Details

Time bar (total: 3.2m)

sample112.0ms

Algorithm
intervals
Results
38.0ms210×body80valid
19.0ms256×pre80true
13.0ms18×body640valid
13.0ms14×body1280valid
4.0ms7×body320valid
2.0ms7×body160valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize41.0ms

Local error

Found 3 expressions with local error:

21.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.1b
(+ (/ (/ (* (+ 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))

rewrite737.0ms

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
499.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
193.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
42.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series867.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
414.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
338.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
115.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify34.2s

Counts
165 → 123
Calls
165 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))))
702.0ms
(/ (* (* (/ (* (+ 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)))
685.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
646.0ms
(/ (* (cbrt (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (cbrt (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))))) 1)
633.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

3.0b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.2b
(* (+ 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)))

rewrite674.0ms

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
380.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
173.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
75.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
39.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series946.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
367.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
240.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
211.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
127.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.4m

Counts
419 → 311
Calls
419 calls:
Slowest
1.4s
(* (* (* (+ 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))))
1.2s
(/ (/ (* (* (- 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)))
796.0ms
(* (sqrt (+ beta alpha)) (sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
746.0ms
(* (+ beta alpha) (sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
706.0ms
(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

prune3.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize43.0ms

Local error

Found 4 expressions with local error:

3.8b
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0))
3.0b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0)
2.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
0.2b
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0)))

rewrite517.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
134×*-un-lft-identity
99×add-sqr-sqrt
90×associate-*r*
66×add-cube-cbrt
22×distribute-lft-out
14×add-exp-log
13×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+
8×pow1
6×log-prod add-log-exp
5×div-inv
4×log-div exp-prod associate-*l* insert-posit16
3×cbrt-undiv div-exp exp-sum prod-exp cbrt-unprod unswap-sqr
2×frac-times exp-diff associate-*l/ log-pow
1×+-commutative sum-log rem-log-exp pow-prod-down associate-*r/ *-commutative rem-exp-log
Counts
4 → 163
Calls
4 calls:
Slowest
220.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
101.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0))
97.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0)))
91.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0)

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
787.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0))
413.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0)))
397.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))) 1.0)
359.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))

simplify42.9s

Counts
188 → 175
Calls
188 calls:
Slowest
1.0s
(* (* (* (+ 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))))))
710.0ms
(* (+ alpha beta) (/ (/ (+ (sqrt beta) (sqrt alpha)) 1) (* (cbrt (+ 2.0 (+ (* 2 i) (+ alpha beta)))) (cbrt (+ 2.0 (+ (* 2 i) (+ alpha beta)))))))
685.0ms
(* (sqrt (+ alpha beta)) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))
681.0ms
(* (sqrt (+ alpha beta)) (sqrt (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta))))))
668.0ms
(* (cbrt (+ alpha beta)) (/ (/ (- beta alpha) (+ (* 2 i) (+ alpha beta))) (+ 2.0 (+ (* 2 i) (+ alpha beta)))))

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize86.0ms

Local error

Found 4 expressions with local error:

8.6b
(+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.5b
(cbrt (+ (+ alpha beta) (* 2 i)))
0.5b
(cbrt (+ (* 2 i) (+ alpha beta)))
0.5b
(cbrt (+ (* 2 i) (+ alpha beta)))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×pow1/3
1×+-commutative sum-log
Counts
4 → 54
Calls
4 calls:
Slowest
120.0ms
(+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
15.0ms
(cbrt (+ (* 2 i) (+ alpha beta)))
11.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
9.0ms
(cbrt (+ (* 2 i) (+ alpha beta)))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
498.0ms
(+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
341.0ms
(cbrt (+ (* 2 i) (+ alpha beta)))
340.0ms
(cbrt (+ (* 2 i) (+ alpha beta)))
195.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))

simplify12.8s

Counts
79 → 66
Calls
79 calls:
Slowest
717.0ms
(* (exp (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (exp 1.0))
565.0ms
(* (* (+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0) (+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)) (+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
534.0ms
(sqrt (+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
522.0ms
(- (* (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* 1.0 1.0))
491.0ms
(log (+ (* (/ (/ (+ alpha beta) (cbrt (+ (* 2 i) (+ alpha beta)))) (cbrt (+ (* 2 i) (+ alpha beta)))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))

prune917.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes313.0ms

Accuracy

9.2% (7.3b remaining)

Error of 11.4b against oracle of 4.2b and baseline of 12.2b

bsearch108.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s6408×body80valid
849.0ms8000×pre80true
362.0ms586×body640valid
353.0ms463×body1280valid
238.0ms341×body320valid
87.0ms202×body160valid