Details

Time bar (total: 42.6s)

sample61.0ms

Algorithm
intervals
Results
19.0ms214×body80valid
11.0ms15×body1280valid
8.0ms256×pre80true
6.0ms15×body640valid
2.0ms7×body320valid
1.0ms5×body160valid

simplify598.0ms

Counts
1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize57.0ms

Local error

Found 3 expressions with local error:

18.8b
(/ (* (+ 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))

rewrite796.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-cbrt-cube add-exp-log
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- insert-posit16 flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 114
Calls
3 calls:
Slowest
543.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
185.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
66.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series808.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
358.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
336.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
114.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts
123 → 123

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize32.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.1b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-cbrt-cube add-exp-log
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l* insert-posit16
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 299
Calls
4 calls:
Slowest
475.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
334.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
161.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
31.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series864.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
321.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
263.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
188.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
90.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.9s

Counts
311 → 311

prune4.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize53.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (* (+ beta alpha) (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))) 1.0)
1.1b
(* (+ beta alpha) (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
0.4b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
0.1b
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

rewrite969.0ms

Algorithm
rewrite-expression-head
Rules
1713×times-frac
1199×*-un-lft-identity
879×add-sqr-sqrt
658×add-cube-cbrt
272×associate-*r*
170×distribute-lft-out
110×associate-/r*
99×distribute-lft-out-- difference-of-squares
76×associate-/r/
62×add-exp-log
43×div-inv
37×flip3-+ flip-+
33×div-exp
32×add-cbrt-cube
15×cbrt-undiv
10×prod-exp
7×pow1 associate-/l* unswap-sqr
6×rec-exp 1-exp add-log-exp
4×associate-*l* cbrt-unprod insert-posit16
2×frac-times clear-num frac-2neg associate-*l/ associate-/l/
1×+-commutative sum-log pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 837
Calls
4 calls:
Slowest
358.0ms
(* (+ beta alpha) (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
324.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
139.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
102.0ms
(+ (* (+ beta alpha) (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(+ (* (+ beta alpha) (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))) 1.0)
306.0ms
(* (+ beta alpha) (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
245.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
183.0ms
(/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

simplify2.0s

Counts
849 → 849

prune12.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize58.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (* (+ beta alpha) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.4b
(log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))
0.1b
(* (+ beta alpha) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.0b
(/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
351×times-frac
321×*-un-lft-identity
222×add-sqr-sqrt
220×log-pow
210×exp-prod
157×add-cube-cbrt
106×associate-*r*
52×distribute-lft-out
30×distribute-lft-out-- difference-of-squares
25×associate-/l*
24×associate-/r/
16×pow1
15×flip3-+ flip-+
12×div-inv
11×add-cbrt-cube add-exp-log
6×add-log-exp
4×associate-/r* associate-*l* insert-posit16
3×log-prod div-sub
2×frac-times cbrt-undiv log-div exp-diff div-exp associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×+-commutative clear-num sum-log frac-2neg rem-log-exp pow-prod-down associate-*r/ *-commutative
Counts
4 → 323
Calls
4 calls:
Slowest
445.0ms
(* (+ beta alpha) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
316.0ms
(/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
136.0ms
(+ (* (+ beta alpha) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
89.0ms
(log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

series893.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(* (+ beta alpha) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
231.0ms
(/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
221.0ms
(+ (* (+ beta alpha) (/ (log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
111.0ms
(log (exp (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

simplify1.9s

Counts
335 → 335

prune5.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

regimes364.0ms

Accuracy

14.7% (5.4b remaining)

Error of 11.2b against oracle of 5.9b and baseline of 12.2b

bsearch111.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s6379×body80valid
802.0ms8000×pre80true
402.0ms512×body1280valid
372.0ms555×body640valid
193.0ms357×body320valid
56.0ms197×body160valid