Details

sample269.0ms

Algorithm

intervals

Results

173.0ms	108×	body	1280	valid
52.0ms	55×	body	640	valid
10.0ms	18×	body	320	valid
9.0ms	60×	body	80	valid
6.0ms	15×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	22
1	56	22
2	59	22
3	59	22

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

4.0ms	(* (sin theta) (sin delta))
4.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin theta) (sin delta))
153.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
180.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	289	930
1	894	837
2	3513	835
3	5002	835

prune374.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
0.4b	(pow (cos delta) 3)
0.5b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `difference-of-squares` `sqr-pow`
6×	`unpow-prod-down` `pow-unpow` `cube-prod` `add-log-exp`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `unpow3`
1×	`difference-cubes` `cube-div` `sub-neg` `asin-acos` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out--`

Counts

4 → 76

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
1.0ms	(pow (cos delta) 3)
3.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.0s

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
732.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
32.0ms	(pow (cos delta) 3)
229.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify89.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	487	1373
1	2447	1276
2	5001	1264

prune585.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (sin phi1) 4)
0.5b	(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (pow (sin phi1) 6) (pow (cos delta) 3)))
0.5b	(pow (sin phi1) 5)
0.6b	(pow (sin phi1) 6)

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow` `add-log-exp`
7×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `diff-log` `pow-exp` `sqr-pow`
2×	`sub-neg` `associate--l+`
1×	`associate--l-` `flip3--` `flip--`

Counts

4 → 67

Calls

4 calls:

1.0ms	(pow (sin phi1) 4)
314.0ms	(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (pow (sin phi1) 6) (pow (cos delta) 3)))
1.0ms	(pow (sin phi1) 5)
2.0ms	(pow (sin phi1) 6)

series363.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sin phi1) 4)
246.0ms	(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (pow (sin phi1) 6) (pow (cos delta) 3)))
41.0ms	(pow (sin phi1) 5)
45.0ms	(pow (sin phi1) 6)

simplify56.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	375	720
1	1511	654
2	5001	635

prune1.0s

Filtered

79 candidates to 51 candidates (64.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize274.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin phi1) 3)
0.5b	(pow (sin phi1) 4)
0.5b	(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (* (pow (sin phi1) 3) (pow (sin phi1) 3)) (pow (cos delta) 3)))
0.5b	(pow (sin phi1) 5)

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow` `add-log-exp`
7×	`pow1` `add-exp-log`
5×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `diff-log` `cube-prod` `pow-exp` `sqr-pow`
2×	`sub-neg` `associate--l+`
1×	`associate--l-` `cube-mult` `flip3--` `unpow3` `flip--` `rem-cube-cbrt`

Counts

4 → 73

Calls

4 calls:

1.0ms	(pow (sin phi1) 3)
2.0ms	(pow (sin phi1) 4)
319.0ms	(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (* (pow (sin phi1) 3) (pow (sin phi1) 3)) (pow (cos delta) 3)))
2.0ms	(pow (sin phi1) 5)

series344.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sin phi1) 3)
29.0ms	(pow (sin phi1) 4)
238.0ms	(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (* (pow (sin phi1) 3) (pow (sin phi1) 3)) (pow (cos delta) 3)))
44.0ms	(pow (sin phi1) 5)

simplify68.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	401	777
1	1745	691
2	5002	684

prune874.0ms

Filtered

85 candidates to 51 candidates (60.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes665.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	96
1	86	96

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.1s	3177×	body	1280	valid
1.7s	1796×	body	640	valid
435.0ms	734×	body	320	valid
337.0ms	1979×	body	80	valid
118.0ms	314×	body	160	valid