Details

Time bar (total: 55.8s)

sample30.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune10.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.7b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
38.7b
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
42.7b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite506.0ms

Algorithm
rewrite-expression-head
Rules
3026×times-frac
2577×associate-*l*
2573×*-un-lft-identity
2204×add-sqr-sqrt
1117×add-cube-cbrt
829×associate-*r*
624×distribute-lft-out
361×unswap-sqr
312×distribute-lft-out--
260×difference-of-squares
259×*-commutative
109×associate-/r*
80×associate-/l*
52×add-exp-log swap-sqr add-cbrt-cube
41×associate-/r/
17×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
14×associate-*l/
11×pow1
6×associate-/l/
4×expm1-log1p-u flip3-- pow-prod-down flip-- fma-udef log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×distribute-rgt-in distribute-lft-in associate-*r/
1×flip3-+ flip-+
Counts
4 → 1868
Calls
4 calls:
52.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
41.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
115.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
60.0ms
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.6s

Counts
4 → 12
Calls
4 calls:
505.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
266.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
802.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
2.0s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify607.0ms

Algorithm
egg-herbie
Counts
1880 → 1880
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0500166446

prune4.6s

Filtered
1880 candidates to 878 candidates (46.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New187191880
Fresh101
Picked101
Done000
Total187391882

Merged error: 35.4b

Counts
1882 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.5b
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
36.8b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))
38.8b
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite3.4s

Algorithm
rewrite-expression-head
Rules
46702×times-frac
41320×*-un-lft-identity
25036×add-sqr-sqrt
15164×add-cube-cbrt
11700×distribute-lft-out
8152×associate-*l*
4992×distribute-lft-out--
4160×difference-of-squares
3160×swap-sqr
2328×associate-*r*
1608×*-commutative unswap-sqr
1557×associate-/r/
1020×associate-/l*
467×associate-/r*
466×div-inv
186×associate-/l/
156×flip3-+ flip-+
57×frac-2neg clear-num
52×add-exp-log flip3-- add-cbrt-cube flip--
30×cbrt-undiv div-exp
4×pow1 expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
1×div-sub
Counts
4 → 13516
Calls
4 calls:
391.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
60.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
57.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))
8.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
776.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
137.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
143.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))
145.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify5.8s

Algorithm
egg-herbie
Counts
13528 → 13528
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
06951605701

prune21.1s

Filtered
13528 candidates to 3493 candidates (25.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New13522613528
Fresh808
Picked101
Done000
Total13531613537

Merged error: 33.9b

Counts
13537 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.3b
(/ (* (fma i 2.0 (+ alpha beta)) 1) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
34.6b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.6b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
93×add-sqr-sqrt
77×*-un-lft-identity
70×add-cube-cbrt
60×sqrt-prod
21×associate-*r* associate-*l*
16×associate-/l*
14×unswap-sqr
13×add-exp-log
12×associate-/r*
11×add-cbrt-cube
7×*-commutative
6×pow1
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×cbrt-undiv
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num div-inv
1×1-exp cbrt-unprod
Counts
4 → 185
Calls
4 calls:
9.0ms
(/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
9.0ms
(/ (* (fma i 2.0 (+ alpha beta)) 1) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
2.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series521.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
203.0ms
(/ (* (fma i 2.0 (+ alpha beta)) 1) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
64.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
57.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify71.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04442633
115442445
250022406

prune630.0ms

Filtered
197 candidates to 102 candidates (51.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1961197
Fresh145
Picked011
Done000
Total1976203

Merged error: 33.9b

Counts
203 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.3b
(/ (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma i 2.0 (+ alpha beta))) 1))
37.2b
(/ (* (sqrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
11337×*-un-lft-identity
10140×times-frac
5010×add-sqr-sqrt
4003×distribute-lft-out
3242×add-cube-cbrt
1736×associate-*l*
1330×distribute-lft-out--
1252×sqrt-prod
532×difference-of-squares
528×associate-*r*
352×unswap-sqr
188×associate-/r/
176×*-commutative
168×div-inv
135×associate-/l*
109×associate-/r*
53×flip3-- flip--
49×add-exp-log
44×add-cbrt-cube
36×associate-/l/
29×div-exp
25×flip3-+ flip-+
24×cbrt-undiv
8×frac-2neg clear-num
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod
2×1-exp
Counts
4 → 3980
Calls
4 calls:
16.0ms
(/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
116.0ms
(/ (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
46.0ms
(/ (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma i 2.0 (+ alpha beta))) 1))
9.0ms
(/ (* (sqrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series2.3s

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.7s
(/ (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
310.0ms
(/ (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma i 2.0 (+ alpha beta))) 1))
165.0ms
(/ (* (sqrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.2s

Algorithm
egg-herbie
Counts
3992 → 3992
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
05002136603

prune7.7s

Filtered
3992 candidates to 1083 candidates (27.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New399203992
Fresh044
Picked011
Done011
Total399263998

Merged error: 33.9b

Counts
3998 → 6

regimes156.0ms

Accuracy

38.3% (2.5b remaining)

Error of 36.1b against oracle of 33.7b and baseline of 37.7b

bsearch94.0ms

Steps
ItersRangePoint
9
7.825171098728971e+194
9.349810284037199e+201
1.2841752931646873e+195

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04447
14647
24647

end0.0ms

sample1.0s

Algorithm
intervals
Results
408.0ms8000×body80valid
406.0ms8000×pre80true