Details

sample185.0ms

Algorithm

intervals

Results

119.0ms	123×	body	1280	valid
37.0ms	72×	body	640	valid
8.0ms	25×	body	320	valid
5.0ms	20×	body	160	valid
2.0ms	16×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	12

prune3.0ms

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: 1.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`add-sqr-sqrt` `sin-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`cos-sum`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cos-diff` `fma-def` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

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

series191.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
95.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify108.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	505	1623
1	1430	1236
2	4873	1161
3	5001	1161

prune343.0ms

Filtered

114 candidates to 66 candidates (57.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	14	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	14	115

Merged error: 0.8b

Counts

115 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
3.2b	(sin (- lambda1 lambda2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`sin-sum`
31×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
12×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-def`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `sin-diff` `flip-+` `sin-mult`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.0ms	(sin (- lambda1 lambda2))

series335.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (sin lambda2))
56.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
211.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
24.0ms	(sin (- lambda1 lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	533	1504
1	1787	1178
2	5001	1097

prune411.0ms

Filtered

114 candidates to 69 candidates (60.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	115	13	128

Merged error: 0.2b

Counts

128 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin lambda1))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

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

series388.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi2) (sin lambda1))
43.0ms	(* (sin lambda1) (sin lambda2))
82.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
218.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	396	684
1	1642	580
2	5001	572

prune457.0ms

Filtered

92 candidates to 70 candidates (76.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 0.2b

Counts

105 → 13

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin lambda1))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (cos phi2) (cos lambda1)) (sin (- lambda2)))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cos phi2) (sin lambda1))
5.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(* (* (cos phi2) (cos lambda1)) (sin (- lambda2)))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi2) (sin lambda1))
44.0ms	(* (sin lambda1) (sin lambda2))
83.0ms	(* (* (cos phi2) (cos lambda1)) (sin (- lambda2)))
222.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	416	694
1	1820	590
2	5001	582

prune395.0ms

Filtered

93 candidates to 70 candidates (75.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	93	13	106

Merged error: 0.2b

Counts

106 → 13

regimes420.0ms

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	35	25
1	35	25

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.4s	3623×	body	1280	valid
1.3s	2325×	body	640	valid
331.0ms	912×	body	320	valid
98.0ms	423×	body	160	valid
78.0ms	717×	body	80	valid