Details

Time bar (total: 3.2m)

sample78.0ms

Algorithm
intervals
Results
26.0ms213×body80valid
12.0ms19×body1280valid
10.0ms256×pre80true
4.0ms11×body320valid
4.0ms7×body640valid
1.0ms6×body160valid

simplify123.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
122.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize39.0ms

Local error

Found 3 expressions with local error:

19.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.6b
(+ (/ (/ (* (+ 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))

rewrite768.0ms

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
521.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
190.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
54.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series817.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
384.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
303.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
130.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify25.7s

Counts
128 → 123
Calls
128 calls:
Slowest
682.0ms
(/ (* (* (/ (* (+ 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)))
652.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
643.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
602.0ms
(* (+ (pow alpha 3) (pow beta 3)) (- (pow beta 3) (pow alpha 3)))
583.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize28.0ms

Local error

Found 4 expressions with local error:

3.5b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.4b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite569.0ms

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
322.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
111.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
94.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
35.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series938.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
351.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
257.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
210.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
120.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.1m

Counts
368 → 311
Calls
368 calls:
Slowest
1.3s
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
1.1s
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
987.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
962.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
711.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize50.0ms

Local error

Found 4 expressions with local error:

3.5b
(+ (* (+ beta alpha) (/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.4b
(* (+ beta alpha) (/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ alpha (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
212×times-frac
202×*-un-lft-identity
183×add-sqr-sqrt
70×add-cube-cbrt
62×associate-*r*
42×associate-/r/
36×distribute-lft-out-- difference-of-squares
30×distribute-lft-out
27×distribute-rgt-out--
24×flip3-+ flip-+
21×div-inv
17×associate-/l*
13×add-cbrt-cube add-exp-log
7×associate-/r*
6×pow1 add-log-exp
4×associate-*l* insert-posit16 associate-/l/
3×cbrt-undiv div-exp
2×frac-times clear-num frac-2neg associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-- div-sub pow-prod-down associate-*r/ *-commutative frac-sub flip-- sub-div
Counts
4 → 223
Calls
4 calls:
Slowest
764.0ms
(* (+ beta alpha) (/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
439.0ms
(/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
203.0ms
(+ (* (+ beta alpha) (/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
34.0ms
(/ alpha (+ (+ alpha beta) (* 2 i)))

series872.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
316.0ms
(* (+ beta alpha) (/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
245.0ms
(+ (* (+ beta alpha) (/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
203.0ms
(/ (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
107.0ms
(/ alpha (+ (+ alpha beta) (* 2 i)))

simplify38.7s

Counts
257 → 235
Calls
257 calls:
Slowest
908.0ms
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i)))) (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i))))) (- (/ beta (+ (+ alpha beta) (* 2 i))) (/ alpha (+ (+ alpha beta) (* 2 i))))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
746.0ms
(/ (/ beta (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
674.0ms
(/ (- (/ (sqrt beta) (sqrt (+ (+ alpha beta) (* 2 i)))) (/ (sqrt alpha) (sqrt (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
504.0ms
(/ (- (/ beta (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))) (/ alpha (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
441.0ms
(/ (- (/ beta (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))) (/ alpha (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize59.0ms

Local error

Found 4 expressions with local error:

3.5b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
3.5b
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
1.4b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
0.3b
(/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
151×*-un-lft-identity
116×add-sqr-sqrt
90×associate-*r*
75×add-cube-cbrt
22×distribute-lft-out
16×distribute-lft-out-- difference-of-squares
15×add-cbrt-cube add-exp-log
12×associate-/r/
9×flip3-+ flip-+
7×pow1
6×div-inv add-log-exp
5×associate-/l*
4×cbrt-undiv log-prod div-exp associate-*l* log-pow insert-posit16
3×exp-prod associate-/r* prod-exp cbrt-unprod unswap-sqr
2×frac-times associate-*l/ associate-/l/
1×+-commutative clear-num sum-log frac-2neg flip3-- div-sub rem-log-exp exp-sum pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 188
Calls
4 calls:
Slowest
288.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
27.0ms
(/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))
20.0ms
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
7.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
410.0ms
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
383.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
299.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
103.0ms
(/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))

simplify36.4s

Counts
175 → 200
Calls
175 calls:
Slowest
965.0ms
(* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (/ (* (* (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))) (/ (- beta alpha) (+ (* 2 i) (+ alpha beta)))) (* (* (+ 2.0 (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
733.0ms
(/ (/ (- beta alpha) (cbrt (+ (* 2 i) (+ alpha beta)))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))
711.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
705.0ms
(/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))
678.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

regimes361.0ms

Accuracy

14.7% (5.3b remaining)

Error of 11.1b against oracle of 5.7b and baseline of 12.0b

bsearch163.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.7s6408×body80valid
393.0ms8000×pre80true
388.0ms566×body640valid
352.0ms497×body1280valid
195.0ms340×body320valid
55.0ms189×body160valid