Details

sample421.0ms

Algorithm

intervals

Results

246.0ms	110×	body	1280	valid
97.0ms	79×	body	640	valid
30.0ms	29×	body	320	valid
9.0ms	16×	body	160	valid
5.0ms	22×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite580.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`add-sqr-sqrt` `sin-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`cos-sum`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cos-diff` `fma-def` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

57.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
26.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
28.0ms	(sin (- lambda1 lambda2))
460.0ms	(cos (- lambda1 lambda2))

series332.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
173.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
41.0ms	(sin (- lambda1 lambda2))
37.0ms	(cos (- lambda1 lambda2))

simplify5.6s

Counts

114 → 114

Iterations

Useful iterations: 4 (4.3s)

Iter	Nodes	Cost
0	242	2795
1	472	2124
2	994	1681
3	2087	1511
4	4462	1150
done	5000	1150

prune491.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda2) (sin lambda1))
0.2b	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (sin lambda2) (cos lambda1))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b	(cos (- lambda1 lambda2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u`
3×	`cos-diff` `sub-neg` `fma-def`
2×	`associate-+r+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+`

Counts

4 → 87

Calls

4 calls:

13.0ms	(* (cos lambda2) (sin lambda1))
58.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (sin lambda2) (cos lambda1))))
16.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms	(cos (- lambda1 lambda2))

series496.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos lambda2) (sin lambda1))
232.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (sin lambda2) (cos lambda1))))
172.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

99 → 99

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	233	1616
1	484	1423
2	1262	1216
3	3684	1172
done	5000	1171

prune948.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sub-neg` `associate-*r/` `prod-diff`
1×	`flip3--` `flip--` `fma-udef` `sin-mult`

Counts

4 → 79

Calls

4 calls:

25.0ms	(* (cos lambda2) (sin lambda1))
94.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (sin lambda2) (cos lambda1))))
26.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(fma (cos phi2) (* (cos lambda1) (cos lambda2)) (cos phi1))

series560.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (cos lambda2) (sin lambda1))
224.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (sin lambda2) (cos lambda1))))
68.0ms	(* (sin lambda1) (sin lambda2))
185.0ms	(fma (cos phi2) (* (cos lambda1) (cos lambda2)) (cos phi1))

simplify2.5s

Counts

91 → 91

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	157	1102
1	338	1078
2	999	970
3	2884	965
done	5001	948

prune656.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma (cos phi2) (* (cos lambda1) (cos lambda2)) (cos phi1))
0.7b	(cbrt (* (cos lambda2) (sin lambda1)))
0.7b	(cbrt (* (cos lambda2) (sin lambda1)))
0.7b	(cbrt (* (cos lambda2) (sin lambda1)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`fma-udef`

Counts

4 → 43

Calls

4 calls:

1.0ms	(fma (cos phi2) (* (cos lambda1) (cos lambda2)) (cos phi1))
8.0ms	(cbrt (* (cos lambda2) (sin lambda1)))
16.0ms	(cbrt (* (cos lambda2) (sin lambda1)))
10.0ms	(cbrt (* (cos lambda2) (sin lambda1)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(fma (cos phi2) (* (cos lambda1) (cos lambda2)) (cos phi1))
100.0ms	(cbrt (* (cos lambda2) (sin lambda1)))
140.0ms	(cbrt (* (cos lambda2) (sin lambda1)))
122.0ms	(cbrt (* (cos lambda2) (sin lambda1)))

simplify1.7s

Counts

55 → 55

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	60	550
1	119	528
2	265	471
3	662	461
4	2141	458
done	5002	455

prune437.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes610.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	27	54
1	36	54
done	36	54

end0.0ms

sample12.1s

Algorithm

intervals

Results

6.9s	3516×	body	1280	valid
2.9s	2346×	body	640	valid
1.4s	988×	body	320	valid
186.0ms	740×	body	80	valid
150.0ms	410×	body	160	valid