Details

Time bar (total: 6.3s)

sample32.0ms

Algorithm
intervals
Results
14.0ms85×body1280valid
4.0ms129×body80valid
3.0ms26×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: 14.9b

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)))))
1.6b
(- 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))
6.0ms
(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))))))

series161.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
82.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0201433
1602413
21998411
35001411

prune126.0ms

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: 14.4b

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 (- 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)))))))
1.1b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite30.0ms

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))
6.0ms
(/ 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))))

series199.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
157.0ms
(/ (- (* 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))))

simplify53.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04071275
115941181
250011177

prune284.0ms

Filtered
122 candidates to 88 candidates (72.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1202122
Fresh112
Picked101
Done000
Total1223125

Merged error: 14.4b

Counts
125 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
1.1b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
41×*-un-lft-identity
36×add-exp-log add-cbrt-cube
25×add-sqr-sqrt add-cube-cbrt
20×associate-*l/
14×cbrt-undiv associate-*r/ div-exp associate-/r/
11×flip3-+ flip-+ associate-/l*
8×prod-exp associate-/r* frac-sub cbrt-unprod div-inv distribute-lft-out
7×associate-/l/
6×flip3-- flip-- add-log-exp
4×pow1
3×frac-2neg clear-num
2×associate--r+
1×distribute-rgt-in sub-neg distribute-lft-in diff-log
Counts
4 → 136
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
15.0ms
(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
14.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
11.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ 1.0 (hypot 1.0 x))
210.0ms
(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
62.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
30.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify124.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08322943
146032523
250012523

prune395.0ms

Filtered
148 candidates to 102 candidates (68.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1471148
Fresh022
Picked011
Done000
Total1474151

Merged error: 14.3b

Counts
151 → 4

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 1.0 (/ (+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (+ (* 1.0 1.0) (* 0.5 0.5))))) (* (+ 1.0 0.5) (hypot 1.0 x)))
0.1b
(* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))
0.1b
(/ (+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (+ (* 1.0 1.0) (* 0.5 0.5))))
1.1b
(+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5))))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
267×associate-*r/
207×flip3-+ flip-+
136×frac-times
128×frac-add distribute-neg-frac
70×associate-*l/
67×associate-/l/
46×add-exp-log add-cbrt-cube
16×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
12×distribute-rgt-in distribute-lft-in
10×associate-/r/
9×pow1
8×add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×associate-+l+ associate-+r+ distribute-neg-in times-frac associate-/l*
3×associate-*l* pow-prod-down
2×neg-sub0 associate-+l- frac-2neg clear-num associate-/r* sum-log div-inv
1×+-commutative div-sub associate-*r* neg-log *-commutative
Counts
4 → 243
Calls
4 calls:
22.0ms
(/ (* 1.0 (/ (+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (+ (* 1.0 1.0) (* 0.5 0.5))))) (* (+ 1.0 0.5) (hypot 1.0 x)))
15.0ms
(* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))
32.0ms
(/ (+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (+ (* 1.0 1.0) (* 0.5 0.5))))
13.0ms
(+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5))))))

series239.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (* 1.0 (/ (+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (+ (* 1.0 1.0) (* 0.5 0.5))))) (* (+ 1.0 0.5) (hypot 1.0 x)))
27.0ms
(* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))
76.0ms
(/ (+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5)))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (+ (* 1.0 1.0) (* 0.5 0.5))))
48.0ms
(+ (- (* (+ (* 1.0 1.0) (* 0.5 0.5)) (* 0.5 (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 (- 1.0 0.5)) (* 0.5 0.5)) (* (hypot 1.0 x) (+ (* (pow 1.0 3) 1.0) (- (* (pow 0.5 3) 0.5))))))

simplify166.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0249311783
1500211032

prune2.5s

Filtered
255 candidates to 222 candidates (87.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2514255
Fresh022
Picked101
Done011
Total2527259

Merged error: 14.1b

Counts
259 → 7

regimes593.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 15.0b and baseline of 15.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02820
13020
23020

end0.0ms

sample836.0ms

Algorithm
intervals
Results
483.0ms2852×body1280valid
116.0ms4007×body80valid
91.0ms659×body640valid
28.0ms313×body320valid
10.0ms169×body160valid