Details

sample257.0ms

Algorithm

intervals

Results

191.0ms	153×	body	1280	valid
39.0ms	59×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	21×	body	80	valid
1.0ms	5×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.9b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
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×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

8.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune410.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	14	99

Merged error: 7.0b

Counts

99 → 14

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 87

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
16.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
9.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series278.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (cos lambda2))
124.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	503	982
1	1905	806
2	5002	801

prune551.0ms

Filtered

99 candidates to 70 candidates (70.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	89	10	99
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Merged error: 0.0b

Counts

113 → 12

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
5×	`sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `cos-mult` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin lambda1) (cos lambda2))
128.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
51.0ms	(* (sin lambda1) (sin (- lambda2)))
176.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	571	1220
1	2581	1073
2	5001	1070

prune686.0ms

Filtered

112 candidates to 85 candidates (75.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 0.0b

Counts

124 → 12

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.3b	(/ (* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.3b	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

39×	`distribute-rgt-in` `distribute-lft-in`
31×	`add-exp-log` `add-cbrt-cube`
28×	`associate-*r/`
17×	`pow1`
15×	`add-sqr-sqrt`
14×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sub-neg` `prod-diff`
9×	`associate-l`
8×	`pow-prod-down` `sin-mult`
7×	`associate-r` `cos-mult`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r` `associate-/r/` `-commutative` `frac-sub` `flip--` `sub-div`
2×	`unswap-sqr`
1×	`frac-2neg` `flip3-+` `frac-add` `sin-neg` `clear-num` `distribute-rgt-neg-out` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 137

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin (- lambda2)))
14.0ms	(* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
23.0ms	(/ (* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
9.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin lambda1) (sin (- lambda2)))
316.0ms	(* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
586.0ms	(/ (* (sin phi1) (* (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
179.0ms	(* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin (- lambda2)))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	750	3772
1	4375	3155
2	5001	3148

prune822.0ms

Filtered

149 candidates to 96 candidates (64.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	150	11	161

Merged error: 0.0b

Counts

161 → 11

regimes445.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	29
1	36	29

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.0s	4697×	body	1280	valid
1.4s	1857×	body	640	valid
473.0ms	566×	body	320	valid
92.0ms	692×	body	80	valid
55.0ms	188×	body	160	valid