Details

Time bar (total: 12.7s)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×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: 55.0b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.5b
(/ (/ (* (* 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))
46.8b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
48×flip3-+ flip-+
39×add-sqr-sqrt
32×frac-times
28×associate-*r/
24×add-cube-cbrt *-un-lft-identity
21×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
15×difference-of-squares
14×associate-/l*
9×pow1 associate-/l/
7×div-inv
6×add-log-exp
5×associate-/r*
3×associate-*r* pow-prod-down
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in associate--l+ clear-num flip--
1×sub-neg diff-log associate-*l* *-commutative
Counts
4 → 180
Calls
4 calls:
12.0ms
(- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
40.0ms
(/ (/ (* (* 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))
28.0ms
(/ (* (* 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:
116.0ms
(- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)
118.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
741.0ms
(/ (/ (* (* 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))
172.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify70.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012225512
150024999

prune553.0ms

Filtered
192 candidates to 137 candidates (71.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1866192
Fresh000
Picked101
Done000
Total1876193

Merged error: 37.2b

Counts
193 → 6

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))))
38.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite164.0ms

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:
23.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
96.0ms
(* (/ (/ (* 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))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.7s

Counts
4 → 12
Calls
4 calls:
328.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
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))))
82.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
113.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify129.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0168310749
150019903

prune1.1s

Filtered
376 candidates to 246 candidates (65.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3715376
Fresh235
Picked101
Done000
Total3748382

Merged error: 37.2b

Counts
382 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
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))))
38.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
328×times-frac
280×add-sqr-sqrt
231×*-un-lft-identity
147×add-cube-cbrt
96×associate-*r*
67×add-exp-log add-cbrt-cube
62×difference-of-squares
36×associate-/r/
31×sqrt-prod distribute-lft-out--
29×cbrt-undiv div-exp
23×associate-/l*
18×flip3-+ prod-exp cbrt-unprod flip-+ div-inv
13×distribute-lft-out
12×associate-/r*
10×associate-*l*
6×pow1
5×associate-/l/
4×add-log-exp
3×frac-2neg clear-num unswap-sqr
2×flip3-- flip--
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 343
Calls
4 calls:
12.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
21.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
66.0ms
(* (/ (* 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))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.8s

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
335.0ms
(/ (/ (+ (* 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))))
118.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify117.0ms

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
015129787
150028932

prune1.0s

Filtered
355 candidates to 225 candidates (63.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3514355
Fresh527
Picked101
Done000
Total3576363

Merged error: 1.8b

Counts
363 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
0.0b
(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.0b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
85×*-un-lft-identity
60×add-sqr-sqrt
58×times-frac
52×add-exp-log add-cbrt-cube
45×associate-*r*
38×add-cube-cbrt
24×distribute-lft-out
18×cbrt-undiv div-exp
16×prod-exp cbrt-unprod
13×associate-*l*
10×associate-/r/
8×pow1
7×associate-/r*
6×associate-/l* difference-of-squares
5×flip3-+ flip-+ div-inv
4×add-log-exp unswap-sqr
3×associate-*r/ sqrt-prod associate-/l/ distribute-lft-out--
2×frac-2neg pow-prod-down clear-num *-commutative
1×frac-times flip3-- associate-*l/ flip--
Counts
4 → 171
Calls
4 calls:
15.0ms
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
19.0ms
(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
15.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
38.0ms
(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))

series861.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
253.0ms
(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
70.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
451.0ms
(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))

simplify73.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
08503435
150022823

prune508.0ms

Filtered
183 candidates to 116 candidates (63.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1803183
Fresh055
Picked101
Done000
Total1818189

Merged error: 1.8b

Counts
189 → 8

regimes159.0ms

Accuracy

33.8% (10.4b remaining)

Error of 12.4b against oracle of 2.0b and baseline of 17.8b

bsearch113.0ms

Steps
ItersRangePoint
7
1.5202990653133135e+149
1.3782502442810265e+151
7.028642830168402e+149
6
6.115752296648957e+121
5.5055953206439605e+122
2.8836921855725802e+122

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06177
16177

end0.0ms

sample654.0ms

Algorithm
intervals
Results
348.0ms8000×body80valid
126.0ms8000×pre80true