Details

Time bar (total: 10.2s)

sample150.0ms

Algorithm
intervals
Results
95.0ms119×body1280valid
31.0ms68×body640valid
5.0ms17×body320valid
4.0ms41×body80valid
2.0ms11×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13910
26710
315310
443910
5183010
6500110

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b
(pow (sin kx) 2.0)
0.2b
(pow (sin ky) 2.0)
3.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
39×add-sqr-sqrt
26×add-cube-cbrt
25×sqrt-prod
24×times-frac
22×unpow-prod-down
10×distribute-lft-out
9×hypot-def
8×add-exp-log associate-/r* sqr-pow
7×pow1
6×pow-unpow add-cbrt-cube
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 117
Calls
4 calls:
11.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
14.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms
(pow (sin kx) 2.0)
108.0ms
(pow (sin ky) 2.0)
80.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03411065
11159981
25001976

prune420.0ms

Filtered
129 candidates to 87 candidates (67.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.1b
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
0.2b
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*l*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*r* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
7.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
4.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series976.0ms

Counts
3 → 9
Calls
3 calls:
254.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
345.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
376.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify38.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02951114
11091988
25001986

prune314.0ms

Filtered
82 candidates to 66 candidates (80.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.1b
(* (/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1)) (sin th))
0.2b
(/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
44×add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
25×associate-*l*
22×unpow-prod-down
18×add-exp-log
10×add-cbrt-cube
8×sqr-pow
7×associate-/r*
6×div-exp
5×pow1
4×prod-exp unswap-sqr
3×expm1-log1p-u associate-*r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv pow-to-exp pow-exp cbrt-unprod div-inv
1×hypot-udef frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 107
Calls
3 calls:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
9.0ms
(* (/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1)) (sin th))
5.0ms
(/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1))

series974.0ms

Counts
3 → 9
Calls
3 calls:
246.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
348.0ms
(* (/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1)) (sin th))
380.0ms
(/ (sin ky) (pow (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) 1))

simplify50.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03941702
115451506
250011498

prune428.0ms

Filtered
116 candidates to 85 candidates (73.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.3b
(* (sin ky) (/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
0.3b
(/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity prod-exp
7×associate-*r*
6×times-frac div-exp
5×pow1 cbrt-unprod
4×cbrt-undiv
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×1-exp div-inv
1×hypot-udef frac-2neg associate-*r/ pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
3 → 64
Calls
3 calls:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
7.0ms
(* (sin ky) (/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
5.0ms
(/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series938.0ms

Counts
3 → 9
Calls
3 calls:
255.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
355.0ms
(* (sin ky) (/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
328.0ms
(/ (* 1 (sin th)) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify42.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0318977
11265805
25002804

prune235.0ms

Filtered
73 candidates to 55 candidates (75.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes274.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01912
11912

end0.0ms

sample4.7s

Algorithm
intervals
Results
3.0s3710×body1280valid
1.1s2044×body640valid
227.0ms710×body320valid
125.0ms1263×body80valid
54.0ms273×body160valid