Details

Time bar (total: 11.5s)

sample36.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
5.0ms256×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: 50.0b

Counts
2 → 2

localize18.0ms

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)))
39.5b
(/ (* 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)))))
40.0b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp prod-exp cbrt-unprod
16×add-sqr-sqrt times-frac
13×add-cube-cbrt *-un-lft-identity
11×pow1
10×associate-*l/ associate-/r*
6×associate-*r*
5×associate-*l*
4×expm1-log1p-u pow-prod-down fma-udef log1p-expm1-u div-inv associate-/l/ add-log-exp
3×flip3-- flip--
2×distribute-rgt-in frac-2neg distribute-lft-in associate-*r/ clear-num *-commutative associate-/l*
1×flip3-+ associate-/r/ flip-+ difference-of-squares unswap-sqr
Counts
4 → 122
Calls
4 calls:
16.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
15.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
23.0ms
(/ (* 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)))))
18.0ms
(/ (* (* (- (* (+ (+ 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:
713.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
264.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
752.0ms
(/ (* 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)))))
1.8s
(/ (* (* (- (* (+ (+ 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))))

simplify53.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
07943237
150022435

prune428.0ms

Filtered
134 candidates to 97 candidates (72.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1295134
Fresh011
Picked101
Done000
Total1306136

Merged error: 43.7b

Counts
136 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
0.0b
(* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
7.3b
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
39.6b
(* (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
37×times-frac
36×add-sqr-sqrt
34×add-exp-log add-cbrt-cube
29×add-cube-cbrt
22×associate-*r*
21×distribute-lft-out
12×associate-*l*
10×cbrt-undiv div-exp prod-exp cbrt-unprod
8×pow1
6×associate-/r* associate-/l*
4×expm1-log1p-u associate-/r/ log1p-expm1-u div-inv add-log-exp
3×flip3-+ flip-+ associate-/l/ unswap-sqr
2×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative fma-udef
1×distribute-rgt-in distribute-lft-in associate-*l/
Counts
4 → 142
Calls
4 calls:
8.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
16.0ms
(* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
20.0ms
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
23.0ms
(* (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
90.0ms
(* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
367.0ms
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
950.0ms
(* (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify110.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06142353
136561904
250031872

prune462.0ms

Filtered
154 candidates to 105 candidates (68.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1540154
Fresh055
Picked011
Done000
Total1546160

Merged error: 43.7b

Counts
160 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
33.9b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
33.9b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
41.3b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
211×times-frac
208×*-un-lft-identity
115×associate-*r*
113×add-sqr-sqrt
98×add-cube-cbrt
66×distribute-lft-out
52×sqrt-prod
45×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-*l*
8×pow1 div-inv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 215
Calls
4 calls:
56.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (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))))
15.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
1000.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
61.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
55.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
477.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
011075954
150015104

prune630.0ms

Filtered
227 candidates to 126 candidates (55.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2270227
Fresh044
Picked011
Done011
Total2276233

Merged error: 43.7b

Counts
233 → 6

localize16.0ms

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))))
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))
45.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite94.0ms

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×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u 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 → 197
Calls
4 calls:
8.0ms
(* i (+ (+ alpha beta) i))
12.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
41.0ms
(/ (/ (* (* 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))
24.0ms
(/ (* (* 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))
101.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
734.0ms
(/ (/ (* (* 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))
171.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify73.0ms

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012345451
150014923

prune590.0ms

Filtered
209 candidates to 148 candidates (70.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2036209
Fresh213
Picked101
Done112
Total2078215

Merged error: 35.7b

Counts
215 → 8

regimes131.0ms

Accuracy

46.7% (2.0b remaining)

Error of 37.9b against oracle of 36.0b and baseline of 39.7b

bsearch65.0ms

Steps
ItersRangePoint
9
1.808064167017952e+153
8.186102315163911e+158
6.474542841003852e+153

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03432
13432

end0.0ms

sample689.0ms

Algorithm
intervals
Results
372.0ms8000×body80valid
134.0ms8000×pre80true