Details

Time bar (total: 24.4s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.9b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.1b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
73.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
52.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
119.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
69.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
103.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
759.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
181.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify71.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012495670
150015161

prune646.0ms

Filtered
212 candidates to 143 candidates (67.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 35.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite712.0ms

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-exp-log add-cbrt-cube
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 364
Calls
4 calls:
138.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
453.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
65.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series2.9s

Counts
4 → 12
Calls
4 calls:
334.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
117.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify125.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0168310749
150019903

prune1.2s

Filtered
376 candidates to 247 candidates (65.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.2b

localize22.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite976.0ms

Algorithm
rewrite-expression-head
Rules
11777×times-frac
6537×add-sqr-sqrt
5431×*-un-lft-identity
4327×add-cube-cbrt
3150×sqrt-prod
1104×difference-of-squares
552×distribute-lft-out--
313×div-inv
302×associate-/r/
152×associate-/r*
142×flip3-+ flip-+
39×add-exp-log
30×add-cbrt-cube
26×div-exp
23×associate-/l*
17×cbrt-undiv
6×pow1
4×sqrt-div add-log-exp
3×1-exp associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num
1×prod-exp cbrt-unprod
Counts
4 → 3531
Calls
4 calls:
182.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
335.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
57.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
54.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.5s

Algorithm
egg-herbie
Counts
3543 → 3543
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
05001182857

prune9.5s

Filtered
3543 candidates to 1510 candidates (42.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ 1 (* (cbrt 1) (cbrt 1))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (cbrt 1)) (+ (+ alpha beta) (* 2.0 i))))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite793.0ms

Algorithm
rewrite-expression-head
Rules
1201×times-frac
878×add-sqr-sqrt
470×*-un-lft-identity
342×add-cube-cbrt
299×associate-*l*
282×sqrt-prod
237×add-exp-log
134×div-exp
126×associate-*r*
98×add-cbrt-cube
94×cbrt-prod
84×difference-of-squares
80×unswap-sqr
64×prod-exp
62×cbrt-undiv
55×div-inv
42×distribute-lft-out--
28×cbrt-unprod
19×associate-/r/
18×sqrt-div
12×rec-exp flip3-+ 1-exp flip-+
8×pow1
4×add-log-exp
3×associate-*r/ associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 638
Calls
4 calls:
688.0ms
(* (/ (/ 1 (* (cbrt 1) (cbrt 1))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (cbrt 1)) (+ (+ alpha beta) (* 2.0 i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
339.0ms
(* (/ (/ 1 (* (cbrt 1) (cbrt 1))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (cbrt 1)) (+ (+ alpha beta) (* 2.0 i))))
54.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
60.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify221.0ms

Algorithm
egg-herbie
Counts
650 → 650
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0312622609
1500121462

prune2.3s

Filtered
650 candidates to 332 candidates (51.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 35.2b

regimes135.0ms

Accuracy

33.8% (2.3b remaining)

Error of 36.7b against oracle of 34.3b and baseline of 37.9b

bsearch70.0ms

Steps
ItersRangePoint
8
6.0872930862645606e+215
3.4856391358730366e+219
6.171242914657571e+215

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04761
14761

end0.0ms

sample661.0ms

Algorithm
intervals
Results
350.0ms8000×body80valid
125.0ms8000×pre80true