Details

Time bar (total: 3.3s)

sample31.0ms

Algorithm
intervals
Results
15.0ms93×body1280valid
4.0ms128×body80valid
2.0ms19×body640valid
1.0ms10×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: 15.2b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
8.0ms
(+ 1.0 (/ 1.0 (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))))))

series198.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms
(/ 1.0 (hypot 1.0 x))
73.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
89.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0221492
1697465
22323463
35001463

prune146.0ms

Filtered
78 candidates to 55 candidates (70.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New75378
Fresh000
Picked101
Done000
Total76379

Merged error: 14.7b

Counts
79 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
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))))))
1.9b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite20.0ms

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×associate--l+
3×sub-neg associate-/r* associate-/l*
2×distribute-rgt-in flip3-- distribute-lft-in sqrt-pow1 flip3-+ sqrt-div frac-sub flip-- flip-+
1×cbrt-undiv +-commutative frac-2neg 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:
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))))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
77.0ms
(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))))))
37.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify42.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0348579
11197545
25002541

prune207.0ms

Filtered
82 candidates to 59 candidates (72.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New78482
Fresh202
Picked101
Done000
Total81485

Merged error: 14.7b

Counts
85 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
1.8b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×add-exp-log add-cbrt-cube
9×pow1
8×add-sqr-sqrt associate-*l/ frac-sub
7×flip3-+ flip-+
6×add-cube-cbrt flip3-- *-un-lft-identity flip-- associate-/l/ add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×associate-*r* associate-*l*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 sqrt-div pow-prod-down associate-/r/ associate--r+
1×sub-neg frac-2neg times-frac pow1/2 diff-log clear-num associate-/r* sqrt-prod *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 82
Calls
4 calls:
29.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
6.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
17.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series213.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
78.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
23.0ms
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
39.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify111.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
06551559
138701302
250031302

prune390.0ms

Filtered
94 candidates to 68 candidates (72.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New90494
Fresh213
Picked101
Done000
Total93598

Merged error: 14.7b

Counts
98 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

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)))
0.0b
(* (+ 1.0 0.5) (hypot 1.0 x))
0.0b
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
1.9b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
14×associate-*r/ associate-*l/
12×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cube-cbrt associate-*l* frac-sub
7×flip3-- flip--
6×flip3-+ associate-*r* prod-exp cbrt-unprod flip-+ associate-/l/ add-log-exp
4×cbrt-undiv div-exp
2×pow-prod-down associate-/r/ *-commutative associate--r+ unswap-sqr
1×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac diff-log clear-num associate-/r* div-inv distribute-lft-out associate-/l* difference-of-squares
Counts
4 → 89
Calls
4 calls:
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)))
5.0ms
(* (+ 1.0 0.5) (hypot 1.0 x))
6.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
7.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series145.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (* 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)))
20.0ms
(* (+ 1.0 0.5) (hypot 1.0 x))
21.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
38.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify84.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05501145
13114962
25003962

prune291.0ms

Filtered
101 candidates to 72 candidates (71.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1010101
Fresh044
Picked011
Done000
Total1015106

Merged error: 14.7b

Counts
106 → 5

regimes87.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02820
13020
23020

end0.0ms

sample828.0ms

Algorithm
intervals
Results
481.0ms2894×body1280valid
118.0ms4033×body80valid
79.0ms607×body640valid
30.0ms298×body320valid
10.0ms168×body160valid