Details

sample607.0ms

Algorithm

intervals

Results

413.0ms	160×	body	1280	valid
64.0ms	60×	body	640	valid
16.0ms	23×	body	320	valid
3.0ms	8×	body	160	valid
1.0ms	5×	body	80	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	43	18
done	43	18

prune70.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.5b	(cos (- lambda1 lambda2))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

46.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

series324.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
81.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
18.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
36.0ms	(cos (- lambda1 lambda2))

simplify8.1s

Counts

86 → 86

Iterations

Useful iterations: done (8.1s)

Iter	Nodes	Cost
0	196	1763
1	377	1589
2	962	1325
3	2320	1281
4	3808	1190
done	5001	1144

prune563.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `cos-mult`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 87

Calls

4 calls:

154.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
29.0ms	(* (sin lambda1) (sin (- lambda2)))
15.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
2.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
92.0ms	(* (sin lambda1) (sin (- lambda2)))
98.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))) R)
16.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	205	2400
1	483	2347
2	1720	1919
done	5000	1885

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
0.3b	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
1.0b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

3.0ms	(exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
33.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

series227.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
112.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
56.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
24.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

simplify4.3s

Counts

77 → 77

Iterations

Useful iterations: 4 (546.0ms)

Iter	Nodes	Cost
0	95	2371
1	141	2269
2	277	1957
3	531	1957
4	807	1951
5	1300	1951
6	2768	1951
done	5000	1951

prune685.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

localize123.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
0.5b	(pow (* (cos lambda2) (cos lambda1)) 3)
1.0b	(acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda2) (cos lambda1)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

12.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
64.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
9.0ms	(pow (* (cos lambda2) (cos lambda1)) 3)
1.0ms	(acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda2) (cos lambda1)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
82.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))
75.0ms	(pow (* (cos lambda2) (cos lambda1)) 3)
58.0ms	(acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (- (pow (* (cos lambda2) (cos lambda1)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))))

simplify1.4s

Counts

112 → 112

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	204	2166
1	478	1714
2	1682	1481
done	5001	1464

prune876.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

regimes1.0s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	30
1	30	30
done	30	30

end0.0ms

sample18.2s

Algorithm

intervals

Results

12.9s	4797×	body	1280	valid
3.4s	2057×	body	640	valid
1.0s	725×	body	320	valid
181.0ms	276×	body	160	valid
36.0ms	141×	body	80	valid
32.0ms	8×	body	2560	valid