Details

Time bar (total: 7.4s)

sample25.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms256×pre80true

simplify83.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

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: 3.3b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 476
Calls
4 calls:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
150.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
165.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify141.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0151312983
1500212137

prune1.2s

Filtered
488 candidates to 299 candidates (61.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4817488
Fresh011
Picked101
Done000
Total4828490

Merged error: 1.6b

Counts
490 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.2b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
81×times-frac
64×add-exp-log
50×add-sqr-sqrt
45×add-cube-cbrt
34×add-cbrt-cube
30×div-exp distribute-lft-out
21×associate-*l*
14×cbrt-undiv prod-exp associate-/l*
12×associate-/r/
10×associate-/r*
9×pow1 div-inv
7×associate-*l/
6×rec-exp 1-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ associate-*r* clear-num flip-+
2×pow-flip pow-prod-down fma-udef unswap-sqr
1×distribute-rgt-in distribute-lft-in *-commutative associate-/l/ inv-pow
Counts
4 → 191
Calls
4 calls:
11.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
10.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
18.0ms
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
7.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
153.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
165.0ms
(/ (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
103.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify108.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07192968
138412593
250012562

prune395.0ms

Filtered
203 candidates to 117 candidates (57.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2003203
Fresh347
Picked011
Done000
Total2038211

Merged error: 0b

Counts
211 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0b
(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0b
(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
1236×times-frac
888×*-un-lft-identity
508×add-sqr-sqrt
492×sqrt-prod
488×add-cube-cbrt
200×distribute-lft-out
72×associate-/r/
38×flip3-+ flip-+
36×div-inv
8×add-exp-log rem-sqrt-square add-cbrt-cube associate-/l*
6×pow1 associate-/r*
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 598
Calls
4 calls:
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
19.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
47.0ms
(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
51.0ms
(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

series768.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
302.0ms
(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
307.0ms
(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

simplify208.0ms

Algorithm
egg-herbie
Counts
610 → 610
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0159820834
1500120270

prune1.5s

Filtered
610 candidates to 332 candidates (54.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New6100610
Fresh066
Picked011
Done011
Total6108618

Merged error: 0b

Counts
618 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ alpha (fma alpha beta 1.0))
0.0b
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
0.1b
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
16.9b
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
58×times-frac
31×add-sqr-sqrt
29×add-cube-cbrt
22×distribute-lft-out
20×add-exp-log add-cbrt-cube
16×associate-/l*
12×associate-*r/
10×associate-/r/
8×flip3-+ flip-+
7×cbrt-undiv div-exp
6×pow1 div-inv add-log-exp
5×associate-*r*
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×fma-def associate-*l* prod-exp cbrt-unprod associate-/l/
2×frac-2neg clear-num
1×+-commutative distribute-rgt-in associate-+r+ distribute-lft-in pow-prod-down sum-log *-commutative fma-udef unswap-sqr
Counts
4 → 141
Calls
4 calls:
3.0ms
(+ alpha (fma alpha beta 1.0))
7.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
14.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
12.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(+ alpha (fma alpha beta 1.0))
38.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))
177.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0))))) (fma 1.0 2.0 (+ alpha beta)))
148.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (* (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))

simplify99.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06262050
131391835
250011834

prune376.0ms

Filtered
153 candidates to 111 candidates (72.5%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1521153
Fresh145
Picked011
Done022
Total1538161

Merged error: 0b

Counts
161 → 8

regimes118.0ms

Accuracy

93.3% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 3.9b

bsearch5.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04742
14742

end0.0ms

sample533.0ms

Algorithm
intervals
Results
295.0ms8000×body80valid
98.0ms8000×pre80true