Details

sample175.0ms

Algorithm

intervals

Results

107.0ms	118×	body	1280	valid
38.0ms	70×	body	640	valid
10.0ms	31×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	22×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize21.0ms

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))
4.9b	(cos (- lambda1 lambda2))
5.1b	(sin (- lambda1 lambda2))

rewrite17.0ms

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))

series154.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
106.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify2.3s

Counts

73 → 73

Iterations

Useful iterations: 5 (1.2s)

Iter	Nodes	Cost
0	172	1599
1	282	1267
2	445	1016
3	804	930
4	1609	785
5	4329	749
done	5000	749

prune288.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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))
4.9b	(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))

series190.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos lambda1) (sin (- lambda2)))
13.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
108.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	179	1345
1	317	1156
2	654	948
3	1398	922
4	2812	848
done	5000	848

prune384.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (sin 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)))
0.5b	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

rewrite14.0ms

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` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef` `sin-mult`

Counts

4 → 62

Calls

4 calls:

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

series338.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos lambda1) (sin (- lambda2)))
56.0ms	(* (sin lambda1) (sin (- lambda2)))
16.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
214.0ms	(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	135	1217
1	287	1184
2	746	1036
3	1859	977
4	4211	976
done	5000	976

prune434.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (cbrt (pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3)))
0.5b	(fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))
0.5b	(cbrt (pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3))
0.6b	(pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 67

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (cbrt (pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3)))
0.0ms	(fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))
1.0ms	(cbrt (pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3))
2.0ms	(pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3)

series695.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (cbrt (pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3)))
187.0ms	(fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1))
183.0ms	(cbrt (pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3))
309.0ms	(pow (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2) (cos phi1)) 3)

simplify2.0s

Counts

79 → 79

Iterations

Useful iterations: 3 (424.0ms)

Iter	Nodes	Cost
0	114	2216
1	223	1946
2	547	1681
3	3250	1678
done	5000	1678

prune380.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes533.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	35
1	29	35
done	29	35

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.3s	3611×	body	1280	valid
1.4s	2273×	body	640	valid
313.0ms	919×	body	320	valid
102.0ms	456×	body	160	valid
80.0ms	741×	body	80	valid