Details

sample247.0ms

Algorithm

intervals

Results

181.0ms	163×	body	1280	valid
38.0ms	60×	body	640	valid
8.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

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: 16.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.7b	(cos (- lambda1 lambda2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

12.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

series178.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
45.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify109.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	264	773
1	1022	656
2	4705	656
3	5002	656

prune315.0ms

Filtered

69 candidates to 49 candidates (71.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	53	16	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	16	70

Merged error: 2.8b

Counts

70 → 16

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `cos-mult`
5×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

9.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
9.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
107.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	419	1435
1	1667	1158
2	5002	1158

prune448.0ms

Filtered

88 candidates to 49 candidates (55.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	69	19	88
Fresh	14	1	15
Picked	1	0	1
Done	0	0	0
Total	84	20	104

Merged error: 2.7b

Counts

104 → 20

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))))) R)
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
5×	`associate-l` `cos-mult`
4×	`add-log-exp`
3×	`associate-l/` `-commutative`
1×	`acos-asin` `frac-times` `associate-*r/` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

9.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
9.0ms	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
108.0ms	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))))) R)
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	419	1394
1	1772	1132
2	5001	1132

prune420.0ms

Filtered

85 candidates to 48 candidates (56.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	73	12	85
Fresh	13	6	19
Picked	1	0	1
Done	0	0	0
Total	87	18	105

Merged error: 2.7b

Counts

105 → 18

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.7b	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`log-prod` `associate-l`
4×	`associate-r` `exp-sum` `add-log-exp`
2×	`cos-mult` `*-commutative` `sin-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `rem-log-exp` `associate-l/` `log-pow`

Counts

4 → 67

Calls

4 calls:

6.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
9.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
109.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
54.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify136.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	317	1708
1	1039	1434
2	4517	1415
3	5001	1413

prune374.0ms

Filtered

79 candidates to 51 candidates (64.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	80	17	97

Merged error: 2.7b

Counts

97 → 17

regimes947.0ms

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	23
1	34	23

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.6s	4788×	body	1280	valid
1.4s	2121×	body	640	valid
302.0ms	673×	body	320	valid
77.0ms	279×	body	160	valid
41.0ms	12×	body	2560	valid
19.0ms	127×	body	80	valid