Details

Time bar (total: 51.9s)

sample47.0ms

Algorithm
intervals
Results
28.0ms256×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: 52.5b

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))))
34.3b
(/ (/ (* (* 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))
45.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite336.0ms

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:
75.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
54.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
121.0ms
(/ (/ (* (* 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))
75.0ms
(/ (* (* 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)))
106.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
771.0ms
(/ (/ (* (* 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))
178.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify77.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012495670
150015161

prune795.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 31.6b

localize19.0ms

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))))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite748.0ms

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:
144.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
476.0ms
(* (/ (/ (* 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))))
35.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
68.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.8s

Counts
4 → 12
Calls
4 calls:
340.0ms
(/ (/ (+ (* 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))))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
123.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify119.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0168310749
150019903

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.6b

localize22.0ms

Local error

Found 4 expressions with local error:

6.7b
(/ (/ (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)))))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.6b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.6b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite804.0ms

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:
197.0ms
(/ (/ (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)))))
37.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
4.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
345.0ms
(/ (/ (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)))))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
56.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
63.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.4s

Algorithm
egg-herbie
Counts
3543 → 3543
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
05001182857

prune10.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 31.6b

localize28.0ms

Local error

Found 4 expressions with local error:

6.7b
(/ (/ (- (+ (+ 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)))) (cbrt 1)))
32.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.6b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.6b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
21695×times-frac
11919×add-sqr-sqrt
9949×*-un-lft-identity
7981×add-cube-cbrt
5904×sqrt-prod
2700×cbrt-prod
1968×difference-of-squares
984×distribute-lft-out--
536×associate-/r/
439×div-inv
250×flip3-+ flip-+
150×associate-/l*
43×associate-/r*
30×add-exp-log
27×add-cbrt-cube
17×cbrt-undiv div-exp
6×pow1
4×sqrt-div add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r/ clear-num
1×prod-exp cbrt-unprod
Counts
4 → 6229
Calls
4 calls:
334.0ms
(/ (/ (- (+ (+ 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)))) (cbrt 1)))
34.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series517.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(/ (/ (- (+ (+ 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)))) (cbrt 1)))
87.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
60.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
55.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify2.7s

Algorithm
egg-herbie
Counts
6241 → 6241
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
05002349706

prune25.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 31.4b

regimes105.0ms

Accuracy

30.4% (3.0b remaining)

Error of 36.4b against oracle of 33.5b and baseline of 37.7b

bsearch80.0ms

Steps
ItersRangePoint
9
8.666603980544823e+220
2.960397706491143e+226
8.747492584922012e+220

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04345
14345

end0.0ms

sample1.3s

Algorithm
intervals
Results
910.0ms8000×body80valid
199.0ms8000×pre80true