Details

sample279.0ms

Algorithm

intervals

Results

192.0ms	147×	body	1280	valid
55.0ms	65×	body	640	valid
10.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	13×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 12.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite33.0ms

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:

5.0ms	(* (sin phi1) (cos phi2))
15.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin phi1) (cos phi2))
94.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	411	1009
1	1289	778
2	5001	776

prune398.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	13	99

Merged error: 4.8b

Counts

99 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))

rewrite29.0ms

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` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 87

Calls

4 calls:

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

series288.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
44.0ms	(* (sin phi1) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	445	971
1	1607	790
2	5001	789

prune458.0ms

Filtered

99 candidates to 67 candidates (67.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	102	10	112

Merged error: 0.1b

Counts

112 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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` `cbrt-unprod`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 93

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* (sin phi1) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
47.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(* (sin phi1) (cos phi2))
179.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify73.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	509	1001
1	2532	874
2	5001	874

prune531.0ms

Filtered

105 candidates to 75 candidates (71.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	106	9	115

Merged error: 0.0b

Counts

115 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/` `unswap-sqr`
2×	`sin-cos-mult` `fma-udef`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--` `sin-mult`

Counts

4 → 87

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
47.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(* (sin phi1) (cos phi2))
183.0ms	(* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	383	863
1	1694	733
2	5001	733

prune419.0ms

Filtered

99 candidates to 68 candidates (68.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	99	9	108

Merged error: 0.0b

Counts

108 → 9

regimes362.0ms

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	30	24
1	30	24

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.1s	4551×	body	1280	valid
1.5s	1995×	body	640	valid
311.0ms	605×	body	320	valid
94.0ms	652×	body	80	valid
62.0ms	197×	body	160	valid