Details

Time bar (total: 12.9s)

sample66.0ms

Algorithm
intervals
Results
48.0ms256×body80valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.4b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.6b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.4b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
21×times-frac
19×add-exp-log
15×sqrt-prod
13×unpow-prod-down
11×associate-*l*
8×add-cbrt-cube
6×pow1 prod-exp associate-/r*
5×associate-*r*
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
3×pow-unpow flip3-+ div-exp flip-+ associate-/l* unswap-sqr sqr-pow
2×pow-to-exp associate-*r/ associate-/r/ div-inv distribute-lft-out
1×cbrt-undiv distribute-rgt-in rem-sqrt-square pow-pow frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num *-commutative cbrt-unprod
Counts
4 → 118
Calls
4 calls:
1.0ms
(pow (sin kx) 2.0)
5.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
41.0ms
(* (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)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
107.0ms
(pow (sin kx) 2.0)
388.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
386.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
319.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05201687
121351580
250031576

prune567.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
1.0b
(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
1.6b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.4b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
17×add-exp-log
14×add-cube-cbrt
13×unpow-prod-down
11×associate-*l*
7×pow1 log-pow
6×exp-prod prod-exp sqrt-prod add-cbrt-cube
5×associate-*r*
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×pow-unpow log-prod times-frac unswap-sqr sqr-pow
2×pow-to-exp flip3-+ sqrt-div associate-*r/ div-exp flip-+ distribute-lft-out
1×distribute-rgt-in rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow1/2 rem-log-exp *-commutative cbrt-unprod div-inv
Counts
4 → 95
Calls
4 calls:
1.0ms
(pow (sin kx) 2.0)
6.0ms
(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
41.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
109.0ms
(pow (sin kx) 2.0)
327.0ms
(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
389.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
316.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04661096
118331042
250011042

prune520.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt Om)
2.2b
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.6b
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.4b
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
54×prod-exp
37×associate-*l*
36×add-sqr-sqrt
34×unpow-prod-down
28×*-un-lft-identity
27×pow-exp
24×add-cube-cbrt
23×times-frac
16×div-exp
13×cbrt-prod
11×pow-to-exp add-cbrt-cube
6×associate-*r/ associate-*r*
5×pow1 distribute-rgt-in distribute-lft-in unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×flip3-+ sqrt-prod flip-+ sqr-pow
2×sqrt-div *-commutative div-inv distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 140
Calls
4 calls:
1.0ms
(cbrt Om)
56.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
57.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt Om)
560.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
567.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
557.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify106.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
08662160
137222054
250032045

prune755.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.2b

localize34.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.3b
(exp (fma (log (/ 2.0 (* (cbrt Om) (cbrt Om)))) 2.0 (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.4b
(sqrt (+ 1.0 (exp (fma (log (/ 2.0 (* (cbrt Om) (cbrt Om)))) 2.0 (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
28.8b
(log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
27×unpow-prod-down *-un-lft-identity
26×associate-*l*
21×add-exp-log add-cube-cbrt
20×times-frac
10×cbrt-prod
8×prod-exp
6×pow1 add-cbrt-cube
5×rem-log-exp associate-*r* add-log-exp unswap-sqr
4×expm1-log1p-u associate-*r/ pow-exp sqrt-prod log1p-expm1-u
3×exp-prod flip3-+ flip-+ distribute-lft-out
2×pow-to-exp log-div sqrt-div div-exp sqr-pow
1×distribute-rgt-in rem-sqrt-square log-prod distribute-lft-in sqrt-pow1 pow1/2 exp-sum log-pow *-commutative cbrt-unprod fma-udef hypot-def div-inv rem-exp-log
Counts
4 → 106
Calls
4 calls:
56.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.0ms
(exp (fma (log (/ 2.0 (* (cbrt Om) (cbrt Om)))) 2.0 (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
6.0ms
(sqrt (+ 1.0 (exp (fma (log (/ 2.0 (* (cbrt Om) (cbrt Om)))) 2.0 (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
18.0ms
(log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

series2.8s

Counts
4 → 12
Calls
4 calls:
432.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
755.0ms
(exp (fma (log (/ 2.0 (* (cbrt Om) (cbrt Om)))) 2.0 (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.2s
(sqrt (+ 1.0 (exp (fma (log (/ 2.0 (* (cbrt Om) (cbrt Om)))) 2.0 (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
463.0ms
(log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

simplify71.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06361781
123351701
250011692

prune787.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes643.0ms

Accuracy

0% (0.6b remaining)

Error of 2.0b against oracle of 1.3b and baseline of 2.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03018
13018

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.6s8000×body80valid