Details

Time bar (total: 3.6s)

sample37.0ms

Algorithm
intervals
Results
19.0ms81×body1280valid
5.0ms143×body80valid
3.0ms16×body640valid
1.0ms12×body320valid
0.0ms4×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

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: 14.4b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×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
4 → 61
Calls
4 calls:
1.0ms
(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)))))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series162.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
6.0ms
(/ 1.0 (hypot 1.0 x))
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
84.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0201433
1602413
21984411
35001411

prune129.0ms

Filtered
73 candidates to 52 candidates (71.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New70373
Fresh000
Picked101
Done000
Total71374

Merged error: 13.8b

Counts
74 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.7b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 associate-*r/ associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-exp clear-num frac-sub flip-- div-inv
1×+-commutative flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 84
Calls
4 calls:
3.0ms
(/ 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))))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series124.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
77.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
35.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify144.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0306616
11080568
24837560
35001560

prune206.0ms

Filtered
96 candidates to 69 candidates (71.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New92496
Fresh202
Picked101
Done000
Total95499

Merged error: 13.8b

Counts
99 → 4

localize20.0ms

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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.7b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log associate-*r/ add-cbrt-cube
4×flip3-+ associate-*l/ frac-sub flip-+
3×flip3-- associate-/r* flip-- associate-/l*
2×sqrt-pow1 sqrt-div associate--r+
1×cbrt-undiv +-commutative distribute-rgt-in sub-neg frac-2neg distribute-lft-in pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod div-inv distribute-lft-out
Counts
4 → 70
Calls
4 calls:
10.0ms
(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))))))
7.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(/ 1.0 (hypot 1.0 x))
81.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
31.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify55.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0445704
11765663
25001663

prune250.0ms

Filtered
82 candidates to 62 candidates (75.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New80282
Fresh123
Picked101
Done000
Total82486

Merged error: 13.7b

Counts
86 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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)))))
0.2b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.7b
(- (* (* 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)))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
173×associate-*r/
48×frac-sub
43×pow1
42×add-exp-log add-cbrt-cube
41×frac-times
39×flip3-- flip--
29×associate-*l/
26×associate-/l/
21×prod-exp cbrt-unprod
17×pow-prod-down
15×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
12×times-frac
8×distribute-rgt-in distribute-lft-in associate--l+ add-log-exp
7×cbrt-undiv div-exp
5×sub-neg difference-of-squares
4×associate-/r/ pow-sqr pow-prod-up associate-/l*
3×associate-/r*
2×flip3-+ pow-plus frac-add flip-+
1×+-commutative pow2 frac-2neg diff-log div-sub swap-sqr associate-*r* associate-*l* clear-num sum-log *-commutative div-inv distribute-lft-out
Counts
4 → 166
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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)))))
10.0ms
(* (* 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)))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
97.0ms
(/ (- (* (* 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)))))
23.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
53.0ms
(- (* (* 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)))))

simplify156.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09593003
149792705
250012705

prune435.0ms

Filtered
178 candidates to 108 candidates (60.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1762178
Fresh033
Picked101
Done000
Total1775182

Merged error: 13.5b

Counts
182 → 5

regimes149.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02629
12629

end0.0ms

sample1.0s

Algorithm
intervals
Results
608.0ms2855×body1280valid
159.0ms4043×body80valid
105.0ms635×body640valid
37.0ms319×body320valid
11.0ms148×body160valid

Profiling

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