Details

sample370.0ms

Algorithm

intervals

Results

234.0ms	117×	body	1280	valid
78.0ms	73×	body	640	valid
16.0ms	27×	body	320	valid
6.0ms	15×	body	160	valid
5.0ms	24×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
2	23
1	20
0	14

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.6b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
4.6b	(cos (- lambda1 lambda2))
4.6b	(sin (- lambda1 lambda2))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum` `sin-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`cos-diff` `sin-diff` `fma-udef`

Counts

4 → 61

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
20.0ms	(cos (- lambda1 lambda2))
32.0ms	(sin (- lambda1 lambda2))

series303.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
210.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
31.0ms	(cos (- lambda1 lambda2))
40.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	1578
2	611
1	290
0	172

prune610.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1)))
0.2b	(* (- (sin lambda1)) (sin lambda2))
0.6b	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1))
4.6b	(sin (- lambda1 lambda2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1)))
14.0ms	(* (- (sin lambda1)) (sin lambda2))
0.0ms	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1))
19.0ms	(sin (- lambda1 lambda2))

series493.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1)))
79.0ms	(* (- (sin lambda1)) (sin lambda2))
350.0ms	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1))
36.0ms	(sin (- lambda1 lambda2))

simplify706.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1274
1	381
0	195

prune861.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda2) (sin lambda1))
0.2b	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1)))
0.2b	(* (- (sin lambda1)) (sin lambda2))
0.6b	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-lft-neg-out` `neg-mul-1` `fma-udef`

Counts

4 → 67

Calls

4 calls:

14.0ms	(* (cos lambda2) (sin lambda1))
0.0ms	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1)))
25.0ms	(* (- (sin lambda1)) (sin lambda2))
1.0ms	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1))

series482.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos lambda2) (sin lambda1))
23.0ms	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1)))
94.0ms	(* (- (sin lambda1)) (sin lambda2))
303.0ms	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (- (sin lambda1)) (sin lambda2))) (cos phi1))

simplify816.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1376
1	330
0	144

prune989.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda2) (sin lambda1))
0.2b	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (log (pow (exp (- (sin lambda1))) (sin lambda2)))) (cos phi1)))
0.6b	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (log (pow (exp (- (sin lambda1))) (sin lambda2)))) (cos phi1))
3.2b	(log (pow (exp (- (sin lambda1))) (sin lambda2)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`log-prod` `add-exp-log`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `rem-log-exp` `associate-r` `associate-l`
1×	`pow-to-exp` `pow-prod-down` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

9.0ms	(* (cos lambda2) (sin lambda1))
0.0ms	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (log (pow (exp (- (sin lambda1))) (sin lambda2)))) (cos phi1)))
0.0ms	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (log (pow (exp (- (sin lambda1))) (sin lambda2)))) (cos phi1))
6.0ms	(log (pow (exp (- (sin lambda1))) (sin lambda2)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos lambda2) (sin lambda1))
33.0ms	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (cos lambda1) (sin lambda2))))) (fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (log (pow (exp (- (sin lambda1))) (sin lambda2)))) (cos phi1)))
411.0ms	(fma (cos phi2) (- (* (cos lambda2) (cos lambda1)) (log (pow (exp (- (sin lambda1))) (sin lambda2)))) (cos phi1))
190.0ms	(log (pow (exp (- (sin lambda1))) (sin lambda2)))

simplify487.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	921
1	301
0	140

prune764.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	36
2	36
1	34
0	24

end0.0ms

sample13.8s

Algorithm

intervals

Results

8.2s	3483×	body	1280	valid
3.1s	2411×	body	640	valid
1.4s	973×	body	320	valid
216.0ms	424×	body	160	valid
145.0ms	709×	body	80	valid