Details

sample398.0ms

Algorithm

intervals

Results

250.0ms	114×	body	1280	valid
83.0ms	76×	body	640	valid
22.0ms	31×	body	320	valid
6.0ms	25×	body	80	valid
5.0ms	10×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	23	19
done	23	19

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.0b	(sin (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`sin-sum`
32×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
11×	`distribute-rgt-in` `cos-sum` `distribute-lft-in`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`cos-diff` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

54.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
15.0ms	(sin (- lambda1 lambda2))
24.0ms	(cos (- lambda1 lambda2))

series387.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
201.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
43.0ms	(sin (- lambda1 lambda2))
38.0ms	(cos (- lambda1 lambda2))

simplify5.6s

Counts

106 → 106

Iterations

Useful iterations: 5 (4.2s)

Iter	Nodes	Cost
0	223	2679
1	396	2016
2	739	1591
3	1279	1421
4	2214	1060
5	4741	825
done	5000	825

prune515.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.7b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
3.0b	(sin (- lambda1 lambda2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`sin-sum`
9×	`prod-diff`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`sub-neg` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
14.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
15.0ms	(sin (- lambda1 lambda2))

series461.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
65.0ms	(* (sin lambda1) (sin lambda2))
331.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
34.0ms	(sin (- lambda1 lambda2))

simplify3.1s

Counts

73 → 73

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	182	1402
1	319	1201
2	589	999
3	1130	956
4	2995	884
done	5002	821

prune665.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `fma-udef` `sin-mult`

Counts

4 → 64

Calls

4 calls:

63.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
21.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series653.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
32.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
59.0ms	(* (sin lambda1) (sin lambda2))
352.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify3.0s

Counts

76 → 76

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	142	1455
1	334	1370
2	1113	1196
3	4028	1194
done	5000	1194

prune655.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
0.7b	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u`
3×	`associate-r` `associate-l` `fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `sin-mult` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

3.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
18.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
4.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

series963.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
74.0ms	(* (sin lambda1) (sin lambda2))
271.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
278.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

simplify3.1s

Counts

75 → 75

Iterations

Useful iterations: 3 (348.0ms)

Iter	Nodes	Cost
0	115	1238
1	218	1174
2	492	1023
3	1209	1020
4	4686	1020
done	5000	1020

prune519.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes686.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	35
1	29	35
done	29	35

end0.0ms

sample11.1s

Algorithm

intervals

Results

7.2s	3601×	body	1280	valid
2.3s	2329×	body	640	valid
573.0ms	931×	body	320	valid
229.0ms	667×	body	80	valid
192.0ms	472×	body	160	valid