Details

Time bar (total: 5.4m)

sample101.0ms

Algorithm
intervals
Results
27.0ms198×body80valid
12.0ms18×body1280valid
11.0ms256×pre80true
10.0ms15×body640valid
10.0ms8×body160valid
8.0ms17×body320valid

simplify125.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
125.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize40.0ms

Local error

Found 3 expressions with local error:

18.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
3.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite824.0ms

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
553.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
216.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
52.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series799.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
356.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
312.0ms
(/ (/ (* (+ 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
710.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
707.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
693.0ms
(/ (* (* (/ (* (+ 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)))
691.0ms
(- (- (log (* (+ alpha beta) (- beta alpha))) (log (+ (+ alpha beta) (* 2 i)))) (log (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
606.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.3b

localize51.0ms

Local error

Found 4 expressions with local error:

5.2b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.6b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite652.0ms

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
350.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
141.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
112.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
39.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series934.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
337.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
248.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
242.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
108.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.2m

Counts
368 → 311
Calls
368 calls:
Slowest
1.2s
(* (* (* (+ 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 alpha)) (sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
1.0s
(/ (/ (* (* (- 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)))
976.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
702.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.2b

localize66.0ms

Local error

Found 4 expressions with local error:

5.2b
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
5.2b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
0.6b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
0.0b
(/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))

rewrite393.0ms

Algorithm
rewrite-expression-head
Rules
306×times-frac
274×*-un-lft-identity
195×add-sqr-sqrt
132×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
27×distribute-lft-out-- difference-of-squares
22×associate-/r/
21×associate-/l*
18×add-cbrt-cube add-exp-log
14×flip3-+ flip-+
11×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×log-prod associate-/r* associate-*l* log-pow insert-posit16
3×exp-prod prod-exp cbrt-unprod unswap-sqr
2×frac-times div-sub associate-*l/
1×+-commutative clear-num sum-log frac-2neg rem-log-exp exp-sum pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
4 → 275
Calls
4 calls:
Slowest
250.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
101.0ms
(/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))
28.0ms
(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))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
435.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
430.0ms
(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))))
337.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
249.0ms
(/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))

simplify1.2m

Counts
332 → 287
Calls
332 calls:
Slowest
1.2s
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) (+ (* 2 i) (+ alpha beta)))) (* (* (+ 2.0 (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
983.0ms
(* (* (* (+ 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))))))
753.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
726.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
721.0ms
(/ (/ (- beta alpha) (+ (pow (* 2 i) 3) (pow (+ alpha beta) 3))) 1)

prune4.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.2b

localize34.0ms

Local error

Found 4 expressions with local error:

8.9b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.2b
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1015×times-frac
755×*-un-lft-identity
655×add-sqr-sqrt
413×add-cube-cbrt
333×sqrt-prod
153×associate-*r*
121×distribute-lft-out
118×associate-*l*
64×add-exp-log
50×add-cbrt-cube
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
37×associate-/l*
35×div-exp unswap-sqr
34×div-inv
24×cbrt-undiv
20×flip3-+ flip-+
14×associate-/r*
12×prod-exp
9×cbrt-unprod
8×sqrt-div
6×pow1 add-log-exp
4×1-exp insert-posit16
2×clear-num frac-2neg div-sub associate-/l/
1×frac-times +-commutative sum-log pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 700
Calls
4 calls:
Slowest
566.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
197.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
137.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
135.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
425.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
324.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
281.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
182.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify2.1m

Counts
962 → 712
Calls
962 calls:
Slowest
1.0s
(* (/ (* (* (/ (+ alpha beta) 1) (/ (+ alpha beta) 1)) (/ (+ alpha beta) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
820.0ms
(* (/ (/ (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* 1 1) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
734.0ms
(* (* (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
647.0ms
(* (/ (/ (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* 1 1) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (* (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
588.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))

prune10.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

regimes480.0ms

Accuracy

13.1% (5.5b remaining)

Error of 11.5b against oracle of 6.1b and baseline of 12.4b

bsearch178.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s6351×body80valid
446.0ms514×body1280valid
405.0ms8000×pre80true
403.0ms552×body640valid
214.0ms371×body320valid
62.0ms212×body160valid