Details

sample265.0ms

Algorithm

intervals

Results

182.0ms	153×	body	1280	valid
53.0ms	71×	body	640	valid
10.0ms	23×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	3×	body	80	valid

simplify15.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize25.0ms

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)
0.9b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b	(cos (- lambda1 lambda2))

rewrite27.0ms

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:

15.0ms	(* (* (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))

series174.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
41.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify4.7s

Counts

86 → 86

Iterations

Useful iterations: 4 (3.9s)

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

prune409.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.9b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 78

Calls

4 calls:

13.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
4.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series239.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
47.0ms	(* (sin lambda1) (sin lambda2))
68.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
16.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify2.5s

Counts

90 → 90

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	143	2023
1	320	1773
2	1046	1429
3	4548	1429
done	5000	1429

prune554.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
0.2b	(* (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)))))))
0.9b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

8.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
8.0ms	(* (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)))))))
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
51.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
38.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
11.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

simplify2.1s

Counts

83 → 83

Iterations

Useful iterations: 3 (804.0ms)

Iter	Nodes	Cost
0	143	2325
1	290	2252
2	892	1952
3	3186	1926
done	5000	1926

prune588.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
0.8b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
0.9b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

5.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
36.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
12.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
11.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Counts

78 → 78

Iterations

Useful iterations: 5 (479.0ms)

Iter	Nodes	Cost
0	98	2330
1	149	2225
2	287	2059
3	514	1971
4	796	1971
5	1503	1969
6	4600	1969
done	5000	1969

prune445.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.6b

regimes674.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	31
1	29	31
done	29	31

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.0s	4821×	body	1280	valid
1.4s	2132×	body	640	valid
267.0ms	628×	body	320	valid
92.0ms	304×	body	160	valid
45.0ms	13×	body	2560	valid
15.0ms	104×	body	80	valid