Details

Time bar (total: 10.3s)

sample40.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
6.0ms256×pre80true

simplify39.0ms

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: 52.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.2b
(/ (/ (* (* 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))
44.9b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
36.0ms
(* i (+ (+ alpha beta) i))
49.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
111.0ms
(/ (/ (* (* 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))
68.0ms
(/ (* (* 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:
22.0ms
(* i (+ (+ alpha beta) i))
105.0ms
(* (* 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))
175.0ms
(/ (* (* 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
201 → 201
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012085419
150014944

prune610.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 30.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 252
Calls
4 calls:
129.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
100.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
33.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
59.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series765.0ms

Counts
4 → 12
Calls
4 calls:
323.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
240.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
85.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
118.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify76.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010985877
150015622

prune840.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 30.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
33.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
336×times-frac
325×*-un-lft-identity
218×add-sqr-sqrt
154×add-cube-cbrt
79×distribute-lft-out
44×associate-/l*
32×associate-/r/ difference-of-squares
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
8×cbrt-undiv div-exp
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
1×flip3-- flip--
Counts
4 → 324
Calls
4 calls:
116.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
130.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
45.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
62.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series932.0ms

Counts
4 → 12
Calls
4 calls:
412.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
338.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
66.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
115.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify88.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011457347
150017126

prune979.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
0.2b
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.2b
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
400×*-un-lft-identity
339×times-frac
176×add-sqr-sqrt
151×add-cube-cbrt
136×distribute-lft-out
90×associate-*r*
29×associate-/l*
26×associate-/r/
22×add-exp-log add-cbrt-cube
14×flip3-+ flip-+
13×associate-/r* div-inv
8×cbrt-undiv div-exp difference-of-squares
6×pow1
5×associate-/l/
4×sqrt-prod distribute-lft-out-- add-log-exp
3×frac-2neg associate-*l* prod-exp clear-num cbrt-unprod unswap-sqr
1×flip3-- associate-*r/ pow-prod-down *-commutative flip--
Counts
4 → 320
Calls
4 calls:
215.0ms
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
117.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
80.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
49.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

series741.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(* i (/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
270.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
161.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
68.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

simplify73.0ms

Algorithm
egg-herbie
Counts
332 → 332
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010475670
150015398

prune918.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.1b

regimes204.0ms

Accuracy

21.4% (10.2b remaining)

Error of 12.2b against oracle of 2.0b and baseline of 15.0b

bsearch229.0ms

Steps
ItersRangePoint
7
4.614439106502894e+145
1.1963549483378118e+147
4.534879616570057e+146
7
1.05606416635184e+81
3.7954374245748784e+82
2.765625260352107e+81
7
1.523107952296189e+43
6.970986088846087e+44
6.893104695094826e+44

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
070157
170157

end0.0ms

sample1.0s

Algorithm
intervals
Results
680.0ms8000×body80valid
174.0ms8000×pre80true