Details

Time bar (total: 8.3s)

sample125.0ms

Algorithm
intervals
Results
71.0ms96×body1280valid
24.0ms59×body640valid
7.0ms75×body80valid
4.0ms15×body320valid
2.0ms11×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
27×add-sqr-sqrt
26×add-cube-cbrt
25×sqrt-prod
24×times-frac
16×unpow-prod-down
10×distribute-lft-out
8×add-exp-log associate-/r*
7×pow1
6×pow-unpow add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
35.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
32.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
109.0ms
(pow (sin kx) 2.0)
105.0ms
(pow (sin ky) 2.0)
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify38.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
03291021
11106946
25002943

prune392.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2)
0.3b
(pow (sin ky) 2)
0.4b
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
3.4b
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
45×sqrt-prod
41×add-sqr-sqrt
34×times-frac
28×add-cube-cbrt
24×associate-*l*
18×unpow-prod-down
12×distribute-lft-out
10×pow1
8×add-exp-log
6×pow-unpow add-cbrt-cube
4×associate-/r/ add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 associate-*r*
2×pow-to-exp pow-pow flip3-+ sqrt-div pow-exp flip-+ div-inv unpow2 sqr-pow
1×pow-flip pow1/2 pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod inv-pow
Counts
4 → 115
Calls
4 calls:
4.0ms
(pow (sin kx) 2)
4.0ms
(pow (sin ky) 2)
81.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
35.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series255.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(pow (sin kx) 2)
18.0ms
(pow (sin ky) 2)
117.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
102.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify45.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03691078
11262985
25002948

prune438.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
3.4b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
32.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (sin kx))
99.0ms
(cbrt (sin kx))
98.0ms
(cbrt (sin kx))
75.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0183511
1496483
22171477
35002476

prune349.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
3.4b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
43.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(cbrt (sin kx))
95.0ms
(cbrt (sin kx))
94.0ms
(cbrt (sin kx))
73.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) 2.0)) (pow (sin ky) 2.0)))

simplify77.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0185700
1497663
22175657
35002656

prune306.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

regimes832.0ms

Accuracy

0% (1.6b remaining)

Error of 13.1b against oracle of 11.5b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02736
12736

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.0s2698×body1280valid
942.0ms1845×body640valid
231.0ms2377×body80valid
210.0ms751×body320valid
61.0ms329×body160valid