Details

sample634.0ms

Algorithm

intervals

Results

393.0ms	151×	body	1280	valid
133.0ms	69×	body	640	valid
19.0ms	22×	body	320	valid
5.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	43	18
done	43	18

prune65.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize32.0ms

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)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.2b	(cos (- lambda1 lambda2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

42.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
24.0ms	(cos (- lambda1 lambda2))

series197.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin phi1) (sin phi2))
85.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
30.0ms	(cos (- lambda1 lambda2))

simplify4.7s

Counts

84 → 84

Iterations

Useful iterations: 5 (1.6s)

Iter	Nodes	Cost
0	187	1607
1	316	1393
2	597	1170
3	942	1127
4	1247	1054
5	1907	990
6	3847	990
done	5001	990

prune649.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize68.0ms

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 lambda1) (sin (- lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite166.0ms

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×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 87

Calls

4 calls:

135.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
19.0ms	(* (sin lambda1) (sin (- lambda2)))
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)))))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
82.0ms	(* (sin lambda1) (sin (- lambda2)))
146.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	213	2480
1	502	2383
2	1803	1919
done	5001	1885

prune862.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2)))))) R)
0.3b	(exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2)))))
0.9b	(log (exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2))))))
1.4b	(acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2))))

rewrite22.0ms

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`
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` `rem-exp-log` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

13.0ms	(* (log (exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2)))))) R)
2.0ms	(exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2)))))
4.0ms	(log (exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2))))

series199.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (log (exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2)))))) R)
66.0ms	(exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2)))))
28.0ms	(log (exp (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2))))))
29.0ms	(acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi1) (sin phi2))))

simplify5.7s

Counts

78 → 78

Iterations

Useful iterations: 5 (921.0ms)

Iter	Nodes	Cost
0	93	2330
1	139	2225
2	267	1971
3	440	1971
4	692	1971
5	1617	1969
6	4919	1969
done	5000	1969

prune782.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (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)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2))))))))) R)
1.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-mult` `*-commutative`
2×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `flip--` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-mult`

Counts

4 → 86

Calls

4 calls:

86.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))
25.0ms	(* (sin phi1) (sin phi2))
8.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2))))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

368.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))
69.0ms	(* (sin phi1) (sin phi2))
110.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2))))))))) R)
42.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	215	2869
1	490	2411
2	1686	2040
done	5000	1850

prune661.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

regimes1.0s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample19.0s

Algorithm

intervals

Results

12.1s	4725×	body	1280	valid
5.1s	2150×	body	640	valid
774.0ms	715×	body	320	valid
145.0ms	271×	body	160	valid
50.0ms	11×	body	2560	valid
37.0ms	130×	body	80	valid