Details

Time bar (total: 14.4s)

sample163.0ms

Algorithm
intervals
Results
88.0ms89×body1280valid
37.0ms63×body640valid
11.0ms27×body320valid
9.0ms70×body80valid
2.0ms7×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13910
26710
315310
443910
5183010
6500110

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

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)))) (sin th))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
4.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
41×*-un-lft-identity
30×associate-*l*
26×times-frac
25×add-cube-cbrt
21×sqrt-prod
20×unpow-prod-down
11×add-exp-log
9×pow1 add-cbrt-cube hypot-def
8×distribute-lft-out sqr-pow
6×pow-unpow
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* unswap-sqr
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 118
Calls
4 calls:
49.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms
(pow (sin kx) 2.0)
1.0ms
(pow (sin ky) 2.0)
17.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series107.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
14.0ms
(pow (sin kx) 2.0)
19.0ms
(pow (sin ky) 2.0)
22.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04031039
11433967
25002965

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.0b

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)))
0.2b
(/ (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)))) (sin th))

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)))
3.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
9.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

series249.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
91.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
100.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

simplify37.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02951114
11091988
25001986

prune909.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.0b

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 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)))))

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:
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)))))

series257.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
90.0ms
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
109.0ms
(* (sin ky) (/ (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 (32.0ms)

IterNodesCost
02911109
11164984
25001983

prune941.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 8.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
0.4b
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
0.4b
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
0.4b
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
103×cbrt-prod
81×add-sqr-sqrt
69×times-frac
57×add-cube-cbrt *-un-lft-identity
16×swap-sqr associate-*r* associate-*l*
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 152
Calls
4 calls:
18.0ms
(* (cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
1.0ms
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
1.0ms
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
2.0ms
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series578.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(* (cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
135.0ms
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
136.0ms
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
137.0ms
(cbrt (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02973637
110493487
250013324

prune2.3s

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 8.0b

regimes2.6s

Accuracy

0% (0.1b remaining)

Error of 9.0b against oracle of 8.8b and baseline of 9.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01511
11511

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.6s2784×body1280valid
1.1s1800×body640valid
350.0ms807×body320valid
303.0ms2256×body80valid
95.0ms353×body160valid