Details

sample175.0ms

Algorithm

intervals

Results

110.0ms	121×	body	1280	valid
39.0ms	77×	body	640	valid
6.0ms	20×	body	320	valid
4.0ms	29×	body	80	valid
2.0ms	9×	body	160	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: 0.3b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite28.0ms

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:

9.0ms	(* (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:

53.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
97.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify110.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

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

prune335.0ms

Filtered

114 candidates to 66 candidates (57.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 0.2b

Counts

115 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`cos-sum`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`sin-sum`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
1×	`sin-diff`

Counts

4 → 84

Calls

4 calls:

5.0ms	(cos (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series71.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cos (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify51.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	235	1339
1	404	983
2	1324	979
3	5002	880

prune332.0ms

Filtered

96 candidates to 52 candidates (54.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 0.2b

Counts

107 → 11

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
2.8b	(sin (- lambda1 lambda2))

rewrite26.0ms

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))
8.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.0ms	(sin (- lambda1 lambda2))

series342.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (sin lambda2))
59.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
214.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
20.0ms	(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

prune395.0ms

Filtered

114 candidates to 69 candidates (60.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 0.1b

Counts

125 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
48.0ms	(* (sin lambda1) (sin lambda2))
138.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
223.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	374	1090
1	1513	949
2	5002	941

prune349.0ms

Filtered

88 candidates to 68 candidates (77.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	87	11	98

Merged error: 0.1b

Counts

98 → 11

regimes383.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	31
1	29	31

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.2s	3521×	body	1280	valid
1.2s	2341×	body	640	valid
330.0ms	976×	body	320	valid
89.0ms	414×	body	160	valid
80.0ms	748×	body	80	valid