Details

Time bar (total: 3.0s)

analyze1.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1

sample36.0ms

Algorithm
intervals
Results
18.0ms83×body1280valid
6.0ms145×body80valid
3.0ms17×body640valid
1.0ms10×body320valid
0.0ms1×body160valid

simplify121.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (120.0ms)

IterNodesCost
0101012
1101012

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 13.7b

Counts
2 → 1

localize7.0ms

Local error

Found 3 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))
0.9b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×times-frac
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series30.0ms

Counts
3 → 9
Calls
3 calls:
12.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms
(/ 1.0 (hypot 1.0 x))
14.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify43.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05379716

prune126.0ms

Filtered
45 candidates to 62 candidates (-37.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New59362
Fresh000
Picked101
Done000
Total60363

Merged error: 13.1b

Counts
63 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.5 (hypot 1.0 x))
0.0b
(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
0.0b
(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.3b
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
22×add-sqr-sqrt
15×times-frac
14×add-cube-cbrt
11×add-exp-log add-cbrt-cube add-log-exp
8×associate-/r*
6×distribute-lft-out
4×pow1 flip3-- associate-*r/ frac-sub flip-- associate-/l/ associate-/l*
3×cbrt-undiv diff-log div-exp sqrt-prod distribute-lft-out--
2×sub-neg frac-2neg flip3-+ clear-num associate-/r/ flip-+ div-inv difference-of-squares
1×+-commutative associate--l- prod-exp associate--l+ sum-log cbrt-unprod
Counts
4 → 91
Calls
4 calls:
3.0ms
(/ 0.5 (hypot 1.0 x))
16.0ms
(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
3.0ms
(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
10.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 0.5 (hypot 1.0 x))
35.0ms
(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
13.0ms
(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
6.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify34.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
051591683

prune259.0ms

Filtered
77 candidates to 103 candidates (-33.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1003103
Fresh022
Picked101
Done000
Total1015106

Merged error: 13.1b

Counts
106 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.5 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.0b
(/ (* 1.0 (- 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
0.3b
(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
14×add-cube-cbrt
11×add-exp-log add-cbrt-cube
8×associate-/r* add-log-exp
6×distribute-lft-out
4×pow1 associate-/l*
3×cbrt-undiv div-exp sqrt-prod
2×flip3-- frac-2neg flip3-+ associate-*r/ clear-num associate-/r/ flip-- flip-+ div-inv associate-/l/ difference-of-squares
1×+-commutative sub-neg diff-log prod-exp sum-log cbrt-unprod distribute-lft-out--
Counts
4 → 83
Calls
4 calls:
3.0ms
(/ 0.5 (hypot 1.0 x))
3.0ms
(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
12.0ms
(/ (* 1.0 (- 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
6.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 0.5 (hypot 1.0 x))
13.0ms
(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
36.0ms
(/ (* 1.0 (- 0.5 (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
6.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049801456
149801456

prune218.0ms

Filtered
69 candidates to 95 candidates (-37.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New94195
Fresh134
Picked011
Done000
Total955100

Merged error: 13.1b

Counts
100 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))) (* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))))
0.1b
(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
0.3b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))
0.5b
(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
28×associate-*r/
22×flip3-+ associate-*l/ flip-+
13×prod-exp cbrt-unprod
12×frac-times
11×pow1 *-un-lft-identity
10×add-sqr-sqrt
8×associate-/r/ frac-sub
7×add-cube-cbrt associate-*l*
6×cbrt-undiv flip3-- div-exp associate-*r* flip-- associate-/l/ add-log-exp
5×distribute-rgt-in distribute-lft-in
4×pow-prod-down
3×distribute-lft-out
2×*-commutative
1×sub-neg frac-2neg times-frac diff-log clear-num associate-/r* sqrt-prod div-inv associate-/l* unswap-sqr
Counts
4 → 115
Calls
4 calls:
20.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))) (* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))))
10.0ms
(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
10.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))
9.0ms
(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))

series78.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))) (* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))))
20.0ms
(* (hypot 1.0 x) (* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))))
3.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* (+ 1.0 0.5) 0.5))
15.0ms
(* (+ 1.0 0.5) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))

simplify35.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
050553708

prune498.0ms

Filtered
97 candidates to 127 candidates (-30.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1252127
Fresh123
Picked101
Done011
Total1275132

Merged error: 13.1b

Counts
132 → 5

regimes94.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.8b and baseline of 14.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07222
17222

end0.0ms

sample1.1s

Algorithm
intervals
Results
622.0ms2834×body1280valid
174.0ms4079×body80valid
107.0ms604×body640valid
42.0ms333×body320valid
12.0ms150×body160valid

Profiling

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