Details

Time bar (total: 16.0s)

sample45.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
6.0ms256×pre80true

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.0b

localize15.0ms

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))))
37.3b
(/ (/ (* (* 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))
46.9b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite311.0ms

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:
71.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
49.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
113.0ms
(/ (/ (* (* 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:
65.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
112.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
773.0ms
(/ (/ (* (* 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))
185.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify74.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012495670
150015161

prune664.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.8b

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))))
35.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite686.0ms

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:
133.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
435.0ms
(* (/ (/ (* 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))))
31.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
63.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.0s

Counts
4 → 12
Calls
4 calls:
338.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.5s
(* (/ (/ (* 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))))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
124.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify120.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0168310749
150019903

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 35.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
2499×times-frac
1610×add-sqr-sqrt
1254×*-un-lft-identity
938×add-cube-cbrt
921×sqrt-prod
900×associate-*r*
298×difference-of-squares
149×distribute-lft-out--
92×associate-/r/
89×add-exp-log add-cbrt-cube
76×sqrt-div
49×div-inv
46×cbrt-undiv div-exp
45×flip3-+ flip-+
42×associate-*l*
21×prod-exp cbrt-unprod
16×unswap-sqr
9×distribute-lft-out
8×pow1
4×add-log-exp
3×associate-*r/ associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times flip3-- frac-2neg pow-prod-down associate-*l/ clear-num *-commutative flip-- associate-/l*
Counts
4 → 1057
Calls
4 calls:
973.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series2.6s

Counts
4 → 12
Calls
4 calls:
2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
61.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
57.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify402.0ms

Algorithm
egg-herbie
Counts
1069 → 1069
Iterations

Useful iterations: 1 (83.0ms)

IterNodesCost
0484540896
1500240086

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 35.8b

localize23.0ms

Local error

Found 4 expressions with local error:

35.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
6×pow1 flip3-+ times-frac associate-/r* sqrt-prod flip-+
4×cbrt-undiv sqrt-div associate-*r/ div-exp associate-/r/ associate-/l/ add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
31.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
56.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
60.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify49.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0334846
11681748
25002746

prune423.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 35.8b

regimes181.0ms

Accuracy

33.6% (2.5b remaining)

Error of 37.0b against oracle of 34.5b and baseline of 38.3b

bsearch48.0ms

Steps
ItersRangePoint
5
1.0843359009408716e+196
3.0836636868756157e+196
1.1060840850187772e+196

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04270
14270

end0.0ms

sample1.0s

Algorithm
intervals
Results
684.0ms8000×body80valid
181.0ms8000×pre80true