Details

sample270.0ms

Algorithm

intervals

Results

135.0ms	108×	body	1280	valid
84.0ms	79×	body	640	valid
20.0ms	41×	body	320	valid
4.0ms	10×	body	160	valid
3.0ms	18×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	20
1	21	20
2	23	19
done	23	19

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.5b	(sin (- lambda1 lambda2))
6.0b	(cos (- lambda1 lambda2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
33.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

series229.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
156.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify5.3s

Counts

81 → 81

Iterations

Useful iterations: 2 (3.7s)

Iter	Nodes	Cost
0	191	1730
1	583	1282
2	4922	1070
done	5000	1070

prune515.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.5b	(sin (- lambda1 lambda2))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
25.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
27.0ms	(sin (- lambda1 lambda2))

series520.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
65.0ms	(* (sin lambda1) (sin lambda2))
379.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
40.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

81 → 81

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	197	1591
1	739	1310
done	5000	1140

prune780.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

23.0ms	(* (sin lambda1) (cos lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
20.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin lambda1) (cos lambda2))
65.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
311.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify976.0ms

Counts

81 → 81

Iterations

Useful iterations: done (972.0ms)

Iter	Nodes	Cost
0	142	1297
1	606	1230
done	5000	1071

prune711.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3)) (fma (cos phi1) (cos phi1) (* (- (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
0.4b	(+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3))
0.6b	(pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3)
1.2b	(- (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
9×	`add-exp-log` `add-cbrt-cube`
8×	`fma-def` `add-log-exp`
7×	`pow1`
5×	`sum-cubes` `distribute-lft-out` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `prod-diff` `associate-/r*`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `pow-exp` `flip-+` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv`

Counts

4 → 104

Calls

4 calls:

76.0ms	(/ (+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3)) (fma (cos phi1) (cos phi1) (* (- (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
22.0ms	(+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3))
28.0ms	(pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3)
17.0ms	(- (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))

series4.4s

Counts

4 → 12

Calls

4 calls:

2.8s	(/ (+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3)) (fma (cos phi1) (cos phi1) (* (- (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1)) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))))
984.0ms	(+ (pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3) (pow (cos phi1) 3))
306.0ms	(pow (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3)
304.0ms	(- (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))

simplify4.2s

Counts

116 → 116

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	246	5413
1	4641	5118
done	5000	5108

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes625.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	75
1	38	75
done	38	75

end0.0ms

sample12.6s

Algorithm

intervals

Results

7.5s	3560×	body	1280	valid
3.5s	2369×	body	640	valid
671.0ms	980×	body	320	valid
205.0ms	407×	body	160	valid
128.0ms	684×	body	80	valid