Details

Time bar (total: 7.1s)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

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: 4.1b

Counts
2 → 2

localize18.0ms

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))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite118.0ms

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)))
39.0ms
(/ (/ (/ (+ (+ (+ 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))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
130.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
142.0ms
(/ (/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

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: 1.7b

Counts
490 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
0.2b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.9b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
967×times-frac
486×*-un-lft-identity
426×add-sqr-sqrt add-cube-cbrt
402×sqrt-prod
182×associate-/l*
79×add-exp-log
49×associate-/r/ add-cbrt-cube
47×div-exp
46×sqrt-div
36×distribute-lft-out
26×cbrt-undiv
25×flip3-+ flip-+ div-inv
18×associate-/r*
13×pow1
10×prod-exp
8×pow-flip
6×cbrt-unprod pow-div
5×rec-exp sqrt-pow1 pow1/2 1-exp
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
2×inv-pow
1×associate-*l/
Counts
4 → 642
Calls
4 calls:
56.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
20.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
8.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (+ beta (+ alpha (fma alpha beta 1.0))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
38.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
70.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
101.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify177.0ms

Algorithm
egg-herbie
Counts
654 → 654
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0192714793
1500213259

prune1.7s

Filtered
654 candidates to 319 candidates (48.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New6513654
Fresh336
Picked011
Done000
Total6547661

Merged error: 0.0b

Counts
661 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))
0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.8b
(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
3.8b
(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
127×*-un-lft-identity
58×times-frac
52×sqrt-prod
51×distribute-lft-out
48×add-sqr-sqrt
42×add-cube-cbrt
14×associate-/r*
10×add-exp-log
8×pow1 sqrt-div add-cbrt-cube associate-/l*
5×flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp
2×cbrt-undiv rem-sqrt-square frac-2neg clear-num hypot-def div-inv associate-/l/
1×rec-exp 1-exp inv-pow
Counts
4 → 160
Calls
4 calls:
14.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))
8.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
6.0ms
(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
6.0ms
(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ beta (+ alpha (fma alpha beta 1.0)))))
64.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
57.0ms
(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))
52.0ms
(sqrt (+ beta (+ alpha (fma alpha beta 1.0))))

simplify62.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05281754
119601584
250021545

prune528.0ms

Filtered
172 candidates to 93 candidates (54.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1711172
Fresh145
Picked011
Done011
Total1727179

Merged error: 0.0b

Counts
179 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite49.0ms

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:
14.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series492.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
201.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
52.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04381732
113661629
250021603

prune472.0ms

Filtered
146 candidates to 103 candidates (70.5%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1451146
Fresh134
Picked011
Done022
Total1467153

Merged error: 0.0b

Counts
153 → 7

regimes85.0ms

Accuracy

69.1% (1.1b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.7b

bsearch82.0ms

Steps
ItersRangePoint
9
1.2638933579139666e+159
6.311864492386349e+166
3.1018492979193925e+159

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04341
14341

end0.0ms

sample532.0ms

Algorithm
intervals
Results
300.0ms8000×body80valid
94.0ms8000×pre80true