Details

Time bar (total: 11.9s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune9.0ms

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

localize20.0ms

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))))

rewrite75.0ms

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)))
20.0ms
(/ (* 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))))

series3.3s

Counts
4 → 12
Calls
4 calls:
498.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
262.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
762.0ms
(/ (* 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))))

simplify45.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07943237
150022435

prune443.0ms

Filtered
134 candidates to 97 candidates (72.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1268134
Fresh011
Picked101
Done000
Total1279136

Merged error: 45.8b

Counts
136 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
9.1b
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
34.7b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (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 beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
61×add-exp-log add-cbrt-cube
47×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
34×associate-/r*
29×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
9×div-inv
6×pow1
5×associate-/l*
4×expm1-log1p-u associate-*l* associate-*l/ associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num
2×flip3-- associate-*r/ flip-- fma-udef
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down *-commutative flip-+ difference-of-squares unswap-sqr
Counts
4 → 176
Calls
4 calls:
15.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
20.0ms
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
21.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

series3.0s

Counts
4 → 12
Calls
4 calls:
266.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
1.9s
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
122.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
744.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09814480
150013634

prune617.0ms

Filtered
188 candidates to 139 candidates (73.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1817188
Fresh628
Picked011
Done000
Total18710197

Merged error: 35.4b

Counts
197 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
0.5b
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
34.7b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
36.8b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
262×times-frac
237×*-un-lft-identity
158×add-sqr-sqrt
132×add-cube-cbrt
63×distribute-lft-out
47×associate-/r*
26×difference-of-squares
18×add-exp-log add-cbrt-cube
13×associate-/l*
12×associate-/r/ div-inv
8×cbrt-undiv div-exp
5×flip3-+ flip-+
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/l/
1×flip3-- div-sub flip--
Counts
4 → 273
Calls
4 calls:
6.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
19.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
20.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

series552.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
143.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
120.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
154.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

simplify74.0ms

Algorithm
egg-herbie
Counts
285 → 285
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09775178
150014779

prune968.0ms

Filtered
285 candidates to 206 candidates (72.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2796285
Fresh628
Picked101
Done101
Total2878295

Merged error: 33.9b

Counts
295 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
0.3b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
0.5b
(/ i (- (/ (fma i 2.0 (+ alpha beta)) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ 1.0 (+ (+ alpha beta) i))))
34.7b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
170×*-un-lft-identity
166×add-sqr-sqrt
82×add-cube-cbrt
32×associate-/r*
24×distribute-lft-out difference-of-squares
16×distribute-lft-out--
15×add-exp-log add-cbrt-cube
14×associate-/l*
8×div-inv
6×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u add-log-exp
2×associate-/l/
1×flip3-- flip3-+ frac-sub flip-- flip-+
Counts
4 → 212
Calls
4 calls:
8.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
6.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
67.0ms
(/ i (- (/ (fma i 2.0 (+ alpha beta)) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ 1.0 (+ (+ alpha beta) i))))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
137.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
149.0ms
(/ i (- (/ (fma i 2.0 (+ alpha beta)) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ 1.0 (+ (+ alpha beta) i))))
122.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

simplify117.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07513671
134953462
250023431

prune935.0ms

Filtered
224 candidates to 163 candidates (72.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2195224
Fresh617
Picked101
Done000
Total2266232

Merged error: 2.0b

Counts
232 → 6

regimes136.0ms

Accuracy

45.5% (8.8b remaining)

Error of 10.7b against oracle of 1.9b and baseline of 18.0b

bsearch23.0ms

Steps
ItersRangePoint
3
4.643101948939184e+144
5.979143538489926e+144
5.227620144367633e+144

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03344
13344

end0.0ms

sample679.0ms

Algorithm
intervals
Results
355.0ms8000×body80valid
135.0ms8000×pre80true