Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	147×	body	1280	valid
0.0hr	65×	body	640	valid
0.0hr	27×	body	320	valid
0.0hr	12×	body	160	valid
0.0hr	5×	body	80	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

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

prune0.0hr

Filtered

1 candidates to 0 candidates (100.0%)

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: 16.1b

Counts

2 → 1

localize0.0hr

Local error

Found 4 expressions with local error:

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

rewrite0.0hr

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:

0.0hr	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.0hr	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.0hr	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.0hr	(cos (- lambda1 lambda2))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.0hr	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.0hr	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.0hr	(cos (- lambda1 lambda2))

simplify0.0hr

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	264	773
1	1022	655
2	4705	655
3	5002	655

prune0.0hr

Filtered

69 candidates to 49 candidates (29.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 3.3b

Counts

70 → 12

localize0.0hr

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)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite0.0hr

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:

0.0hr	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.0hr	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.0hr	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.0hr	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.0hr	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.0hr	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.0hr	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify0.0hr

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	419	1435
1	1667	1157
2	5002	1157

prune0.0hr

Filtered

88 candidates to 49 candidates (44.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	88	12	100

Merged error: 3.2b

Counts

100 → 12

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
4.5b	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

0.0hr	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.0hr	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.0hr	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
0.0hr	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.0hr	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.0hr	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
0.0hr	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify0.0hr

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (0.0hr)

Iter	Nodes	Cost
0	302	1377
1	1092	1132
2	4682	1127
3	5001	1126

prune0.0hr

Filtered

77 candidates to 51 candidates (33.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	75	14	89

Merged error: 3.2b

Counts

89 → 14

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
0.3b	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
0.6b	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r`
4×	`add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`acos-asin` `sin-mult`

Counts

4 → 66

Calls

4 calls:

0.0hr	(* (sin phi1) (sin phi2))
0.0hr	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
0.0hr	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
0.0hr	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (sin phi1) (sin phi2))
0.0hr	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
0.0hr	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
0.0hr	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

simplify0.0hr

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	298	1196
1	1107	995
2	4609	995
3	5002	995

prune0.0hr

Filtered

78 candidates to 51 candidates (34.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 3.2b

Counts

92 → 13

regimes0.0hr

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0hr

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	36	23
1	36	23

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	4826×	body	1280	valid
0.0hr	2022×	body	640	valid
0.0hr	710×	body	320	valid
0.0hr	293×	body	160	valid
0.0hr	15×	body	2560	valid
0.0hr	135×	body	80	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling