Details

sample243.0ms

Algorithm

intervals

Results

167.0ms	154×	body	1280	valid
43.0ms	66×	body	640	valid
10.0ms	25×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	3×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	19
1	26	19
2	33	19
3	35	19
done	35	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize28.0ms

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)
1.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.6b	(cos (- lambda1 lambda2))

rewrite31.0ms

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:

11.0ms	(* (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)))))
10.0ms	(cos (- lambda1 lambda2))

series131.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin phi1) (sin phi2))
47.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

67 → 67

Iterations

Useful iterations: 3 (210.0ms)

Iter	Nodes	Cost
0	111	1035
1	198	1027
2	435	893
3	686	887
4	916	887
5	1536	887
6	3401	887
done	5000	887

prune304.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.7b

localize32.0ms

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)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite38.0ms

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` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 65

Calls

4 calls:

15.0ms	(* (sin lambda1) (sin (- lambda2)))
13.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (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)))))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin lambda1) (sin (- lambda2)))
50.0ms	(* (sin phi1) (sin phi2))
74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify4.7s

Counts

77 → 77

Iterations

Useful iterations: 3 (409.0ms)

Iter	Nodes	Cost
0	143	1487
1	270	1473
2	722	1270
3	1538	1200
4	2742	1200
5	4495	1200
done	5000	1200

prune484.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.6b

localize35.0ms

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)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
3.0b	(log (exp (* (sin lambda1) (sin (- lambda2)))))

rewrite28.0ms

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×	`exp-neg` `pow-prod-down` `prod-exp` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `log-div` `exp-prod` `exp-to-pow` `rem-log-exp` `log-rec` `sin-mult`

Counts

4 → 61

Calls

4 calls:

12.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (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)))))))))
7.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin phi1) (sin phi2))
76.0ms	(* (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)))))))))
57.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

simplify3.4s

Counts

73 → 73

Iterations

Useful iterations: 3 (285.0ms)

Iter	Nodes	Cost
0	132	1553
1	231	1441
2	573	1244
3	1130	1174
4	2075	1174
5	4983	1174
done	5001	1174

prune492.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.6b

localize36.0ms

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 (pow (exp (sin lambda1)) (sin (- lambda2)))))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin (- lambda2))))))))
3.0b	(log (pow (exp (sin lambda1)) (sin (- lambda2))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
7×	`log-prod`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`unpow-prod-down` `rem-log-exp`
2×	`pow-neg` `log-div` `pow-prod-down` `prod-exp` `sin-neg` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `acos-asin` `pow-to-exp` `log-rec` `pow-exp` `log-pow` `sin-diff` `sin-mult` `pow-sub` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

11.0ms	(* (sin phi1) (sin phi2))
8.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin (- lambda2)))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin (- lambda2))))))))
8.0ms	(log (pow (exp (sin lambda1)) (sin (- lambda2))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin phi1) (sin phi2))
81.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin (- lambda2)))))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin (- lambda2))))))))
122.0ms	(log (pow (exp (sin lambda1)) (sin (- lambda2))))

simplify2.9s

Counts

78 → 78

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	154	1648
1	280	1511
2	676	1273
3	1438	1233
4	4215	1226
done	5001	1226

prune401.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.6b

regimes984.0ms

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	29
1	31	29
done	31	29

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.8s	4776×	body	1280	valid
1.3s	2013×	body	640	valid
332.0ms	759×	body	320	valid
85.0ms	288×	body	160	valid
55.0ms	16×	body	2560	valid
21.0ms	151×	body	80	valid