Details

Time bar (total: 4.2s)

sample44.0ms

Algorithm
intervals
Results
25.0ms86×body1280valid
5.0ms131×body80valid
4.0ms23×body640valid
1.0ms8×body320valid
1.0ms8×body160valid

simplify8.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.9b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
2.1b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
11×add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 calls:
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series27.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms
(/ 1.0 (hypot 1.0 x))
16.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify57.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0203385
1642358
21977356
35002355

prune131.0ms

Filtered
62 candidates to 44 candidates (29.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New57562
Fresh000
Picked101
Done000
Total58563

Merged error: 14.4b

Counts
63 → 5

localize13.0ms

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 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.5b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
8×associate-*r/
6×add-log-exp
4×pow1 flip3-- associate--l+ frac-sub flip-- associate-/l/ distribute-lft-out
3×cbrt-undiv sub-neg frac-2neg div-exp clear-num div-inv
2×distribute-rgt-in distribute-lft-in associate-/r/
1×flip3-+ diff-log div-sub flip-+
Counts
4 → 110
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 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))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
35.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 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))))

simplify51.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04071275
115941181
250021177

prune353.0ms

Filtered
122 candidates to 88 candidates (27.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1184122
Fresh314
Picked101
Done000
Total1225127

Merged error: 14.3b

Counts
127 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.2b
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.5b
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
24×add-sqr-sqrt
22×add-cube-cbrt times-frac
17×add-exp-log add-cbrt-cube
10×associate-/r*
7×associate-/l*
6×cbrt-undiv div-exp associate-/r/ add-log-exp
5×div-inv
4×pow1
3×distribute-rgt-out-- frac-2neg flip3-+ clear-num flip-+
2×prod-exp cbrt-unprod distribute-lft-out
1×sub-neg flip3-- diff-log associate-*r/ frac-sub flip-- associate-/l/ distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 101
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
17.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series106.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
32.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
65.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify54.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04011320
117401175
250011148

prune415.0ms

Filtered
113 candidates to 81 candidates (28.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1103113
Fresh314
Picked101
Done000
Total1144118

Merged error: 14.1b

Counts
118 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.5b
(- (/ (* 1.0 (- 1.0 0.5)) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
2.4b
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
78×associate-*r/
52×sqrt-div
28×flip3-+ flip-+
17×frac-sub
12×pow1 add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
8×frac-times unpow-prod-down pow-pow cube-prod add-log-exp
6×add-exp-log pow-unpow associate-*l/ add-cbrt-cube
5×sub-div
4×cube-div distribute-rgt-out-- sqrt-pow1 sqrt-prod associate-/r/
2×cube-mult pow-to-exp sub-neg flip3-- pow1/2 diff-log unpow3 pow-prod-down pow-exp sqrt-pow2 flip-- div-inv rem-cube-cbrt sqr-pow
1×distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
9.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
9.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
41.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
21.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
23.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
166.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
39.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify109.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06922604
128702284
250012276

prune1.0s

Filtered
126 candidates to 76 candidates (39.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1242126
Fresh123
Picked101
Done000
Total1264130

Merged error: 14.1b

Counts
130 → 4

regimes195.0ms

Accuracy

0% (0.2b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03174
13174

end0.0ms

sample1.1s

Algorithm
intervals
Results
647.0ms2888×body1280valid
161.0ms4039×body80valid
112.0ms633×body640valid
36.0ms289×body320valid
14.0ms151×body160valid

Profiling

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