Details

Time bar (total: 10.2s)

sample154.0ms

Algorithm
intervals
Results
92.0ms119×body1280valid
32.0ms68×body640valid
8.0ms41×body80valid
6.0ms17×body320valid
2.0ms11×body160valid

simplify53.0ms

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: 3.6b

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 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)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
103.0ms
(pow (sin kx) 2.0)
105.0ms
(pow (sin ky) 2.0)
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03411066
11157981
25002976

prune422.0ms

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)))
6.0ms
(* (/ (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))))

series960.0ms

Counts
3 → 9
Calls
3 calls:
251.0ms
(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))
372.0ms
(/ (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

prune321.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

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 th) (/ (sin ky) (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))))

rewrite13.0ms

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:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
7.0ms
(* (sin th) (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
4.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series984.0ms

Counts
3 → 9
Calls
3 calls:
245.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
365.0ms
(* (sin th) (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
374.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02771107
11127981
25001980

prune308.0ms

Pruning

9 alts after pruning (8 fresh and 1 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 ky) (/ (sin th) (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))))

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:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
7.0ms
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
4.0ms
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series917.0ms

Counts
3 → 9
Calls
3 calls:
246.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
353.0ms
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
319.0ms
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify41.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02911109
11164984
25002983

prune286.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes284.0ms

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
01511
11511

end0.0ms

sample4.8s

Algorithm
intervals
Results
3.1s3710×body1280valid
986.0ms2044×body640valid
243.0ms710×body320valid
127.0ms1263×body80valid
62.0ms273×body160valid