Details

Time bar (total: 1.3m)

sample90.0ms

Algorithm
intervals
Results
24.0ms12×body320valid
21.0ms202×body80valid
9.0ms22×body640valid
9.0ms256×pre80true
8.0ms15×body1280valid
1.0ms5×body160valid

simplify146.0ms

Calls
1 calls:
Slowest
146.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize41.0ms

Local error

Found 3 expressions with local error:

19.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.5b
(+ (/ (/ (* (+ 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))

rewrite208.0ms

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
149.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
31.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
26.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series754.0ms

Calls
3 calls:
Slowest
338.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
323.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
93.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify28.9s

Calls
139 calls:
Slowest
815.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
764.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
632.0ms
(* (+ (pow alpha 3) (pow beta 3)) (- (pow beta 3) (pow alpha 3)))
615.0ms
(/ (* (* (/ (* (+ 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)))
599.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize38.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (* 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))))
0.1b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite31.0ms

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
14.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
6.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
5.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
4.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)

series865.0ms

Calls
4 calls:
Slowest
373.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
275.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
114.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
103.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))

simplify11.8s

Calls
90 calls:
Slowest
835.0ms
(/ (* (* (* (+ 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)))))
696.0ms
(/ (* (* (* (+ 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)))))
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)))))
489.0ms
(* (- beta alpha) (fma 2 i (+ beta alpha)))
471.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize18.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
1.5b
(log (exp (+ (* 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))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-*r*
12×times-frac
7×pow1
6×flip3-+ flip-+
5×cbrt-undiv div-exp associate-/l/
4×expm1-log1p-u frac-times log-prod associate-*l/ prod-exp log-pow cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×exp-prod associate-/r* associate-*l*
2×associate-*r/ associate-/r/ div-inv
1×+-commutative clear-num fma-def frac-2neg rem-log-exp exp-sum pow-prod-down *-commutative associate-/l*
Calls
4 calls:
Slowest
19.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
18.0ms
(log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)))
12.0ms
(* (+ 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)

series870.0ms

Calls
4 calls:
Slowest
322.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))
220.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
215.0ms
(log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)))
112.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))

simplify14.2s

Calls
70 calls:
Slowest
793.0ms
(/ (* (* (* (+ 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)))))
673.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
656.0ms
(/ (* (* (* (+ 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)))))
635.0ms
(/ (* (* (* (+ 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)))))
516.0ms
(sqrt (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0))))
1.5b
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
1.5b
(log (exp (+ (* 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))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-*r*
11×log-prod
10×add-exp-log
9×pow1 times-frac add-cbrt-cube log-pow
6×exp-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ associate-*l* flip-+
2×frac-times rem-log-exp associate-*l/ prod-exp cbrt-unprod
1×cbrt-undiv +-commutative fma-def div-exp exp-sum pow-prod-down associate-*r/ *-commutative div-inv
Calls
4 calls:
Slowest
13.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))
12.0ms
(log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)))
11.0ms
(log (log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0))))
3.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)

series1.1s

Calls
4 calls:
Slowest
466.0ms
(log (log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0))))
275.0ms
(+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)
240.0ms
(log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)))
144.0ms
(* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha))))

simplify11.1s

Calls
55 calls:
Slowest
561.0ms
(cbrt (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0))
473.0ms
(log (sqrt (log (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)))))
471.0ms
(log (* (cbrt (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0))) (cbrt (exp (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0)))))
469.0ms
(log (exp (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))))
454.0ms
(log (+ (* 1 (/ (* (+ beta alpha) (/ (- beta alpha) (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha))))) 1.0))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

regimes450.0ms

Accuracy

8.4% (5.7b remaining)

Error of 11.6b against oracle of 5.8b and baseline of 12.1b

bsearch61.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.1s6392×body80valid
472.0ms530×body1280valid
384.0ms8000×pre80true
379.0ms558×body640valid
169.0ms335×body320valid
54.0ms185×body160valid