Details

Time bar (total: 9.1s)

sample110.0ms

Algorithm
intervals
Results
59.0ms87×body1280valid
24.0ms63×body640valid
6.0ms70×body80valid
5.0ms20×body320valid
3.0ms16×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: 13.3b

localize23.0ms

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)
3.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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:
50.0ms
(* (/ (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)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms
(pow (sin kx) 2.0)
104.0ms
(pow (sin ky) 2.0)
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04031038
11435967
25002965

prune477.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (sin ky) (sin kx))
0.2b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (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 (sin ky) (sin kx))
3.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
9.0ms
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series498.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(hypot (sin ky) (sin kx))
158.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
223.0ms
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify139.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0287725
11045645
24965644
35001644

prune290.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.7b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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 (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
2.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series877.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
217.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
215.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
216.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify48.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02912447
19932341
250012212

prune689.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (hypot (sin ky) (sin kx)))
0.6b
(cbrt (sin ky))
0.6b
(cbrt (sin ky))
0.6b
(cbrt (sin ky))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
0.0ms
(cbrt (hypot (sin ky) (sin kx)))
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))

series436.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (hypot (sin ky) (sin kx)))
94.0ms
(cbrt (sin ky))
95.0ms
(cbrt (sin ky))
97.0ms
(cbrt (sin ky))

simplify151.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0136317
1328287
21001278
34375278
45001278

prune257.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.7b

regimes869.0ms

Accuracy

0% (0.1b remaining)

Error of 9.1b against oracle of 8.9b and baseline of 9.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107
1107

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.9s2711×body1280valid
916.0ms1903×body640valid
210.0ms2259×body80valid
207.0ms779×body320valid
61.0ms348×body160valid