Details

Time bar (total: 6.8s)

sample25.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify86.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune12.0ms

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: 4.6b

Counts
2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 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))
4.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

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:
23.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 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)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
158.0ms
(/ (/ (/ (+ (+ (+ 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))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify142.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4808488
Fresh011
Picked101
Done000
Total4819490

Merged error: 1.4b

Counts
490 → 9

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))
4.4b
(/ (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:
10.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
10.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
21.0ms
(/ (/ 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))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
150.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
157.0ms
(/ (/ 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))
97.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify110.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07192968
138412593
250012562

prune404.0ms

Filtered
203 candidates to 117 candidates (57.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2021203
Fresh268
Picked011
Done000
Total2048212

Merged error: 0.0b

Counts
212 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.2b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
44×add-sqr-sqrt
42×times-frac
40×sqrt-prod
38×add-cube-cbrt
14×associate-/l*
10×distribute-lft-out
8×add-exp-log sqrt-div add-cbrt-cube
6×pow1 associate-/r*
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num associate-/r/ hypot-def div-inv
Counts
4 → 134
Calls
4 calls:
13.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
10.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series502.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
203.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04381732
113661629
250021603

prune409.0ms

Filtered
146 candidates to 103 candidates (70.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1460146
Fresh066
Picked011
Done011
Total1468154

Merged error: 0.0b

Counts
154 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.9b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
4.3b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
756×times-frac
594×*-un-lft-identity
419×sqrt-prod
372×add-sqr-sqrt add-cube-cbrt
111×distribute-lft-out
61×associate-/l*
40×sqrt-div associate-/r/
26×associate-/r*
24×add-exp-log
21×flip3-+ flip-+
20×div-inv
18×add-cbrt-cube
12×div-exp
8×cbrt-undiv
6×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
3×pow-flip
2×rec-exp 1-exp
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 587
Calls
4 calls:
8.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
21.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
30.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
106.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
174.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
104.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify161.0ms

Algorithm
egg-herbie
Counts
599 → 599
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0136913739
1500112934

prune1.2s

Filtered
599 candidates to 257 candidates (42.9%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New5990599
Fresh055
Picked011
Done022
Total5998607

Merged error: 0.0b

Counts
607 → 8

regimes95.0ms

Accuracy

71.4% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.9b

bsearch63.0ms

Steps
ItersRangePoint
8
5.063094154997107e+154
1.7952942819324793e+158
3.668381532556198e+155

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03825
13825

end0.0ms

sample565.0ms

Algorithm
intervals
Results
308.0ms8000×body80valid
98.0ms8000×pre80true