Details

sample376.0ms

Algorithm

intervals

Results

190.0ms	115×	body	1280	valid
116.0ms	61×	body	640	valid
21.0ms	35×	body	320	valid
7.0ms	15×	body	160	valid
6.0ms	30×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize85.0ms

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))

rewrite465.0ms

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:

42.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
11.0ms	(sin (- lambda1 lambda2))
14.0ms	(cos (- lambda1 lambda2))

series334.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
171.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
35.0ms	(sin (- lambda1 lambda2))
30.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1926
1	493
0	223

prune670.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize80.0ms

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))

rewrite72.0ms

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:

18.0ms	(* (sin lambda1) (sin lambda2))
37.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
10.0ms	(sin (- lambda1 lambda2))

series514.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin lambda1) (sin lambda2))
113.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
289.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
42.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	2289
1	537
0	230

prune884.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

18.0ms	(* (cos phi2) (sin lambda2))
18.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(* (sin lambda1) (* (cos lambda2) (cos phi2)))
1.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series563.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cos phi2) (sin lambda2))
68.0ms	(* (sin lambda1) (sin lambda2))
141.0ms	(* (sin lambda1) (* (cos lambda2) (cos phi2)))
274.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify938.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1474
1	343
0	139

prune940.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (sin lambda1) (* (cos lambda2) (cos phi2)))
0.6b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda2) (sin lambda1))))) (cos phi1))
3.5b	(log (exp (* (sin lambda2) (sin lambda1))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

18.0ms	(* (sin lambda2) (sin lambda1))
50.0ms	(* (sin lambda1) (* (cos lambda2) (cos phi2)))
1.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda2) (sin lambda1))))) (cos phi1))
7.0ms	(log (exp (* (sin lambda2) (sin lambda1))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin lambda2) (sin lambda1))
117.0ms	(* (sin lambda1) (* (cos lambda2) (cos phi2)))
289.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda2) (sin lambda1))))) (cos phi1))
66.0ms	(log (exp (* (sin lambda2) (sin lambda1))))

simplify704.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1041
1	285
0	130

prune690.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes894.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	46
3	46
2	45
1	39
0	24

end0.0ms

sample13.2s

Algorithm

intervals

Results

7.9s	3510×	body	1280	valid
3.5s	2346×	body	640	valid
769.0ms	959×	body	320	valid
305.0ms	475×	body	160	valid
178.0ms	710×	body	80	valid