Details

sample329.0ms

Algorithm

intervals

Results

159.0ms	111×	body	1280	valid
73.0ms	79×	body	640	valid
67.0ms	34×	body	320	valid
4.0ms	20×	body	80	valid
4.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(sin (- lambda1 lambda2))
3.6b	(cos (- lambda1 lambda2))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
17×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`associate-+r+` `sub-neg`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 69

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
163.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
38.0ms	(sin (- lambda1 lambda2))
31.0ms	(cos (- lambda1 lambda2))

simplify2.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
3	2883
2	911
1	372
0	191

prune915.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.6b	(cos (- lambda1 lambda2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

67.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
20.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))

series457.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
29.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
167.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
27.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1793
1	455
0	208

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize115.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l`
2×	`fma-udef`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

30.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(+ (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
1.0ms	(fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))

series613.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda1) (sin lambda2))
321.0ms	(+ (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
31.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
199.0ms	(fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))

simplify1.4s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	1040
1	272
0	121

prune833.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b	(fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))
0.7b	(log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`log-prod` `log-pow`
7×	`fma-def`
6×	`pow1` `exp-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-+l+` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-udef`
2×	`exp-sum`
1×	`+-commutative` `sum-log` `flip3-+` `rem-log-exp` `flip-+`

Counts

4 → 61

Calls

4 calls:

14.0ms	(+ (log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.0ms	(fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))
2.0ms	(log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))))

series750.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(+ (log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2)))
19.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
228.0ms	(fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))
178.0ms	(log (exp (fma (* (cos phi2) (cos lambda1)) (cos lambda2) (cos phi1))))

simplify1.9s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
2	1286
1	256
0	116

prune902.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	34
1	34
0	27

end0.0ms

sample10.7s

Algorithm

intervals

Results

6.1s	3488×	body	1280	valid
2.5s	2375×	body	640	valid
965.0ms	976×	body	320	valid
492.0ms	726×	body	80	valid
188.0ms	435×	body	160	valid