Details

Time bar (total: 1.8m)

sample3.1s

Algorithm
intervals
Results
2.9s726×body10240exit
112.0ms120×body1280valid
42.0ms61×body640valid
9.0ms23×body320valid
5.0ms42×body80valid
3.0ms10×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13910
26710
315310
443910
5183010
6500110

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

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 ky) 2.0)
0.2b
(pow (sin kx) 2.0)
5.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite46.0ms

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:
23.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms
(pow (sin ky) 2.0)
1.0ms
(pow (sin kx) 2.0)
17.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
106.0ms
(pow (sin ky) 2.0)
110.0ms
(pow (sin kx) 2.0)
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03411065
11159981
25001976

prune416.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

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)))
0.2b
(* (/ (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))))

rewrite14.0ms

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:
0.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
8.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
3.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series955.0ms

Counts
3 → 9
Calls
3 calls:
250.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
336.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
369.0ms
(/ (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

prune340.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
104×add-sqr-sqrt
92×*-un-lft-identity
90×add-cube-cbrt
44×associate-*l*
36×add-exp-log
20×add-cbrt-cube
16×associate-/r*
15×div-exp
10×div-inv
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×associate-*r* cbrt-unprod
2×frac-2neg clear-num associate-/r/
1×hypot-udef pow-flip pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 191
Calls
4 calls:
0.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
2.0ms
(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
22.0ms
(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
5.0ms
(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

series1.2s

Counts
4 → 12
Calls
4 calls:
254.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
283.0ms
(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))
359.0ms
(* (/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky))) (sin th))
292.0ms
(/ 1 (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin ky)))

simplify83.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06933162
131342842
250022742

prune677.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 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)))
0.3b
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.3b
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*l* 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 associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
0.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
3.0ms
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
8.0ms
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series936.0ms

Counts
3 → 9
Calls
3 calls:
253.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
323.0ms
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
360.0ms
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02911109
11164984
25001983

prune421.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes309.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01511
11511

end0.0ms

sample1.7m

Algorithm
intervals
Results
1.6m23597×body10240exit
3.5s3672×body1280valid
1.3s2094×body640valid
303.0ms734×body320valid
145.0ms1202×body80valid
88.0ms298×body160valid