Details

Time bar (total: 8.9s)

sample39.0ms

Algorithm
intervals
Results
18.0ms85×body1280valid
6.0ms139×body80valid
3.0ms18×body640valid
1.0ms11×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 13.9b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(hypot 1.0 x)
1.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
12×prod-diff
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u fma-neg associate-/r* sqrt-prod log1p-expm1-u associate-/l*
1×cbrt-undiv sub-neg hypot-udef flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 70
Calls
3 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
1.0ms
(hypot 1.0 x)
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series539.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(/ 1.0 (hypot 1.0 x))
64.0ms
(hypot 1.0 x)
369.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0467896
11795649
25001646

prune180.0ms

Filtered
79 candidates to 63 candidates (79.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New77279
Fresh000
Picked101
Done000
Total78280

Merged error: 13.2b

Counts
80 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×hypot-udef fma-udef
Counts
4 → 78
Calls
4 calls:
1.0ms
(hypot 1.0 x)
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
1.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series410.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(hypot 1.0 x)
107.0ms
(/ 1.0 (hypot 1.0 x))
99.0ms
(/ 1.0 (hypot 1.0 x))
150.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0285518
11019474
25002470

prune277.0ms

Filtered
90 candidates to 80 candidates (88.9%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh101
Picked011
Done000
Total90292

Merged error: 0.0b

Counts
92 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b
(* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))
0.2b
(- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))
17.6b
(fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
94×times-frac
82×unpow-prod-down
74×associate-*r*
73×*-un-lft-identity
63×add-cube-cbrt
29×add-exp-log
24×sqrt-prod sqr-pow
13×unswap-sqr
11×add-cbrt-cube
10×div-exp prod-exp
9×prod-diff
6×pow1 pow-to-exp pow-exp add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u distribute-lft-out
3×fma-neg associate-*l* associate-/l*
2×cbrt-undiv associate-/r/ cbrt-unprod fma-udef div-inv
1×sub-neg flip3-- frac-2neg flip3-+ diff-log associate-*r/ pow-prod-down clear-num *-commutative flip-- flip-+ associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 188
Calls
4 calls:
5.0ms
(/ (fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
21.0ms
(* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))
4.0ms
(- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))
1.0ms
(fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5))))))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.5s
(/ (fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
160.0ms
(* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))
369.0ms
(- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))
266.0ms
(fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- 0.5 (fma 0.5 (/ 1 (sqrt 1.0)) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012093376
150012903

prune867.0ms

Filtered
200 candidates to 125 candidates (62.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1982200
Fresh000
Picked101
Done011
Total1993202

Merged error: 0b

Counts
202 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- (- 0.5 (* 0.5 (/ 1 (sqrt 1.0)))) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b
(* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))
17.6b
(fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- (- 0.5 (* 0.5 (/ 1 (sqrt 1.0)))) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
103×times-frac
95×add-sqr-sqrt
82×unpow-prod-down
74×associate-*r*
72×*-un-lft-identity
64×add-cube-cbrt
31×add-exp-log
24×sqrt-prod sqr-pow
13×add-cbrt-cube unswap-sqr
11×div-exp
10×prod-exp
7×associate-/r*
6×pow1 pow-to-exp pow-exp associate-/l*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out add-log-exp
3×cbrt-undiv associate-*l* div-inv
2×frac-2neg clear-num associate-/r/ cbrt-unprod
1×flip3-+ associate-*r/ pow-prod-down *-commutative flip-+ fma-udef
Counts
4 → 188
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ (fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- (- 0.5 (* 0.5 (/ 1 (sqrt 1.0)))) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
24.0ms
(* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))
1.0ms
(fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- (- 0.5 (* 0.5 (/ 1 (sqrt 1.0)))) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ 1.0 (hypot 1.0 x))
1.3s
(/ (fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- (- 0.5 (* 0.5 (/ 1 (sqrt 1.0)))) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
156.0ms
(* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))
267.0ms
(fma 0.25 (/ (pow x 2) (pow (sqrt 1.0) 3)) (- (- 0.5 (* 0.5 (/ 1 (sqrt 1.0)))) (* 0.1875 (/ (pow x 4) (pow (sqrt 1.0) 5)))))

simplify57.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012242882
150012679

prune935.0ms

Filtered
200 candidates to 135 candidates (67.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2000200
Fresh011
Picked011
Done011
Total2003203

Merged error: 0b

Counts
203 → 3

regimes121.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 14.9b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04452
14452

end0.0ms

sample1.1s

Algorithm
intervals
Results
613.0ms2807×body1280valid
162.0ms4079×body80valid
107.0ms627×body640valid
39.0ms324×body320valid
13.0ms163×body160valid