Details

Time bar (total: 11.9s)

sample42.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
9.0ms256×pre80true

simplify39.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 56.0b

Counts
2 → 1

localize14.0ms

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))))
40.1b
(/ (/ (* (* 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))
47.6b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite89.0ms

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:
8.0ms
(* i (+ (+ alpha beta) i))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.0ms
(/ (/ (* (* 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))
23.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.0s

Counts
4 → 12
Calls
4 calls:
26.0ms
(* i (+ (+ alpha beta) i))
103.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
735.0ms
(/ (/ (* (* 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))))

simplify72.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012085419
150014944

prune542.0ms

Filtered
201 candidates to 138 candidates (68.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1956201
Fresh000
Picked101
Done000
Total1966202

Merged error: 37.5b

Counts
202 → 6

localize17.0ms

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))))
39.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
39.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite166.0ms

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:
22.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
95.0ms
(* (/ (/ (* 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))))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.0s

Counts
4 → 12
Calls
4 calls:
326.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.4s
(* (/ (/ (* 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))))
114.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify122.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0168310749
150019903

prune1.0s

Filtered
376 candidates to 246 candidates (65.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3715376
Fresh325
Picked101
Done000
Total3757382

Merged error: 37.5b

Counts
382 → 7

localize18.0ms

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))) (/ (+ (* 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))))
39.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
39.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
85×add-exp-log add-cbrt-cube
79×times-frac
63×*-un-lft-identity
61×add-sqr-sqrt
42×associate-*l*
41×add-cube-cbrt
40×cbrt-undiv div-exp
21×prod-exp cbrt-unprod
18×associate-/r/
15×associate-*r*
12×associate-/r*
10×flip3-+ flip-+
9×div-inv distribute-lft-out
7×associate-/l/
6×pow1
5×associate-/l*
4×associate-*r/ add-log-exp difference-of-squares unswap-sqr
3×frac-2neg clear-num
2×frac-times associate-*l/ sqrt-prod distribute-lft-out--
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 191
Calls
4 calls:
39.0ms
(/ (* (/ (/ (* 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)))
43.0ms
(* (/ (/ (* 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))))
11.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* 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))) (+ (+ (+ 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)))
612.0ms
(* (/ (/ (* 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))))
119.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
85.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify66.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011465216
150024213

prune523.0ms

Filtered
203 candidates to 136 candidates (67.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2030203
Fresh066
Picked011
Done000
Total2037210

Merged error: 37.5b

Counts
210 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

39.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
39.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
39.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
39.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
12×associate-/r*
8×flip3-+ associate-/r/ flip-+ associate-/l/ associate-/l*
6×cbrt-undiv div-exp
4×pow1 frac-2neg associate-*r/ clear-num div-inv add-log-exp
2×prod-exp cbrt-unprod
Counts
4 → 112
Calls
4 calls:
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
13.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
113.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
85.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
86.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify56.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03541472
119031306
250011306

prune530.0ms

Filtered
124 candidates to 100 candidates (80.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1240124
Fresh055
Picked011
Done011
Total1247131

Merged error: 37.5b

Counts
131 → 7

regimes126.0ms

Accuracy

36.9% (2.3b remaining)

Error of 36.3b against oracle of 34.0b and baseline of 37.7b

bsearch58.0ms

Steps
ItersRangePoint
8
1.3478212714648215e+197
4.723273997492102e+200
1.7833663987886256e+197

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03329
13329

end0.0ms

sample767.0ms

Algorithm
intervals
Results
413.0ms8000×body80valid
175.0ms8000×pre80true

Profiling

Loading profile data...