Details

sample380.0ms

Algorithm

intervals

Results

237.0ms	115×	body	1280	valid
67.0ms	61×	body	640	valid
29.0ms	35×	body	320	valid
7.0ms	15×	body	160	valid
6.0ms	30×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.7b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

60.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
21.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

series328.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
169.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
45.0ms	(sin (- lambda1 lambda2))
36.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts

106 → 106

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	223	2679
1	493	2042
2	1926	1593
done	5000	1493

prune645.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
3.7b	(sin (- lambda1 lambda2))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

33×	`sin-sum`
30×	`add-sqr-sqrt`
27×	`prod-diff`
26×	`*-un-lft-identity` `add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sub-neg`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-diff` `fma-udef` `sin-mult`

Counts

4 → 94

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
44.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
11.0ms	(sin (- lambda1 lambda2))

series540.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin lambda1) (sin lambda2))
68.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
363.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
37.0ms	(sin (- lambda1 lambda2))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	230	2377
1	537	1875
2	2289	1496
done	5000	1423

prune840.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin lambda1) (cos lambda2)) (cos phi2))
0.2b	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.6b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`associate-r`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`distribute-lft-neg-out` `associate-*l/` `sin-neg` `distribute-rgt-neg-out` `fma-udef` `sin-cos-mult` `sin-mult` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

26.0ms	(* (* (sin lambda1) (cos lambda2)) (cos phi2))
37.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
10.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series553.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (* (sin lambda1) (cos lambda2)) (cos phi2))
120.0ms	(* (* (cos lambda1) (sin (- lambda2))) (cos phi2))
69.0ms	(* (sin lambda1) (sin lambda2))
278.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify1.1s

Counts

85 → 85

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	153	992
1	371	955
2	1770	803
done	5001	798

prune886.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `fma-udef` `sin-mult` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

11.0ms	(* (sin lambda2) (sin lambda1))
2.0ms	(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) 3))
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
2.0ms	(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) 3)

series1.2s

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin lambda2) (sin lambda1))
300.0ms	(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) 3))
312.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1))
502.0ms	(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi1)) 3)

simplify2.0s

Counts

91 → 91

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	125	1880
1	307	1647
2	1520	1428
done	5002	1425

prune677.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes930.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	42
1	34	42
done	34	42

end0.0ms

sample13.1s

Algorithm

intervals

Results

7.9s	3510×	body	1280	valid
3.0s	2346×	body	640	valid
1.1s	959×	body	320	valid
301.0ms	475×	body	160	valid
182.0ms	710×	body	80	valid