Details

Time bar (total: 1.5m)

sample46.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
7.0ms256×pre80true

simplify1.2s

Counts
1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize39.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (+ 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)

rewrite891.0ms

Algorithm
rewrite-expression-head
Rules
4332×*-un-lft-identity
2696×times-frac
2173×distribute-lft-out
778×add-sqr-sqrt add-cube-cbrt
166×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
13×add-log-exp
10×cbrt-undiv div-exp
6×sum-log
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1221
Calls
4 calls:
Slowest
315.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
229.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
181.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
93.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
219.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
197.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
126.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
18.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.3s

Counts
1233 → 1233

prune14.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize58.0ms

Local error

Found 4 expressions with local error:

9.2b
(* (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) 1) (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
1.9b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
1.9b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
0.2b
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))

rewrite804.0ms

Algorithm
rewrite-expression-head
Rules
766×*-un-lft-identity
680×times-frac
407×add-sqr-sqrt
294×distribute-lft-out
226×add-cube-cbrt
211×associate-*r*
195×sqrt-prod
84×add-exp-log
79×associate-*l*
52×div-exp
44×unswap-sqr
42×add-cbrt-cube
21×prod-exp
19×cbrt-undiv
15×1-exp
14×associate-/r/
11×div-inv
10×flip3-+ flip-+
9×cbrt-unprod
8×pow1
7×associate-/l*
6×sqrt-div
5×associate-/r*
4×insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 475
Calls
4 calls:
Slowest
446.0ms
(* (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) 1) (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
161.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))
101.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
79.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series677.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
319.0ms
(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))
182.0ms
(* (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) 1) (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
93.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
82.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify1.3s

Counts
487 → 487

prune6.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

localize66.0ms

Local error

Found 4 expressions with local error:

13.0b
(/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) (/ (+ 2 (+ beta alpha)) (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))))
2.2b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.2b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.2b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

rewrite411.0ms

Algorithm
rewrite-expression-head
Rules
5143×times-frac
4931×*-un-lft-identity
2027×distribute-lft-out
1485×add-sqr-sqrt add-cube-cbrt
812×cbrt-prod
260×div-inv
210×associate-/r*
89×associate-/r/
61×add-exp-log
43×flip3-+ flip-+
42×div-exp
31×add-cbrt-cube
24×cbrt-undiv
7×associate-/l*
6×cbrt-div 1-exp prod-exp
4×pow1 insert-posit16 add-log-exp
3×pow1/3 cbrt-unprod
1×clear-num frac-2neg associate-/l/
Counts
4 → 1769
Calls
4 calls:
Slowest
210.0ms
(/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) (/ (+ 2 (+ beta alpha)) (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))))
35.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
33.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
28.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
219.0ms
(/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) (/ (+ 2 (+ beta alpha)) (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))))
103.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
86.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
75.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify5.2s

Counts
1781 → 1781

prune28.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.9b

localize68.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
1.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
1.9b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.6b
(* (/ (* (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))) 1) (/ (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
3694×*-un-lft-identity
2308×times-frac
1875×distribute-lft-out
840×associate-*r*
825×cbrt-prod
693×add-sqr-sqrt
647×add-cube-cbrt
80×associate-/r/
43×flip3-+ add-exp-log flip-+
41×div-inv
24×add-cbrt-cube
16×div-exp
15×associate-/r* unswap-sqr
14×prod-exp
12×associate-/l*
10×cbrt-undiv
8×cbrt-unprod
7×associate-*l*
6×pow1 associate-/l/
4×1-exp insert-posit16 add-log-exp
3×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 1029
Calls
4 calls:
Slowest
999.0ms
(* (/ (* (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))) 1) (/ (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))
177.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
174.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
164.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series594.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(* (/ (* (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))) 1) (/ (cbrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2)))
128.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
113.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
94.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.5s

Counts
1041 → 1041

prune18.1s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.9b

regimes117.0ms

Accuracy

0% (2.2b remaining)

Error of 3.3b against oracle of 1.1b and baseline of 3.3b

bsearch3.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.2s8000×body80valid
308.0ms8000×pre80true