Details

sample619.0ms

Algorithm

intervals

Results

342.0ms	147×	body	1280	valid
156.0ms	79×	body	640	valid
17.0ms	20×	body	320	valid
4.0ms	7×	body	160	valid
1.0ms	4×	body	80	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
3	36
2	33
1	26
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize100.0ms

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))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.6b	(cos (- lambda1 lambda2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
18.0ms	(* (sin phi1) (sin phi2))
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
20.0ms	(cos (- lambda1 lambda2))

series227.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
62.0ms	(* (sin phi1) (sin phi2))
22.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
60.0ms	(cos (- lambda1 lambda2))

simplify3.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
3	4255
2	654
1	207
0	111

prune775.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite41.0ms

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×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

17.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
10.0ms	(* (sin phi1) (sin phi2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sin lambda1) (sin lambda2))
111.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
86.0ms	(* (sin phi1) (sin phi2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1001
1	277
0	134

prune909.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize108.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.8b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.4b	(log (exp (* (sin phi1) (sin phi2))))

rewrite37.0ms

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`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 59

Calls

4 calls:

5.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
24.0ms	(* (sin phi1) (sin phi2))
3.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.0ms	(log (exp (* (sin phi1) (sin phi2))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
78.0ms	(* (sin phi1) (sin phi2))
31.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
58.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify3.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	4382
2	730
1	228
0	119

prune995.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (sin phi1))
0.4b	(exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1)))))
0.5b	(log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1))))))
0.8b	(acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`log-pow`
3×	`acos-asin` `log-prod` `associate-r` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr` `rem-exp-log`

Counts

4 → 55

Calls

4 calls:

16.0ms	(* (sin phi2) (sin phi1))
5.0ms	(exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1)))))
13.0ms	(log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1))))))
5.0ms	(acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin phi2) (sin phi1))
65.0ms	(exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1)))))
26.0ms	(log (exp (acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1))))))
27.0ms	(acos (+ (* (cos phi2) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi1))) (* (sin phi2) (sin phi1))))

simplify2.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	2390
2	518
1	196
0	108

prune843.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 3.2b

regimes2.4s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample17.6s

Algorithm

intervals

Results

12.3s	4851×	body	1280	valid
3.3s	2089×	body	640	valid
1.0s	678×	body	320	valid
167.0ms	246×	body	160	valid
37.0ms	7×	body	2560	valid
31.0ms	133×	body	80	valid