Details

Time bar (total: 18.9s)

sample32.0ms

Algorithm
intervals
Results
16.0ms99×body1280valid
4.0ms125×body80valid
2.0ms18×body640valid
1.0ms8×body320valid
0.0ms6×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0196
1266
2336
3356
4416
5446
6446

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.3b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
2×flip3-+ sqrt-div associate-*r/ sqrt-prod flip-+
1×+-commutative sub-neg flip3-- frac-2neg pow1/2 clear-num *-commutative flip-- div-inv
Counts
4 → 15
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series803.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ 1.0 (hypot 1.0 x))
100.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
256.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
348.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify36.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0355358
11216340
25001326

prune108.0ms

Filtered
27 candidates to 26 candidates (96.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New23427
Fresh000
Picked101
Done000
Total24428

Merged error: 14.7b

Counts
28 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.9b
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
3×flip3-+ flip-+
2×sqrt-div associate-*r/ sqrt-prod associate-/r/
1×+-commutative frac-2neg pow1/2 clear-num *-commutative fma-udef div-inv
Counts
4 → 14
Calls
4 calls:
4.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms
(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
262.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
327.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.2s
(/ (fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
158.0ms
(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify72.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0712741
13139701
25001689

prune167.0ms

Filtered
26 candidates to 26 candidates (100.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New24226
Fresh213
Picked101
Done000
Total27330

Merged error: 0.1b

Counts
30 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.0b
(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.9b
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
12×sqr-pow
8×unpow3 prod-diff
6×unpow-prod-down sqrt-prod
3×*-commutative
2×difference-cubes flip3-- fma-neg flip-- associate-/l/ associate-/l* difference-of-squares
1×pow-to-exp sub-neg pow-pow frac-2neg pow1/2 div-sub clear-num sqrt-pow2 fma-udef div-inv
Counts
4 → 32
Calls
4 calls:
9.0ms
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.0ms
(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
3.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
7.0ms
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series8.2s

Counts
4 → 12
Calls
4 calls:
5.7s
(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
582.0ms
(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
669.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.2s
(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify59.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
017992551
150012445

prune379.0ms

Filtered
44 candidates to 36 candidates (81.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New42244
Fresh022
Picked101
Done000
Total43447

Merged error: 0.1b

Counts
47 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b
(/ (- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.0b
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)
1.9b
(- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×sqr-pow
6×unpow-prod-down prod-diff
4×unpow3
3×*-commutative
2×flip3-- fma-neg flip-- associate-/l/ difference-of-squares
1×pow-to-exp sub-neg frac-2neg div-sub clear-num fma-udef div-inv associate-/l*
Counts
4 → 25
Calls
4 calls:
1.0ms
(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
7.0ms
(/ (- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
3.0ms
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)
6.0ms
(- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2))

series5.6s

Counts
4 → 12
Calls
4 calls:
579.0ms
(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
4.0s
(/ (- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
440.0ms
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)
546.0ms
(- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2))

simplify45.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012971835
150021765

prune284.0ms

Filtered
37 candidates to 32 candidates (86.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New34337
Fresh123
Picked101
Done000
Total36541

Merged error: 0.1b

Counts
41 → 5

regimes201.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.2b

bsearch143.0ms

Steps
ItersRangePoint
9
2.5653698016906928e-06
357.20278190505735
0.001424442805013217
9
-0.005814372128176944
-5.336234557171703e-11
-0.002877539079495299

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06079
16079

end0.0ms

sample796.0ms

Algorithm
intervals
Results
459.0ms2868×body1280valid
115.0ms4026×body80valid
79.0ms609×body640valid
28.0ms328×body320valid
9.0ms169×body160valid