Details

sample1.2s

Algorithm

intervals

Results

639.0ms	57×	body	640	valid
397.0ms	167×	body	1280	valid
23.0ms	22×	body	320	valid
3.0ms	6×	body	160	valid
1.0ms	4×	body	80	valid

simplify50.0ms

Counts

1 → 1

Iterations

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

prune75.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.7b	(cos (- lambda1 lambda2))

rewrite59.0ms

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` `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 → 72

Calls

4 calls:

24.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
22.0ms	(cos (- lambda1 lambda2))

series189.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin phi1) (sin phi2))
94.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
31.0ms	(cos (- lambda1 lambda2))

simplify2.5s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	3105
3	1330
2	611
1	335
0	187

prune882.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite36.0ms

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` `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 → 72

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
17.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin phi1) (sin phi2))
85.0ms	(* (sin lambda1) (sin lambda2))
157.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
38.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify3.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5004
4	3118
3	1572
2	675
1	291
0	142

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))
0.3b	(* (exp (log (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))) R)
0.7b	(log (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))
0.9b	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `log-prod`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `exp-sum` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`unswap-sqr`
1×	`acos-asin` `rem-log-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 58

Calls

4 calls:

1.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))
27.0ms	(* (exp (log (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))) R)
2.0ms	(log (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))

series665.0ms

Counts

4 → 12

Calls

4 calls:

456.0ms	(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))
110.0ms	(* (exp (log (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))) R)
74.0ms	(log (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))
24.0ms	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))

simplify4.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
4	4921
3	1292
2	470
1	206
0	115

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.4b

localize115.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))
0.5b	(log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))))
0.7b	(log (log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))))
0.9b	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`log-prod`
9×	`add-sqr-sqrt` `exp-prod` `*-un-lft-identity` `log-pow` `add-cube-cbrt`
7×	`pow1`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`acos-asin`
2×	`exp-diff` `rem-log-exp`
1×	`log-div` `rem-exp-log`

Counts

4 → 60

Calls

4 calls:

2.0ms	(exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))
3.0ms	(log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))))
5.0ms	(log (log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))))
1.0ms	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))
21.0ms	(log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))))
40.0ms	(log (log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1)))))))
13.0ms	(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (* (cos phi2) (cos phi1)) (* (sin phi2) (sin phi1))))

simplify4.8s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
8	4197
7	1695
6	960
5	607
4	360
3	257
2	172
1	120
0	89

prune971.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.3b

regimes1.4s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample17.1s

Algorithm

intervals

Results

11.2s	4738×	body	1280	valid
4.4s	2174×	body	640	valid
870.0ms	676×	body	320	valid
130.0ms	262×	body	160	valid
58.0ms	12×	body	2560	valid
34.0ms	142×	body	80	valid