Details

Time bar (total: 23.2s)

sample44.0ms

Algorithm
intervals
Results
13.0ms199×body80valid
7.0ms256×pre80true
7.0ms20×body1280valid
4.0ms17×body640valid
3.0ms17×body320valid
0.0ms3×body160valid

simplify123.0ms

Calls
1 calls:
Slowest
123.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize24.0ms

Local error

Found 2 expressions with local error:

1.1b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×fma-def
4×add-cbrt-cube add-exp-log associate-/r/
3×associate-/r* flip3-+ flip-+ associate-/l*
2×expm1-log1p-u pow1 div-sub insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
1×cbrt-undiv +-commutative clear-num frac-2neg flip3-- div-exp associate-+l- flip--
Calls
2 calls:
Slowest
29.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
6.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series65.0ms

Calls
2 calls:
Slowest
35.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
30.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.6s

Calls
51 calls:
Slowest
608.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
270.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
251.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
238.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
236.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune584.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.9b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
6×associate-/r* fma-neg associate-/r/
5×associate-/l*
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
3×clear-num frac-2neg flip3-+ flip3-- flip-+ flip--
2×frac-sub
1×sub-neg div-sub distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
99.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
15.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.0ms
(/ alpha (+ (+ alpha beta) 2.0))
4.0ms
(/ beta (+ (+ alpha beta) 2.0))

series161.0ms

Calls
4 calls:
Slowest
59.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
41.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
36.0ms
(/ beta (+ (+ alpha beta) 2.0))
24.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify4.9s

Calls
34 calls:
Slowest
638.0ms
(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
339.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
331.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
320.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
317.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.5b
(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
0.0b
(/ (+ (+ alpha beta) 2.0) beta)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-/r*
6×fma-neg
5×pow1 add-exp-log associate-/r/ div-inv
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg flip3-+ flip-+ associate-/l*
2×associate-/l/
1×rec-exp sub-neg flip3-- pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
19.0ms
(/ (+ (+ alpha beta) 2.0) beta)
16.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.0ms
(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
4.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series171.0ms

Calls
4 calls:
Slowest
66.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
46.0ms
(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
37.0ms
(/ alpha (+ (+ alpha beta) 2.0))
22.0ms
(/ (+ (+ alpha beta) 2.0) beta)

simplify3.6s

Calls
30 calls:
Slowest
630.0ms
(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
532.0ms
(+ (pow (+ alpha beta) 3) (pow 2.0 3))
339.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
339.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
323.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))

prune833.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.3b

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.5b
(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
0.0b
(/ (+ (+ alpha beta) 2.0) beta)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 fma-neg
5×log-prod add-exp-log
4×expm1-log1p-u associate-/r* add-cbrt-cube log-pow insert-posit16 log1p-expm1-u div-inv add-log-exp
3×exp-prod associate-/r/ associate-/l*
2×clear-num sub-neg frac-2neg flip3-+ exp-sum flip-+ associate-/l/
1×log-div rec-exp flip3-- exp-diff rem-log-exp pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
23.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
16.0ms
(/ (+ (+ alpha beta) 2.0) beta)
8.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
3.0ms
(/ 1 (/ (+ (+ alpha beta) 2.0) beta))

series178.0ms

Calls
4 calls:
Slowest
61.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
60.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
42.0ms
(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
14.0ms
(/ (+ (+ alpha beta) 2.0) beta)

simplify4.2s

Calls
35 calls:
Slowest
577.0ms
(+ (pow (+ alpha beta) 3) (pow 2.0 3))
523.0ms
(/ alpha (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
388.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
349.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
348.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.3b

regimes107.0ms

Accuracy

75.4% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.5b

bsearch76.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
588.0ms5868×body80valid
440.0ms802×body1280valid
344.0ms8000×pre80true
317.0ms724×body640valid
136.0ms402×body320valid
61.0ms204×body160valid