Details

sample266.0ms

Algorithm

intervals

Results

197.0ms	163×	body	1280	valid
42.0ms	67×	body	640	valid
6.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid
0.0ms	3×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.6b	(cos (- lambda1 lambda2))

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`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

series121.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (sin phi2))
48.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	200	661
1	565	569
2	1790	569
3	5001	569

prune293.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (sin lambda2))
46.0ms	(* (sin phi1) (sin phi2))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	929
1	831	774
2	1930	774
3	3056	774
4	5001	774

prune388.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
4.4b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
1.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin phi1) (sin phi2))
69.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
46.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify67.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	219	996
1	658	837
2	1441	837
3	2189	837
4	5001	837

prune411.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))))
0.8b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
4.4b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`exp-prod` `log-pow`
6×	`pow1` `log-prod` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`acos-asin`
2×	`exp-diff` `rem-log-exp`
1×	`log-div` `exp-to-pow` `rem-exp-log`

Counts

4 → 50

Calls

4 calls:

1.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))))
2.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
1.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))))
17.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
49.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 5 (51.0ms)

Iter	Nodes	Cost
0	142	1181
1	289	1012
2	532	1012
3	793	1012
4	1696	1012
5	5002	1008

prune334.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.6b

regimes604.0ms

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	23
1	36	23

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.7s	4779×	body	1280	valid
1.5s	2141×	body	640	valid
305.0ms	681×	body	320	valid
77.0ms	270×	body	160	valid
19.0ms	128×	body	80	valid
17.0ms	5×	body	2560	valid