Details

sample248.0ms

Algorithm

intervals

Results

176.0ms	153×	body	1280	valid
44.0ms	71×	body	640	valid
9.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	1×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0b	(cos (- lambda1 lambda2))

rewrite17.0ms

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:

8.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

series117.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (sin phi2))
43.0ms	(* (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)))))
17.0ms	(cos (- lambda1 lambda2))

simplify3.4s

Counts

67 → 67

Iterations

Useful iterations: 3 (186.0ms)

Iter	Nodes	Cost
0	111	1035
1	199	1027
2	443	889
3	1149	887
4	4527	887
done	5000	887

prune302.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (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)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `cos-mult`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`frac-times` `associate-*r/` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/`

Counts

4 → 76

Calls

4 calls:

25.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (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)))))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
45.0ms	(* (sin phi1) (sin phi2))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify714.0ms

Counts

88 → 88

Iterations

Useful iterations: done (711.0ms)

Iter	Nodes	Cost
0	195	2211
1	489	2178
2	1735	1781
done	5000	1779

prune498.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))) R)
0.4b	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
0.9b	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
1.2b	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

7.0ms	(* (log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))) R)
1.0ms	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
3.0ms	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))) R)
45.0ms	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
17.0ms	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
17.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

simplify1.6s

Counts

70 → 70

Iterations

Useful iterations: 5 (600.0ms)

Iter	Nodes	Cost
0	107	2374
1	183	2277
2	368	2025
3	570	2025
4	875	1929
5	2133	1927
done	5001	1927

prune394.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.6b	(pow (* (cos lambda1) (cos lambda2)) 3)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

76×	`cos-mult`
60×	`frac-add`
58×	`sin-mult`
46×	`pow1`
35×	`associate-/r/`
34×	`frac-times` `associate-*r/`
31×	`associate-*l/`
28×	`add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down`
12×	`prod-exp` `cbrt-unprod`
9×	`cube-div` `associate-/l/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`flip3-+` `pow-sqr` `pow-prod-up` `flip-+` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `times-frac` `div-exp` `associate-/r*`
2×	`flip3--` `pow-pow` `pow-plus` `pow-exp` `frac-sub` `flip--` `sub-div` `rem-cube-cbrt`
1×	`pow2` `acos-asin` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `cube-prod` `swap-sqr` `associate-r` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 135

Calls

4 calls:

126.0ms	(/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))

series911.0ms

Counts

4 → 12

Calls

4 calls:

722.0ms	(/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
55.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
59.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
75.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))

simplify457.0ms

Counts

147 → 147

Iterations

Useful iterations: done (448.0ms)

Iter	Nodes	Cost
0	413	8034
1	1204	6775
done	5000	6631

prune828.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.7b

regimes758.0ms

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	30
1	34	30
done	34	30

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.7s	4797×	body	1280	valid
1.4s	2144×	body	640	valid
277.0ms	667×	body	320	valid
77.0ms	264×	body	160	valid
20.0ms	7×	body	2560	valid
18.0ms	123×	body	80	valid