Details

sample890.0ms

Algorithm

intervals

Results

604.0ms	163×	body	1280	valid
134.0ms	66×	body	640	valid
24.0ms	19×	body	320	valid
6.0ms	6×	body	160	valid
1.0ms	2×	body	80	valid

simplify28.0ms

Calls

1 calls:

Slowest

27.0ms

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize64.0ms

Local error

Found 4 expressions with local error:

3.5b	(cos (- lambda1 lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log`
9×	`add-cbrt-cube`
9×	`pow1`
6×	`add-cube-cbrt`
6×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
4×	`add-log-exp`
4×	`log1p-expm1-u`
4×	`associate-l`
4×	`expm1-log1p-u`
3×	`cbrt-unprod`
3×	`prod-exp`
3×	`pow-prod-down`
3×	`associate-r`
3×	`cos-diff`
2×	`*-commutative`
2×	`cos-sum`
1×	`cos-mult`
1×	`associate-*l/`
1×	`distribute-lft-in`
1×	`sub-neg`
1×	`acos-asin`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

22.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
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

110.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
27.0ms	(cos (- lambda1 lambda2))
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.2s

Calls

30 calls:

Slowest

246.0ms	(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
241.0ms	(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
215.0ms	(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
78.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
58.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.6b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
11×	`add-cbrt-cube`
11×	`pow1`
8×	`add-cube-cbrt`
8×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`associate-l`
6×	`cos-mult`
6×	`associate-r`
4×	`add-log-exp`
4×	`log1p-expm1-u`
4×	`cbrt-unprod`
4×	`prod-exp`
4×	`pow-prod-down`
4×	`expm1-log1p-u`
3×	`sin-mult`
3×	`*-commutative`
3×	`associate-*r/`
3×	`frac-times`
2×	`flip-+`
2×	`frac-add`
2×	`flip3-+`
1×	`associate-*l/`
1×	`distribute-lft-in`
1×	`acos-asin`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

38.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
7.0ms	(* (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))))))

series416.0ms

Calls

4 calls:

Slowest

236.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
99.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
62.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify5.1s

Calls

45 calls:

Slowest

489.0ms	(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
309.0ms	(* 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))))))
249.0ms	(* (* (* (* (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)))))
241.0ms	(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
240.0ms	(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

5.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
4.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
3.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series200.0ms

Calls

4 calls:

Slowest

76.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
67.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
29.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
28.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify6.2s

Calls

30 calls:

Slowest

580.0ms	(sqrt (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
313.0ms	(log (* (cbrt (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) (cbrt (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))))
312.0ms	(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
296.0ms	(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
264.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.3b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (* (cos lambda1) (cos lambda2)) 3)
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (- (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda2) (sin lambda1)) (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1`
22×	`add-exp-log`
22×	`add-cbrt-cube`
15×	`pow-prod-down`
10×	`cbrt-unprod`
10×	`prod-exp`
5×	`cos-mult`
4×	`rem-cube-cbrt`
4×	`add-log-exp`
4×	`log1p-expm1-u`
4×	`add-cube-cbrt`
4×	`pow-prod-up`
4×	`pow-exp`
4×	`*-un-lft-identity`
4×	`pow-pow`
4×	`expm1-log1p-u`
4×	`add-sqr-sqrt`
2×	`cube-prod`
2×	`unpow3`
2×	`pow-plus`
2×	`unpow-prod-down`
2×	`pow-to-exp`
2×	`cube-mult`
2×	`cube-div`
1×	`sin-mult`
1×	`*-commutative`
1×	`associate-*r/`
1×	`associate-*l/`
1×	`associate-l`
1×	`associate-r`
1×	`frac-times`
1×	`acos-asin`
1×	`pow2`

Calls

4 calls:

Slowest

26.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
7.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
3.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (- (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda2) (sin lambda1)) (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))))))

series264.0ms

Calls

4 calls:

Slowest

92.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
65.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
63.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (- (* (sin lambda2) (sin lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda2) (sin lambda1)) (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))))))
43.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

simplify4.0s

Calls

57 calls:

Slowest

702.0ms	(* (* (* (* (cos lambda2) (cos lambda2)) (cos lambda2)) (* (* (cos lambda1) (cos lambda1)) (cos lambda1))) (* (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1))))
537.0ms	(* (* (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1))) (* (* (* (cos lambda2) (cos lambda2)) (cos lambda2)) (* (* (cos lambda1) (cos lambda1)) (cos lambda1))))
496.0ms	(* (* (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1))) (* (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1))))
284.0ms	(pow (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))) 3)
248.0ms	(pow (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 3)

prune3.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.3b

regimes1.3s

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample23.6s

Algorithm

intervals

Results

17.1s	4855×	body	1280	valid
4.5s	2080×	body	640	valid
1.3s	635×	body	320	valid
255.0ms	285×	body	160	valid
83.0ms	140×	body	80	valid
58.0ms	10×	body	2560	valid