Details

sample103.0ms

Algorithm

intervals

Results

40.0ms	91×	body	1280	valid
21.0ms	255×	body	80	valid
17.0ms	58×	body	640	valid
7.0ms	32×	body	320	valid
3.0ms	16×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

2 → 87

Calls

2 calls:

21.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series271.0ms

Counts

2 → 6

Calls

2 calls:

213.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	479	795
1	2384	738
2	5002	725

prune245.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
1×	`frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+`

Counts

2 → 83

Calls

2 calls:

19.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
9.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series303.0ms

Counts

2 → 6

Calls

2 calls:

209.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
94.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	314	880
1	1523	816
2	5002	800

prune214.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.3b	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
102×	`sqrt-prod`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt` `*-un-lft-identity`
78×	`cbrt-prod`
58×	`associate-r`
38×	`add-exp-log`
29×	`add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sqrt-div` `associate-/l*`
4×	`add-log-exp`
3×	`flip3-+` `associate-*r/` `pow-prod-down` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-l` `associate-l/` `clear-num` `-commutative`

Counts

4 → 201

Calls

4 calls:

9.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
73.0ms	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
219.0ms	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
36.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
36.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify122.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	703	3560
1	3971	3228
2	5001	3067

prune586.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0)))))
0.3b	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0))))))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

383×	`add-exp-log`
220×	`prod-exp`
134×	`add-cbrt-cube`
128×	`add-sqr-sqrt`
120×	`cbrt-prod`
117×	`times-frac`
105×	`div-exp`
96×	`cbrt-unprod`
78×	`sqrt-prod`
77×	`associate-r`
66×	`*-un-lft-identity`
57×	`add-cube-cbrt`
49×	`cbrt-undiv`
27×	`unswap-sqr`
20×	`pow1` `rec-exp` `1-exp`
10×	`associate-*r/`
9×	`pow-prod-down`
8×	`associate-l`
6×	`frac-times`
4×	`sqrt-div` `associate-*l/` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `*-commutative` `flip-+` `div-inv`

Counts

4 → 281

Calls

4 calls:

72.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0)))))
174.0ms	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0))))))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0)))))
223.0ms	(* (* (cos th) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (cbrt (sqrt 2.0))))))
41.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
36.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify77.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1441	7798
1	5001	6199

prune681.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes166.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	2496×	body	1280	valid
661.0ms	8079×	body	80	valid
624.0ms	2118×	body	640	valid
239.0ms	1068×	body	320	valid
78.0ms	492×	body	160	valid