Details

sample261.0ms

Algorithm

intervals

Results

181.0ms	138×	body	1280	valid
47.0ms	61×	body	640	valid
9.0ms	20×	body	320	valid
4.0ms	27×	body	80	valid
3.0ms	10×	body	160	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: 12.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(cos (- lambda1 lambda2))
2.5b	(sin (- lambda1 lambda2))

rewrite30.0ms

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

series188.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

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

prune398.0ms

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: 6.8b

Counts

99 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(cos (- lambda1 lambda2))

rewrite30.0ms

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×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 86

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(cos (- lambda1 lambda2))

series279.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos lambda1) (sin lambda2))
129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify60.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	462	959
1	1689	784
2	5001	783

prune456.0ms

Filtered

98 candidates to 65 candidates (66.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	103	9	112

Merged error: 0.1b

Counts

112 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

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

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

Counts

4 → 90

Calls

4 calls:

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

series632.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
282.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
44.0ms	(* (sin lambda1) (sin lambda2))
174.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify88.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	592	1295
1	2847	1150
2	5002	1149

prune534.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin 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))) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-l`
12×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-*l/`
2×	`fma-udef`
1×	`distribute-lft-neg-out` `distribute-lft-neg-in` `distribute-rgt-in` `neg-mul-1` `flip3--` `distribute-rgt-neg-in` `distribute-lft-in` `sin-cos-mult` `flip--` `distribute-neg-frac` `sin-mult`

Counts

4 → 90

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (- (* (sin phi1) (cos phi2))) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
132.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
43.0ms	(* (sin lambda1) (sin lambda2))
186.0ms	(* (- (* (sin phi1) (cos phi2))) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	416	912
1	1889	810
2	5001	810

prune486.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	102	10	112

Merged error: 0.0b

Counts

112 → 10

regimes385.0ms

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

6.2s	4567×	body	1280	valid
1.4s	1972×	body	640	valid
277.0ms	575×	body	320	valid
94.0ms	680×	body	80	valid
74.0ms	206×	body	160	valid