Details

Time bar (total: 6.6s)

sample38.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
5.0ms256×pre80true

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.8b

Counts
2 → 1

localize15.0ms

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))))
35.7b
(/ (/ (* (* 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))))

rewrite90.0ms

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:
13.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.0ms
(/ (/ (* (* 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))
22.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
23.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
391.0ms
(/ (/ (* (* 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))
52.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify96.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
012495670
150015161

prune503.0ms

Filtered
143 candidates to 212 candidates (-48.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2048212
Fresh000
Picked101
Done000
Total2058213

Merged error: 33.9b

Counts
213 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* 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))))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
264×times-frac
191×add-sqr-sqrt
178×*-un-lft-identity
110×add-cube-cbrt
96×associate-*r*
74×add-exp-log add-cbrt-cube
42×associate-*l*
40×associate-/r/
35×cbrt-undiv div-exp
30×difference-of-squares
21×flip3-+ flip-+
20×div-inv
19×distribute-lft-out
17×prod-exp cbrt-unprod
15×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r*
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 304
Calls
4 calls:
19.0ms
(/ (/ (* 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))))
14.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
373.0ms
(* (/ (/ (* 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))))
15.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
26.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify98.0ms

Algorithm
egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015818513
150017655

prune891.0ms

Filtered
210 candidates to 316 candidates (-50.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3097316
Fresh437
Picked101
Done000
Total31410324

Merged error: 33.8b

Counts
324 → 10

localize19.0ms

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))))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite108.0ms

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:
36.0ms
(/ (* (/ (/ (* 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)))
40.0ms
(* (/ (/ (* 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))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series533.0ms

Counts
4 → 12
Calls
4 calls:
387.0ms
(/ (* (/ (/ (* 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)))
101.0ms
(* (/ (/ (* 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))))
15.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
29.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify67.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011465216
150024213

prune445.0ms

Filtered
135 candidates to 203 candidates (-50.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2012203
Fresh279
Picked101
Done000
Total2049213

Merged error: 33.8b

Counts
213 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
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))))
35.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
82×add-exp-log add-cbrt-cube
59×*-un-lft-identity
46×add-sqr-sqrt
44×times-frac
35×cbrt-undiv div-exp
33×add-cube-cbrt
24×prod-exp cbrt-unprod
15×associate-*r*
13×distribute-lft-out
12×associate-/r*
10×associate-*l* associate-/r/
9×associate-/l*
7×associate-/l/
6×pow1 flip3-+ flip-+
5×div-inv
4×add-log-exp difference-of-squares
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/ sqrt-prod distribute-lft-out-- unswap-sqr
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 171
Calls
4 calls:
12.0ms
(/ (+ (+ 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))) (/ (+ (* 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)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
12.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series716.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
566.0ms
(/ (* (/ (* 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)))
102.0ms
(* (/ (* 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))))
30.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify60.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09684517
150013534

prune332.0ms

Filtered
116 candidates to 183 candidates (-57.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1803183
Fresh448
Picked101
Done000
Total1857192

Merged error: 2.4b

Counts
192 → 7

regimes226.0ms

Accuracy

44.5% (9.1b remaining)

Error of 10.8b against oracle of 1.7b and baseline of 18.1b

bsearch19.0ms

Steps
ItersRangePoint
6
5.851278856495366e+127
3.4119510700925925e+128
3.3765035963023935e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05254
15254

end0.0ms

sample1.1s

Algorithm
intervals
Results
595.0ms8000×body80valid
173.0ms8000×pre80true

Profiling

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