Details

sample978.0ms

Algorithm

intervals

Results

594.0ms	152×	body	1280	valid
133.0ms	72×	body	640	valid
103.0ms	21×	body	320	valid
5.0ms	7×	body	160	valid
2.0ms	5×	body	80	valid

simplify8.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize118.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.7b	(cos (- lambda1 lambda2))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
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:

25.0ms	(* (sin phi1) (sin phi2))
18.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
6.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
98.0ms	(cos (- lambda1 lambda2))

series170.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin phi1) (sin phi2))
62.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
33.0ms	(cos (- lambda1 lambda2))

simplify84.0ms

Counts: 67 → 67

prune466.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
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:

26.0ms	(* (sin lambda1) (sin lambda2))
26.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sin lambda1) (sin lambda2))
70.0ms	(* (sin phi1) (sin phi2))
107.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
42.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify82.0ms

Counts: 76 → 76

prune672.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.4b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin phi2))
0.3b	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.8b	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

13.0ms	(* (sin phi1) (sin phi2))
20.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin phi1) (sin phi2))
117.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
105.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
43.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify88.0ms

Counts: 73 → 73

prune834.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (log (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.8b	(log (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.1b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.9b	(log (exp (* (sin phi1) (sin phi2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

24.0ms	(* (exp (log (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(log (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
7.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(log (exp (* (sin phi1) (sin phi2))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (exp (log (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
103.0ms	(log (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
39.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
73.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify153.0ms

Counts: 68 → 68

prune671.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.4b

regimes2.0s

Accuracy

6.2% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify117.0ms

end0.0ms

sample19.8s

Algorithm

intervals

Results

14.1s	4802×	body	1280	valid
3.8s	2090×	body	640	valid
818.0ms	684×	body	320	valid
162.0ms	274×	body	160	valid
91.0ms	15×	body	2560	valid
39.0ms	138×	body	80	valid