Details

sample115.0ms

Algorithm

intervals

Results

64.0ms	91×	body	1280	valid
22.0ms	56×	body	640	valid
6.0ms	75×	body	80	valid
5.0ms	19×	body	320	valid
3.0ms	15×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize22.0ms

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 ky) 2.0)
0.2b	(pow (sin kx) 2.0)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

85.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
4.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
106.0ms	(pow (sin ky) 2.0)
110.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	391	990
1	1382	928
2	5001	927

prune420.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.2b	(pow (sin ky) 2)
0.2b	(pow (sin kx) 2)
2.5b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 103

Calls

4 calls:

87.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
4.0ms	(pow (sin ky) 2)
4.0ms	(pow (sin kx) 2)
29.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
19.0ms	(pow (sin ky) 2)
23.0ms	(pow (sin kx) 2)
78.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify50.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	982
1	1374	902
2	5001	899

prune394.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.2b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

4.0ms	(pow (sin kx) 2.0)
37.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
83.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow (sin kx) 2.0)
135.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
150.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	412	1572
1	1672	1426
2	5001	1423

prune451.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`sqrt-prod`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`unpow-prod-down` `sqrt-div` `distribute-lft-out`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (sin ky))
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (sin ky))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	171	583
1	424	554
2	1478	552
3	5002	551

prune317.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.0b

regimes1.1s

Accuracy

0% (1.6b remaining)

Error of 12.7b against oracle of 11.1b and baseline of 12.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	34
1	22	34

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.0s	2727×	body	1280	valid
940.0ms	1864×	body	640	valid
197.0ms	754×	body	320	valid
194.0ms	2300×	body	80	valid
62.0ms	355×	body	160	valid