Details

sample247.0ms

Algorithm

intervals

Results

176.0ms	156×	body	1280	valid
43.0ms	64×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	4×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	41	18
done	41	18

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.6b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.5b	(cos (- lambda1 lambda2))

rewrite24.0ms

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:

12.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms	(cos (- lambda1 lambda2))

series169.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
40.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify4.5s

Counts

86 → 86

Iterations

Useful iterations: 4 (3.7s)

Iter	Nodes	Cost
0	196	1763
1	380	1589
2	1010	1325
3	2804	1281
4	4588	1190
done	5000	1190

prune366.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite40.0ms

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:

28.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
53.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
12.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify938.0ms

Counts

99 → 99

Iterations

Useful iterations: done (935.0ms)

Iter	Nodes	Cost
0	202	2400
1	477	2347
2	1734	1919
done	5000	1917

prune593.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3)))))) R)
0.4b	(pow (* (sin (- lambda2)) (sin lambda1)) 3)
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))))
25.9b	(cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`distribute-lft-neg-out` `acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `cube-neg` `sin-neg` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3)))))) R)
4.0ms	(pow (* (sin (- lambda2)) (sin lambda1)) 3)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))))
2.0ms	(cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))

series191.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3)))))) R)
72.0ms	(pow (* (sin (- lambda2)) (sin lambda1)) 3)
13.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))))))
52.0ms	(cbrt (pow (* (sin (- lambda2)) (sin lambda1)) 3))

simplify2.0s

Counts

88 → 88

Iterations

Useful iterations: 3 (563.0ms)

Iter	Nodes	Cost
0	151	1879
1	310	1637
2	868	1445
3	3726	1365
done	5000	1365

prune558.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2)))))) R)
0.3b	(log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2))))
0.3b	(expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2)))
0.7b	(acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

3.0ms	(* (acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2)))))) R)
0.0ms	(log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2))))
0.0ms	(expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2)))
0.0ms	(acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2))))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2)))))) R)
253.0ms	(log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2))))
254.0ms	(expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2)))
15.0ms	(acos (fma (sin phi1) (sin phi2) (log1p (expm1 (* (* (cos phi1) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi2))))))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: 3 (230.0ms)

Iter	Nodes	Cost
0	111	1740
1	209	1611
2	573	1401
3	1786	1397
done	5001	1397

prune309.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

regimes528.0ms

Accuracy

0% (0.4b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	26
1	26	26
done	26	26

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.9s	4828×	body	1280	valid
1.3s	2038×	body	640	valid
313.0ms	708×	body	320	valid
78.0ms	291×	body	160	valid
21.0ms	6×	body	2560	valid
19.0ms	130×	body	80	valid