Details

sample1.0s

Algorithm

intervals

Results

569.0ms	167×	body	1280	valid
108.0ms	61×	body	640	valid
68.0ms	20×	body	320	valid
5.0ms	5×	body	160	valid
2.0ms	3×	body	80	valid

simplify50.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	39
3	39
2	38
1	27
0	17

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.6b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b	(cos (- lambda1 lambda2))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 76

Calls

4 calls:

23.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
24.0ms	(* (sin phi1) (sin phi2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
23.0ms	(cos (- lambda1 lambda2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
102.0ms	(* (sin phi1) (sin phi2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
33.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

88 → 88

Iterations

Iter	Nodes
5	2706
4	1736
3	1070
2	587
1	329
0	191

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 76

Calls

4 calls:

10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
21.0ms	(* (sin lambda1) (sin lambda2))
22.0ms	(* (sin phi1) (sin phi2))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
53.0ms	(* (sin lambda1) (sin lambda2))
55.0ms	(* (sin phi1) (sin phi2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Counts

88 → 88

Iterations

Iter	Nodes
4	2884
3	1542
2	675
1	293
0	146

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
1.1b	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 76

Calls

4 calls:

12.0ms	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
24.0ms	(* (sin lambda1) (sin lambda2))
17.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
79.0ms	(* (sin lambda1) (sin lambda2))
72.0ms	(* (sin phi1) (sin phi2))
19.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.6s

Counts

88 → 88

Iterations

Iter	Nodes
4	3010
3	1604
2	710
1	296
0	147

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.8b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
1.1b	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.6b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

23.0ms	(* (sin lambda1) (sin lambda2))
24.0ms	(* (sin phi1) (sin phi2))
2.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
9.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin lambda1) (sin lambda2))
67.0ms	(* (sin phi1) (sin phi2))
15.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
71.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify1.6s

Counts

84 → 84

Iterations

Iter	Nodes
4	2498
3	1294
2	558
1	263
0	139

prune2.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.8b

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	34
1	34
0	26

end0.0ms

sample24.0s

Algorithm

intervals

Results

17.4s	4785×	body	1280	valid
4.9s	2104×	body	640	valid
1.0s	705×	body	320	valid
251.0ms	276×	body	160	valid
63.0ms	12×	body	2560	valid
47.0ms	120×	body	80	valid