Details

Time bar (total: 3.5s)

sample44.0ms

Algorithm
intervals
Results
22.0ms99×body1280valid
7.0ms23×body640valid
5.0ms120×body80valid
1.0ms8×body320valid
0.0ms6×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune3.0ms

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: 15.0b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series188.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms
(/ 1.0 (hypot 1.0 x))
73.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
83.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify69.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0221492
1697465
22323463
35001463

prune156.0ms

Filtered
78 candidates to 55 candidates (70.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New73578
Fresh000
Picked101
Done000
Total74579

Merged error: 14.5b

Counts
79 → 5

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

rewrite22.0ms

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
7×pow1
6×associate-*r/ associate-/r* associate-/l* add-log-exp
4×associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 sqrt-div div-exp clear-num frac-sub flip-- div-inv
1×flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-+
Counts
4 → 85
Calls
4 calls:
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series117.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
10.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
32.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify44.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0299576
11026547
25001544

prune233.0ms

Filtered
97 candidates to 70 candidates (72.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New92597
Fresh404
Picked101
Done000
Total975102

Merged error: 14.5b

Counts
102 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.1b
(pow (/ 1.0 (hypot 1.0 x)) 3)
1.3b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
19.4b
(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×cbrt-prod
26×unpow-prod-down cube-prod
8×pow1
7×add-exp-log add-cbrt-cube
6×associate-*r/ add-log-exp
4×cube-div associate--l+ div-inv
3×sub-neg pow-unpow cbrt-div
2×distribute-rgt-in cube-mult flip3-- distribute-lft-in sqrt-pow1 sqrt-div unpow3 pow-exp frac-sub flip-- rem-cube-cbrt sqr-pow
1×cbrt-undiv pow-to-exp pow-pow flip3-+ pow1/2 pow1/3 diff-log div-exp pow-prod-down sqrt-prod rem-cbrt-cube flip-+
Counts
4 → 119
Calls
4 calls:
11.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(pow (/ 1.0 (hypot 1.0 x)) 3)
7.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
5.0ms
(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series146.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
33.0ms
(pow (/ 1.0 (hypot 1.0 x)) 3)
32.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
6.0ms
(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify69.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0506901
12170797
25002789

prune253.0ms

Filtered
131 candidates to 68 candidates (51.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1292131
Fresh134
Picked101
Done000
Total1315136

Merged error: 14.5b

Counts
136 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
0.1b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.3b
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
173×associate-*r/
48×frac-sub
44×add-exp-log add-cbrt-cube
43×pow1
41×frac-times
39×flip3-- flip--
29×associate-*l/
26×associate-/l/
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac prod-exp cbrt-unprod
17×pow-prod-down
8×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate--l+
7×associate-/l*
6×associate-/r* add-log-exp
5×sub-neg difference-of-squares
4×associate-/r/ pow-sqr pow-prod-up
2×frac-2neg pow-plus frac-add clear-num div-inv
1×pow2 flip3-+ diff-log div-sub swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 181
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
26.0ms
(/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
16.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
15.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

series188.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
98.0ms
(/ (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
24.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
60.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

simplify55.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09333000
150022730

prune506.0ms

Filtered
193 candidates to 118 candidates (61.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1876193
Fresh224
Picked101
Done000
Total1908198

Merged error: 14.3b

Counts
198 → 8

regimes164.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02917
12917

end0.0ms

sample1.0s

Algorithm
intervals
Results
612.0ms2798×body1280valid
157.0ms4101×body80valid
104.0ms609×body640valid
41.0ms327×body320valid
13.0ms165×body160valid

Profiling

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