Details

sample323.0ms

Algorithm

intervals

Results

198.0ms	107×	body	1280	valid
71.0ms	61×	body	640	valid
12.0ms	19×	body	320	valid
11.0ms	51×	body	80	valid
8.0ms	18×	body	160	valid

simplify8.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite17.0ms

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:

5.0ms	(* (sin theta) (sin delta))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin theta) (sin delta))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
148.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
177.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (25.0ms)

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

prune375.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.3b	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `log-prod` `add-cbrt-cube` `add-log-exp`
4×	`log-pow`
3×	`associate-r` `associate-l` `associate--r+`
2×	`distribute-lft-out--`
1×	`sub-neg` `asin-acos` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `difference-of-squares` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
150.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
172.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
152.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	250	1229
1	686	1110
2	2590	1106
3	5002	1106

prune415.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.5b	(- (cos delta) (log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
2.3b	(log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
2.8b	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

39×	`log-prod`
20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`sin-sum`
16×	`add-cube-cbrt`
12×	`exp-sum`
9×	`pow1` `distribute-rgt-in` `distribute-lft-in` `associate--r+`
8×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod`
3×	`associate-r` `associate-l`
2×	`rem-log-exp` `distribute-lft-out--`
1×	`sub-neg` `log-div` `asin-acos` `flip3--` `exp-to-pow` `exp-diff` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `difference-of-squares` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

8.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
8.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
4.0ms	(log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
3.0ms	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
175.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
151.0ms	(log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
7.0ms	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify114.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	391	2431
1	1084	2283
2	4203	2259
3	5001	2155

prune601.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.9b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.9b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.9b	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod` `log-pow`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
12×	`pow1` `exp-prod` `sqrt-prod`
8×	`add-exp-log`
4×	`log-div` `asin-acos` `pow1/2` `exp-diff` `sqrt-div` `rem-log-exp` `add-cbrt-cube` `add-log-exp`

Counts

4 → 84

Calls

4 calls:

4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
67.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
64.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
70.0ms	(log (sqrt (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 7 (74.0ms)

Iter	Nodes	Cost
0	86	1716
1	103	1552
2	117	1552
3	152	1552
4	276	1552
5	663	1552
6	2884	1552
7	5001	1544

prune789.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes271.0ms

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	51	72
1	51	72

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.2s	3169×	body	1280	valid
1.7s	1784×	body	640	valid
430.0ms	690×	body	320	valid
333.0ms	2037×	body	80	valid
121.0ms	320×	body	160	valid