Details

sample251.0ms

Algorithm

intervals

Results

175.0ms	151×	body	1280	valid
40.0ms	59×	body	640	valid
12.0ms	30×	body	320	valid
4.0ms	14×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12
done	45	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize31.0ms

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)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b	(cos (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 72

Calls

4 calls:

12.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
13.0ms	(cos (- lambda1 lambda2))

series128.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin phi1) (sin phi2))
46.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify62.0ms

Counts

84 → 84

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	323	995
1	789	819
2	2620	818
3	5002	793
done	5002	793

prune361.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.7b

localize31.0ms

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)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite33.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 72

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
12.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (sin lambda2))
46.0ms	(* (sin phi1) (sin phi2))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify79.0ms

Counts

84 → 84

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	274	1015
1	872	860
2	2115	860
3	3356	860
4	5001	860
done	5001	860

prune491.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.6b

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)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.9b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite26.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 67

Calls

4 calls:

12.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
4.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin phi1) (sin phi2))
81.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
55.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify68.0ms

Counts

79 → 79

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	1094
1	699	935
2	1610	935
3	2413	935
4	5001	935
done	5001	935

prune546.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.6b

localize45.0ms

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)))))))))
0.9b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.9b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite17.0ms

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`acos-asin`
2×	`exp-diff` `rem-log-exp`
1×	`log-div` `exp-to-pow` `rem-exp-log`

Counts

4 → 58

Calls

4 calls:

3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))))
6.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
5.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series137.0ms

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)))))))))
18.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))
23.0ms	(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))))

simplify64.0ms

Counts

70 → 70

Iterations

Useful iterations: 5 (53.0ms)

Iter	Nodes	Cost
0	156	1309
1	326	1140
2	686	1140
3	1000	1140
4	1956	1140
5	5001	1136
done	5001	1136

prune398.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.5b

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	21
1	34	21
done	34	21

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.0s	4852×	body	1280	valid
1.4s	2067×	body	640	valid
305.0ms	665×	body	320	valid
89.0ms	278×	body	160	valid
25.0ms	8×	body	2560	valid
20.0ms	133×	body	80	valid