Details

sample175.0ms

Algorithm

intervals

Results

106.0ms	121×	body	1280	valid
38.0ms	62×	body	640	valid
11.0ms	31×	body	320	valid
3.0ms	15×	body	160	valid
3.0ms	27×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	23	19
done	23	19

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
1.6b	(cos (- lambda1 lambda2))
1.6b	(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `sin-sum`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`cos-diff` `sin-diff` `fma-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series151.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
102.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
16.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: 5 (1.0s)

Iter	Nodes	Cost
0	172	1599
1	282	1267
2	445	1016
3	802	930
4	1609	785
5	4301	748
done	5001	748

prune294.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
1.6b	(cos (- lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum`
9×	`prod-diff`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`cos-diff` `sub-neg` `pow-prod-down` `prod-exp` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin (- lambda2)))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
7.0ms	(cos (- lambda1 lambda2))

series184.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos lambda1) (sin (- lambda2)))
12.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
105.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts

73 → 73

Iterations

Useful iterations: 4 (916.0ms)

Iter	Nodes	Cost
0	179	1345
1	317	1156
2	652	966
3	1399	922
4	2840	848
done	5000	848

prune393.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite11.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-neg` `distribute-rgt-neg-out` `fma-udef` `sin-mult`

Counts

4 → 61

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin (- lambda2)))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
4.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series305.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (cos lambda1) (sin (- lambda2)))
15.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
46.0ms	(* (sin lambda1) (sin lambda2))
191.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.2s

Counts

73 → 73

Iterations

Useful iterations: 4 (982.0ms)

Iter	Nodes	Cost
0	138	1148
1	281	1090
2	691	949
3	1711	948
4	4133	947
done	5000	947

prune439.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))
0.5b	(+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

rewrite23.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `distribute-lft-in` `sin-neg` `sum-log` `distribute-rgt-neg-out`

Counts

4 → 68

Calls

4 calls:

13.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
5.0ms	(* (cos lambda1) (sin (- lambda2)))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))
3.0ms	(+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

series380.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
52.0ms	(* (cos lambda1) (sin (- lambda2)))
15.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1)))
176.0ms	(+ (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

simplify2.3s

Counts

80 → 80

Iterations

Useful iterations: 3 (852.0ms)

Iter	Nodes	Cost
0	155	1612
1	391	1509
2	1260	1343
3	4949	1331
done	5000	1331

prune437.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes494.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	75
1	43	75
2	51	75
done	51	75

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.4s	3520×	body	1280	valid
1.3s	2367×	body	640	valid
356.0ms	960×	body	320	valid
108.0ms	435×	body	160	valid
75.0ms	718×	body	80	valid