Details

sample257.0ms

Algorithm

intervals

Results

187.0ms	163×	body	1280	valid
39.0ms	63×	body	640	valid
9.0ms	22×	body	320	valid
2.0ms	6×	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: 18.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b	(cos (- lambda1 lambda2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

32.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
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))

series186.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
46.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	388	1113
1	1250	911
2	5001	909
done	5001	909

prune349.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (sin lambda1) (sin lambda2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 78

Calls

4 calls:

6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
43.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
11.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
116.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
74.0ms	(* (sin lambda1) (sin lambda2))
34.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify46.0ms

Counts

90 → 90

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	325	1357
1	1237	1141
2	5001	1141
done	5001	1141

prune469.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda1) (sin lambda2))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
0.6b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`acos-asin` `log-prod` `associate-r` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `sin-mult` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (sin lambda2))
48.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
22.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify101.0ms

Counts

75 → 75

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	204	1410
1	517	1249
2	1188	1249
3	1882	1249
4	3716	1249
5	5002	1249
done	5002	1249

prune485.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
7.1b	(cbrt (* (sin lambda1) (sin lambda2)))
7.1b	(cbrt (* (sin lambda1) (sin lambda2)))
7.1b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`
1×	`acos-asin`

Counts

4 → 46

Calls

4 calls:

2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))
96.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
98.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
101.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify155.0ms

Counts

58 → 58

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	167	782
1	416	689
2	1278	665
3	4462	639
4	5001	639
done	5001	639

prune399.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 2.7b

regimes920.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	34
1	38	34
done	38	34

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.6s	4752×	body	1280	valid
1.6s	2141×	body	640	valid
274.0ms	667×	body	320	valid
79.0ms	286×	body	160	valid
57.0ms	16×	body	2560	valid
21.0ms	141×	body	80	valid