Details

sample639.0ms

Algorithm

intervals

Results

456.0ms	162×	body	1280	valid
77.0ms	63×	body	640	valid
15.0ms	18×	body	320	valid
5.0ms	6×	body	160	valid
3.0ms	7×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
3	36
2	33
1	26
0	17

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (sin phi1))
0.2b	(* R (acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
0.5b	(acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))
3.2b	(cos (- lambda1 lambda2))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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:

18.0ms	(* (sin phi2) (sin phi1))
11.0ms	(* R (acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
4.0ms	(acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))
20.0ms	(cos (- lambda1 lambda2))

series183.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sin phi2) (sin phi1))
36.0ms	(* R (acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
13.0ms	(acos (+ (* (cos (- lambda1 lambda2)) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))
51.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	3988
2	635
1	210
0	111

prune663.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (sin phi1))
0.2b	(* (sin lambda2) (sin lambda1))
0.3b	(* R (acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
0.5b	(acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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:

17.0ms	(* (sin phi2) (sin phi1))
19.0ms	(* (sin lambda2) (sin lambda1))
10.0ms	(* R (acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
5.0ms	(acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin phi2) (sin phi1))
86.0ms	(* (sin lambda2) (sin lambda1))
78.0ms	(* R (acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1)))))
18.0ms	(acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (* (sin phi2) (sin phi1))))

simplify542.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	933
1	275
0	134

prune965.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.3b	(* R (acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (pow (exp (sin phi1)) (sin phi2))))))
0.5b	(acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (pow (exp (sin phi1)) (sin phi2)))))
3.9b	(log (pow (exp (sin phi1)) (sin phi2)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
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-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `pow-to-exp` `pow-exp` `log-pow` `sin-mult` `sqr-pow`

Counts

4 → 63

Calls

4 calls:

19.0ms	(* (sin lambda2) (sin lambda1))
11.0ms	(* R (acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (pow (exp (sin phi1)) (sin phi2))))))
5.0ms	(acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (pow (exp (sin phi1)) (sin phi2)))))
11.0ms	(log (pow (exp (sin phi1)) (sin phi2)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin lambda2) (sin lambda1))
68.0ms	(* R (acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (pow (exp (sin phi1)) (sin phi2))))))
39.0ms	(acos (+ (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))) (log (pow (exp (sin phi1)) (sin phi2)))))
154.0ms	(log (pow (exp (sin phi1)) (sin phi2)))

simplify543.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
2	786
1	263
0	134

prune995.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))))
0.4b	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))
0.4b	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))
0.5b	(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
3×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 64

Calls

4 calls:

31.0ms	(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))))
8.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))
5.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))
3.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* R (log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))))
22.0ms	(log (exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))))
60.0ms	(exp (acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))))))))
36.0ms	(acos (+ (* (sin phi2) (sin phi1)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))))))

simplify2.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
5	4154
4	2815
3	1279
2	487
1	206
0	112

prune766.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.9b

regimes2.1s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample19.4s

Algorithm

intervals

Results

14.0s	4718×	body	1280	valid
3.6s	2172×	body	640	valid
624.0ms	648×	body	320	valid
306.0ms	312×	body	160	valid
60.0ms	12×	body	2560	valid
39.0ms	138×	body	80	valid