Details

sample1.5s

Algorithm

intervals

Results

1.2s	152×	body	1280	valid
125.0ms	72×	body	640	valid
16.0ms	18×	body	320	valid
11.0ms	2×	body	2560	valid
4.0ms	7×	body	160	valid
4.0ms	5×	body	80	valid

simplify57.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	17	635
1	27	610
2	38	610
3	39	610
done	39	610

prune82.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.5b

localize87.0ms

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)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.5b	(cos (- lambda1 lambda2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
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:

20.0ms	(* (sin phi1) (sin phi2))
12.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
25.0ms	(cos (- lambda1 lambda2))

series246.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin phi1) (sin phi2))
97.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
22.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
51.0ms	(cos (- lambda1 lambda2))

simplify4.1s

Counts

84 → 84

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	187	41907
1	335	38914
2	611	36961
3	1330	36936
4	3105	35967
done	5000	35942

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.7b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite26.0ms

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×	`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:

9.0ms	(* (sin phi1) (sin phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* (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))))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin phi1) (sin phi2))
85.0ms	(* (sin lambda1) (sin lambda2))
106.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
35.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify5.8s

Counts

84 → 84

Iterations

Useful iterations: 3 (950.0ms)

Iter	Nodes	Cost
0	142	44660
1	291	42527
2	675	41887
3	1572	41807
4	3118	41807
done	5004	41807

prune1000.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.6b

localize104.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.4b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

18.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
3.0ms	(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))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin lambda1) (sin lambda2))
130.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
38.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
91.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify5.6s

Counts

79 → 79

Iterations

Useful iterations: 2 (320.0ms)

Iter	Nodes	Cost
0	127	49981
1	244	41869
2	527	41229
3	1262	41229
4	2756	41229
done	5000	41229

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.6b

localize125.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))
0.4b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))))
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

18.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))) R)
3.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))) R)
57.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))))))
13.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))))
24.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))))

simplify8.1s

Counts

78 → 78

Iterations

Useful iterations: 5 (2.8s)

Iter	Nodes	Cost
0	106	73142
1	166	67290
2	341	67070
3	681	67005
4	1111	67005
5	2315	66727
done	5002	66727

prune913.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.6b

regimes2.4s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	24	942
1	28	942
done	28	942

end0.0ms

sample19.8s

Algorithm

intervals

Results

14.6s	4762×	body	1280	valid
3.2s	2125×	body	640	valid
679.0ms	695×	body	320	valid
655.0ms	267×	body	160	valid
93.0ms	17×	body	2560	valid
40.0ms	136×	body	80	valid