Details

Time bar (total: 46.2s)

sample32.0ms

Algorithm
intervals
Results
17.0ms99×body1280valid
4.0ms125×body80valid
2.0ms18×body640valid
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

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: 15.3b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
2×flip3-+ sqrt-div associate-*r/ sqrt-prod flip-+
1×+-commutative sub-neg flip3-- frac-2neg pow1/2 clear-num *-commutative flip-- div-inv
Counts
4 → 15
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series186.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
26.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
70.0ms
(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))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 4 (85.0ms)

IterNodesCost
0112181
1263178
2949176
33293175
45002173

prune45.0ms

Filtered
27 candidates to 15 candidates (55.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New25227
Fresh000
Picked101
Done000
Total26228

Merged error: 14.8b

Counts
28 → 2

localize13.0ms

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 (sqrt (* 0.5 (+ 1.0 (/ 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)))))))
1.9b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
30×associate-*r/
16×frac-sub
10×flip3-- flip-- associate-/l/
9×clear-num
5×frac-2neg
4×associate--l+ un-div-inv
3×sub-neg flip3-+ flip-+
2×distribute-rgt-in distribute-lft-in sqrt-div sqrt-prod associate-/r/
1×+-commutative pow1/2 div-sub *-commutative div-inv
Counts
4 → 40
Calls
4 calls:
3.0ms
(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))))))
13.0ms
(/ (- (* 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)))))))
7.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
75.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
153.0ms
(/ (- (* 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)))))))
32.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify44.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0359611
11437603
25002595

prune145.0ms

Filtered
52 candidates to 38 candidates (73.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New49352
Fresh011
Picked101
Done000
Total50454

Merged error: 14.8b

Counts
54 → 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 (sqrt (* 0.5 (+ 1.0 (/ 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))))
1.9b
(- (* (* 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)))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
694×associate-*r/
260×frac-times
192×clear-num frac-sub
157×flip3-- flip--
96×frac-2neg un-div-inv
86×associate-*l/
24×frac-add
18×distribute-rgt-in distribute-lft-in
15×flip3-+ flip-+
10×*-commutative
9×sub-neg
8×associate-+l+ associate--l+
7×associate-*r*
4×div-inv difference-of-squares
3×+-commutative swap-sqr associate-*l*
1×pow2
Counts
4 → 291
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
14.0ms
(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
7.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 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)))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
128.0ms
(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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))))
59.0ms
(- (* (* 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)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
303 → 303
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
026027771
150017729

prune548.0ms

Filtered
303 candidates to 101 candidates (33.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3012303
Fresh123
Picked101
Done000
Total3034307

Merged error: 14.8b

Counts
307 → 4

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5))) (* (* (+ 1.0 0.5) (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5)))) (/ (hypot 1.0 x) 1.0)))
0.0b
(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
0.1b
(* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5))
1.9b
(- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
8248×associate-*r/
7376×frac-times
5368×associate-*l/
3168×frac-sub
2228×flip3-+ flip-+
2217×clear-num
2126×flip3-- flip--
1586×associate-/l/
1465×frac-2neg
752×un-div-inv
36×associate-/r/
24×frac-add
10×distribute-rgt-in distribute-lft-in
8×associate-+l+
7×associate-*r* associate-*l* *-commutative
5×sub-neg associate-/r*
3×div-inv
2×+-commutative
1×div-sub
Counts
4 → 3316
Calls
4 calls:
217.0ms
(/ (- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5))) (* (* (+ 1.0 0.5) (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5)))) (/ (hypot 1.0 x) 1.0)))
12.0ms
(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
14.0ms
(* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5))
102.0ms
(- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5))) (* (* (+ 1.0 0.5) (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5)))) (/ (hypot 1.0 x) 1.0)))
128.0ms
(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
13.0ms
(* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5))
72.0ms
(- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5)))

simplify1.8s

Algorithm
egg-herbie
Counts
3328 → 3328
Iterations

Useful iterations: 0 (108.0ms)

IterNodesCost
07293188128

prune40.0s

Filtered
3328 candidates to 3315 candidates (99.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New332533328
Fresh213
Picked101
Done000
Total332843332

Merged error: 14.7b

Counts
3332 → 4

regimes93.0ms

Accuracy

0% (0.1b remaining)

Error of 15.2b against oracle of 15.1b and baseline of 15.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07995
17995

end0.0ms

sample904.0ms

Algorithm
intervals
Results
527.0ms2868×body1280valid
125.0ms4026×body80valid
91.0ms609×body640valid
34.0ms328×body320valid
10.0ms169×body160valid