Details

sample175.0ms

Algorithm

intervals

Results

107.0ms	118×	body	1280	valid
35.0ms	70×	body	640	valid
10.0ms	31×	body	320	valid
5.0ms	22×	body	80	valid
3.0ms	15×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
4.9b	(cos (- lambda1 lambda2))
5.1b	(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `sin-sum`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series158.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
111.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify924.0ms

Counts

73 → 73

Iterations

Useful iterations: 3 (234.0ms)

Iter	Nodes	Cost
0	172	1599
1	282	1267
2	482	980
3	1289	822
done	5001	822

prune293.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
4.9b	(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-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×	`cos-diff` `sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
7.0ms	(cos (- lambda1 lambda2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
12.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
110.0ms	(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (409.0ms)

Iter	Nodes	Cost
0	171	1296
1	297	1124
2	675	920
3	2220	840
done	5000	840

prune370.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin 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)))
0.5b	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite10.0ms

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×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef` `sin-mult`

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (sin 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)))
0.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series306.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos lambda1) (sin lambda2))
47.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
200.0ms	(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify810.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (278.0ms)

Iter	Nodes	Cost
0	122	1099
1	251	1058
2	624	921
3	1827	920
done	5001	920

prune394.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)))
0.5b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
0.5b	(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3))
0.6b	(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 67

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)))
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
1.0ms	(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3))
1.0ms	(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)

series736.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)))
197.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
198.0ms	(cbrt (pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3))
326.0ms	(pow (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)) 3)

simplify2.1s

Counts

79 → 79

Iterations

Useful iterations: 3 (402.0ms)

Iter	Nodes	Cost
0	105	2204
1	205	1944
2	585	1679
3	3906	1676
done	5001	1676

prune305.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes489.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	52
1	30	52
done	30	52

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.3s	3611×	body	1280	valid
1.2s	2273×	body	640	valid
316.0ms	919×	body	320	valid
108.0ms	456×	body	160	valid
85.0ms	741×	body	80	valid