Details

Time bar (total: 24.8s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify38.0ms

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: 54.2b

localize14.0ms

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))))
38.0b
(/ (/ (* (* 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))
46.1b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite344.0ms

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)))
49.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
132.0ms
(/ (/ (* (* 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))
70.0ms
(/ (* (* 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:
61.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
108.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
755.0ms
(/ (/ (* (* 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))
187.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify76.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012495670
150015161

prune648.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.4b

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))))
36.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite685.0ms

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:
132.0ms
(/ (/ (+ (* 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))))
63.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.0s

Counts
4 → 12
Calls
4 calls:
466.0ms
(/ (/ (+ (* 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))))
120.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify116.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0168710749
150019903

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.4b

localize21.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (/ (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)))))
36.3b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.3b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite705.0ms

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:
175.0ms
(/ (/ (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)))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series541.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (/ (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)))))
59.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
54.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
91.0ms
(/ (* 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

prune9.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
36.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
36.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite540.0ms

Algorithm
rewrite-expression-head
Rules
166×times-frac
145×add-sqr-sqrt
110×*-un-lft-identity
96×associate-*r*
94×add-exp-log add-cbrt-cube
76×add-cube-cbrt
43×cbrt-undiv div-exp
30×difference-of-squares
25×prod-exp cbrt-unprod
22×associate-/r/
15×sqrt-prod distribute-lft-out--
12×flip3-+ flip-+
11×div-inv
10×associate-/r*
9×associate-*l*
7×associate-/l/
6×pow1
5×associate-/l*
4×associate-*r/ add-log-exp
3×frac-2neg clear-num unswap-sqr
2×frac-times associate-*l/ distribute-lft-out
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 238
Calls
4 calls:
162.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
268.0ms
(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
62.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
35.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.1s

Counts
4 → 12
Calls
4 calls:
2.2s
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
646.0ms
(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
118.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
87.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify77.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013696476
150015398

prune670.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 35.4b

regimes133.0ms

Accuracy

35.4% (2.4b remaining)

Error of 36.6b against oracle of 34.3b and baseline of 37.9b

bsearch44.0ms

Steps
ItersRangePoint
7
8.300760801844528e+223
2.701294951651229e+225
8.391679193531258e+223

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03329
13329

end0.0ms

sample660.0ms

Algorithm
intervals
Results
348.0ms8000×body80valid
123.0ms8000×pre80true