Details

sample1.2s

Algorithm

intervals

Results

963.0ms	150×	body	1280	valid
124.0ms	64×	body	640	valid
37.0ms	27×	body	320	valid
5.0ms	1×	body	2560	valid
5.0ms	7×	body	160	valid
3.0ms	7×	body	80	valid

simplify72.0ms

Calls

1 calls:

Slowest

71.0ms

(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize94.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (- lambda1 lambda2))
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`cos-sum` `*-commutative`
1×	`acos-asin` `cos-diff` `sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`

Calls

4 calls:

Slowest

7.0ms	(* (sin phi1) (sin phi2))
6.0ms	(cos (- lambda1 lambda2))
5.0ms	(* (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)))))

series221.0ms

Calls

4 calls:

Slowest

83.0ms	(* (sin phi1) (sin phi2))
67.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
53.0ms	(cos (- lambda1 lambda2))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify694.0ms

Calls

26 calls:

Slowest

135.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
70.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
67.0ms	(* (acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2)))) R)
61.0ms	(acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2))))
56.0ms	(* (acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2)))) R)

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
6×	`associate-r` `cos-mult`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Calls

4 calls:

Slowest

23.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
8.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series422.0ms

Calls

4 calls:

Slowest

275.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
68.0ms	(* (sin phi1) (sin phi2))
63.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify6.3s

Calls

45 calls:

Slowest

540.0ms	(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
522.0ms	(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
475.0ms	(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
438.0ms	(* 2 (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
342.0ms	(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize40.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (* (sin phi1) (sin phi2)))
8.9b	(cbrt (* (sin phi1) (sin phi2)))
8.9b	(cbrt (* (sin phi1) (sin phi2)))
0.5b	(acos (+ (* (* (cbrt (* (sin phi1) (sin phi2))) (cbrt (* (sin phi1) (sin phi2)))) (cbrt (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`
1×	`acos-asin`

Calls

4 calls:

Slowest

8.0ms	(cbrt (* (sin phi1) (sin phi2)))
5.0ms	(cbrt (* (sin phi1) (sin phi2)))
5.0ms	(cbrt (* (sin phi1) (sin phi2)))
3.0ms	(acos (+ (* (* (cbrt (* (sin phi1) (sin phi2))) (cbrt (* (sin phi1) (sin phi2)))) (cbrt (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series481.0ms

Calls

4 calls:

Slowest

157.0ms	(cbrt (* (sin phi1) (sin phi2)))
154.0ms	(cbrt (* (sin phi1) (sin phi2)))
154.0ms	(cbrt (* (sin phi1) (sin phi2)))
16.0ms	(acos (+ (* (* (cbrt (* (sin phi1) (sin phi2))) (cbrt (* (sin phi1) (sin phi2)))) (cbrt (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.4s

Calls

18 calls:

Slowest

238.0ms	(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
225.0ms	(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
224.0ms	(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
218.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
202.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize42.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (* (sin phi1) (sin phi2)))
8.9b	(cbrt (* (sin phi1) (sin phi2)))
0.6b	(cbrt (sin phi2))
0.6b	(cbrt (sin phi1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`cbrt-div` `sin-mult`

Calls

4 calls:

Slowest

3.0ms	(cbrt (* (sin phi1) (sin phi2)))
2.0ms	(cbrt (* (sin phi1) (sin phi2)))
1.0ms	(cbrt (sin phi1))
1.0ms	(cbrt (sin phi2))

series543.0ms

Calls

4 calls:

Slowest

151.0ms	(cbrt (sin phi1))
141.0ms	(cbrt (* (sin phi1) (sin phi2)))
131.0ms	(cbrt (* (sin phi1) (sin phi2)))
119.0ms	(cbrt (sin phi2))

simplify910.0ms

Calls

22 calls:

Slowest

288.0ms	(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
229.0ms	(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
141.0ms	(- (pow phi1 1/3) (+ (* 1/3240 (pow (pow phi1 13) 1/3)) (* 1/18 (pow (pow phi1 7) 1/3))))
111.0ms	(- (pow phi2 1/3) (+ (* 1/3240 (pow (pow phi2 13) 1/3)) (* 1/18 (pow (pow phi2 7) 1/3))))
23.0ms	(cbrt (- (cos (- phi1 phi2)) (cos (+ phi1 phi2))))

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

regimes991.0ms

Accuracy

0% (0.4b remaining)

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

bsearch8.0ms

end0.0ms

sample24.0s

Algorithm

intervals

Results

16.8s	4779×	body	1280	valid
5.5s	2132×	body	640	valid
957.0ms	681×	body	320	valid
268.0ms	249×	body	160	valid
54.0ms	10×	body	2560	valid
54.0ms	149×	body	80	valid