2 i (+ beta alpha))) (cbrt (fma 2 i (+ beta alpha)))))))

prune6.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

regimes493.0ms

Accuracy

17% (5.4b remaining)

Error of 11.5b against oracle of 6.1b and baseline of 12.6b

bsearch159.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s6329×body80valid
576.0ms357×body320valid
511.0ms497×body1280valid
355.0ms615×body640valid
337.0ms8000×pre80true
87.0ms202×body160valid