Details

Time bar (total: 17.3s)

sample26.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×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: 3.1b

Counts
2 → 2

localize12.0ms

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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms

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)
19.0ms
(/ (/ (+ (+ (+ 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))
18.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
133.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms
(/ (/ (/ (+ (+ (+ 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))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify152.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0151312983
1500212137

prune992.0ms

Filtered
488 candidates to 299 candidates (61.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4817488
Fresh101
Picked101
Done000
Total4837490

Merged error: 0.7b

Counts
490 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
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)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite55.0ms

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
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
11.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
19.0ms
(/ (/ 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))))

series569.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
152.0ms
(* (/ (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))
101.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify112.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07192968
138412593
250012562

prune391.0ms

Filtered
203 candidates to 117 candidates (57.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2021203
Fresh246
Picked011
Done000
Total2046210

Merged error: 0.0b

Counts
210 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.2b
(/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.9b
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
2.7b
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
14328×times-frac
10257×*-un-lft-identity
5414×add-sqr-sqrt add-cube-cbrt
3762×sqrt-prod
2770×distribute-lft-out
831×associate-/l*
246×associate-/r/
244×sqrt-div
161×div-inv
124×flip3-+ flip-+
34×add-exp-log add-cbrt-cube
20×cbrt-undiv div-exp
19×associate-/r*
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
Counts
4 → 4451
Calls
4 calls:
326.0ms
(/ (/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
48.0ms
(/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
24.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
13.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series614.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(/ (/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
149.0ms
(/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
192.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
107.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify1.7s

Algorithm
egg-herbie
Counts
4463 → 4463
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
05001173358

prune8.9s

Filtered
4463 candidates to 1851 candidates (41.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New446304463
Fresh044
Picked011
Done011
Total446364469

Merged error: 0.0b

Counts
4469 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
0.0b
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.2b
(/ 1 (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
377×*-un-lft-identity
310×times-frac
147×add-sqr-sqrt
138×add-cube-cbrt
136×distribute-lft-out
85×associate-*l*
54×add-exp-log
34×add-cbrt-cube
24×div-exp
20×associate-/r*
15×div-inv
14×cbrt-undiv
12×prod-exp associate-/l*
9×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r/ unswap-sqr
2×pow-flip flip3-+ pow-prod-down associate-*l/ flip-+ fma-udef
1×distribute-rgt-in distribute-lft-in *-commutative inv-pow
Counts
4 → 305
Calls
4 calls:
16.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
25.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
23.0ms
(/ 1 (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
10.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series609.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
228.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
158.0ms
(/ 1 (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
97.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify146.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
08885411
144414945
250014943

prune549.0ms

Filtered
317 candidates to 179 candidates (56.5%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New3161317
Fresh123
Picked011
Done022
Total3176323

Merged error: 0.0b

Counts
323 → 6

regimes66.0ms

Accuracy

70.3% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.5b

bsearch70.0ms

Steps
ItersRangePoint
9
1.0718434718451636e+149
7.711875273557896e+157
9.661050671120662e+155

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03923
13923

end0.0ms

sample630.0ms

Algorithm
intervals
Results
351.0ms8000×body80valid
131.0ms8000×pre80true