Details

Time bar (total: 6.0m)

sample40.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
7.0ms256×pre80true

simplify130.0ms

Calls
1 calls:
Slowest
130.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize30.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 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)

rewrite123.0ms

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))
31.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
26.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
8.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series519.0ms

Calls
4 calls:
Slowest
205.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
203.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
96.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
15.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.7m

Calls
523 calls:
Slowest
1.0s
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
828.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (cbrt (+ (+ 1.0 (+ beta alpha)) 2)))
818.0ms
(/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 2 (+ beta alpha)))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) 1)
704.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
672.0ms
(/ (/ (* (* (+ 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))))

prune4.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize11.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b
(+ 2 (+ 1.0 (+ beta alpha)))

rewrite126.0ms

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-+r+
Calls
4 calls:
Slowest
53.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
33.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
31.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
1.0ms
(+ 2 (+ 1.0 (+ beta alpha)))

series550.0ms

Calls
4 calls:
Slowest
220.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
169.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
132.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
28.0ms
(+ 2 (+ 1.0 (+ beta alpha)))

simplify1.7m

Calls
524 calls:
Slowest
1.3s
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
677.0ms
(/ (/ (* (* (+ 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))))
665.0ms
(/ (/ (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))
656.0ms
(/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))))
635.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha))))

prune4.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize13.0ms

Local error

Found 4 expressions with local error:

12.2b
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
12.2b
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
768×times-frac
366×add-sqr-sqrt
346×*-un-lft-identity add-cube-cbrt
318×sqrt-prod
56×associate-/r/
30×flip3-+ flip-+
28×div-inv
8×rem-sqrt-square add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
4×pow1 insert-posit16 add-log-exp associate-/l/
2×cbrt-undiv clear-num frac-2neg pow1/2 sqrt-div div-exp
Calls
4 calls:
Slowest
25.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
17.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
15.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
9.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))

series1.0s

Calls
4 calls:
Slowest
431.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
383.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
110.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
87.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.3m

Calls
398 calls:
Slowest
971.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
890.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
772.0ms
(sqrt (/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (* (cbrt (+ 2 (+ 1.0 (+ beta alpha)))) (cbrt (+ 2 (+ 1.0 (+ beta alpha)))))))
633.0ms
(sqrt (/ (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1) (* (cbrt (+ 2 (+ 1.0 (+ beta alpha)))) (cbrt (+ 2 (+ 1.0 (+ beta alpha)))))))
541.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ 1.0 (+ beta alpha))))))

prune7.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize79.0ms

Local error

Found 4 expressions with local error:

12.2b
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
4.6b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
4.3b
(sqrt (/ (/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) 1) (* (cbrt (+ 2 (+ 1.0 (+ beta alpha)))) (cbrt (+ 2 (+ 1.0 (+ beta alpha)))))))
3.2b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
407×times-frac
204×add-sqr-sqrt
192×*-un-lft-identity add-cube-cbrt
187×sqrt-prod
38×associate-/r/
23×flip3-+ flip-+
17×div-inv
12×cbrt-div
9×associate-/r*
8×add-cbrt-cube add-exp-log
6×rem-sqrt-square associate-/l*
4×frac-times pow1 sqrt-div insert-posit16 add-log-exp associate-/l/
2×cbrt-undiv clear-num frac-2neg pow1/2 div-exp associate-*l/ associate-*r/
Calls
4 calls:
Slowest
23.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
18.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
16.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
6.0ms
(sqrt (/ (/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) 1) (* (cbrt (+ 2 (+ 1.0 (+ beta alpha)))) (cbrt (+ 2 (+ 1.0 (+ beta alpha)))))))

series1.0s

Calls
4 calls:
Slowest
420.0ms
(sqrt (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ 1.0 (+ beta alpha)))))
337.0ms
(sqrt (/ (/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) 1) (* (cbrt (+ 2 (+ 1.0 (+ beta alpha)))) (cbrt (+ 2 (+ 1.0 (+ beta alpha)))))))
135.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
134.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify49.4s

Calls
274 calls:
Slowest
992.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
843.0ms
(+ (pow 1.0 3) (pow (+ (* alpha beta) (+ beta alpha)) 3))
826.0ms
(sqrt (/ (/ (/ 1 (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) (* (cbrt (+ 2 (+ beta alpha))) (cbrt (+ 2 (+ beta alpha))))) (* (cbrt (+ 2 (+ 1.0 (+ beta alpha)))) (cbrt (+ 2 (+ 1.0 (+ beta alpha)))))))
823.0ms
(sqrt (/ (/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) 1) (* (cbrt (+ (pow 2 3) (pow (+ 1.0 (+ beta alpha)) 3))) (cbrt (+ (pow 2 3) (pow (+ 1.0 (+ beta alpha)) 3))))))
608.0ms
(- (+ (* 1.0 (sqrt 1/2)) (+ (* beta (sqrt 1/2)) (* (sqrt 1/2) alpha))) (+ (* 0.125 (/ beta (sqrt 1/2))) (* 0.5 (* (sqrt 1/8) alpha))))

prune6.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes155.0ms

Accuracy

53% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.4b

bsearch101.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.2s8000×body80valid
268.0ms8000×pre80true