Details

Time bar (total: 11.8s)

sample43.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (* 2.0 l) Om) 2.0)
0.3b
(pow (sin ky) 2.0)
2.0b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-sqr-sqrt unpow-prod-down
18×*-un-lft-identity
14×add-cube-cbrt
11×associate-*l*
7×pow1 pow-exp prod-exp
6×pow-unpow times-frac add-cbrt-cube
5×associate-*r*
4×div-exp add-log-exp sqr-pow
3×pow-to-exp sqrt-prod unswap-sqr
2×pow-pow flip3-+ sqrt-div associate-*r/ flip-+ div-inv distribute-lft-out
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod
Counts
4 → 92
Calls
4 calls:
3.0ms
(pow (/ (* 2.0 l) Om) 2.0)
1.0ms
(pow (sin ky) 2.0)
40.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series866.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(pow (/ (* 2.0 l) Om) 2.0)
102.0ms
(pow (sin ky) 2.0)
371.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
312.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0499898
11982856
25003856

prune432.0ms

Filtered
104 candidates to 71 candidates (68.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin ky))
0.7b
(cbrt (sin ky))
2.0b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))
10.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×add-exp-log
11×add-cube-cbrt *-un-lft-identity associate-*l*
8×unpow-prod-down
6×cbrt-prod prod-exp add-cbrt-cube
5×pow1
4×add-log-exp
3×times-frac associate-*r* pow-exp sqrt-prod unswap-sqr
2×flip3-+ pow1/3 sqrt-div associate-*r/ div-exp flip-+ sqr-pow
1×distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))
28.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))

series862.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(cbrt (sin ky))
94.0ms
(cbrt (sin ky))
374.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))
300.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))

simplify54.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04221295
116181225
250021218

prune452.0ms

Filtered
84 candidates to 62 candidates (73.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin ky))
0.7b
(cbrt (sin ky))
1.6b
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))
2.0b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity associate-*l*
8×unpow-prod-down
6×cbrt-prod prod-exp add-cbrt-cube
5×pow1 log-prod add-log-exp
3×times-frac associate-*r* pow-exp log-pow unswap-sqr
2×distribute-rgt-in distribute-lft-in pow1/3 associate-*r/ div-exp exp-sum sqr-pow
1×pow-to-exp exp-prod exp-to-pow flip3-+ rem-log-exp *-commutative cbrt-unprod flip-+ div-inv
Counts
4 → 73
Calls
4 calls:
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))
4.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))
25.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))

series960.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (sin ky))
99.0ms
(cbrt (sin ky))
386.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))
372.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))

simplify58.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03971298
115021154
250021147

prune496.0ms

Filtered
85 candidates to 65 candidates (76.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.3b

localize50.0ms

Local error

Found 4 expressions with local error:

5.2b
(sqrt (+ (pow 1.0 3) (pow (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) 3)))
6.1b
(sqrt (+ (* 1.0 1.0) (- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))))
13.4b
(- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))
18.8b
(/ (sqrt (+ (pow 1.0 3) (pow (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) 3))) (sqrt (+ (* 1.0 1.0) (- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))))))))

rewrite604.0ms

Algorithm
rewrite-expression-head
Rules
74×associate-*r/
70×sqrt-prod
54×*-un-lft-identity
48×times-frac
40×add-sqr-sqrt
38×add-cube-cbrt
28×flip3-+ flip-+
16×frac-sub
8×distribute-rgt-in frac-times distribute-lft-in sqrt-div sum-cubes distribute-lft-out associate-/l*
6×pow1 add-exp-log associate-*l/ associate-/r* add-cbrt-cube add-log-exp
4×associate--l+ associate--r+ sub-div
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv sub-neg sqrt-undiv flip3-- distribute-rgt-out-- frac-2neg diff-log div-exp clear-num flip-- div-inv
Counts
4 → 152
Calls
4 calls:
18.0ms
(sqrt (+ (pow 1.0 3) (pow (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) 3)))
246.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))))
61.0ms
(- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))
272.0ms
(/ (sqrt (+ (pow 1.0 3) (pow (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) 3))) (sqrt (+ (* 1.0 1.0) (- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))))))))

series3.9s

Counts
4 → 12
Calls
4 calls:
705.0ms
(sqrt (+ (pow 1.0 3) (pow (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) 3)))
829.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))))
563.0ms
(- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))))
1.8s
(/ (sqrt (+ (pow 1.0 3) (pow (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) 3))) (sqrt (+ (* 1.0 1.0) (- (* (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))) (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))))) (* 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0)))))))))

simplify237.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
086717051
1410115327
2500215294

prune1.0s

Filtered
164 candidates to 104 candidates (63.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.3b

regimes311.0ms

Accuracy

0% (0.5b remaining)

Error of 1.8b against oracle of 1.3b and baseline of 1.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03526
13526

end0.0ms

sample1.0s

Algorithm
intervals
Results
813.0ms8000×body80valid