Details

sample267.0ms

Algorithm

intervals

Results

178.0ms	147×	body	1280	valid
45.0ms	65×	body	640	valid
12.0ms	27×	body	320	valid
4.0ms	12×	body	160	valid
1.0ms	5×	body	80	valid

simplify5.0ms

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

prune6.0ms

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

localize23.0ms

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))

rewrite15.0ms

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:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
6.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

series62.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
24.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

simplify101.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (7.0ms)

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

prune164.0ms

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

localize32.0ms

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)))
0.2b	(* (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))))))

rewrite23.0ms

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:

8.0ms	(* (* (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))))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
27.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
42.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (11.0ms)

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

prune166.0ms

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

localize38.0ms

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)))))

rewrite17.0ms

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:

8.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
3.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
27.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify127.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (115.0ms)

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

prune176.0ms

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

localize35.0ms

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)))))

rewrite18.0ms

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:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
8.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
2.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
43.0ms	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
25.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
12.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (7.0ms)

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

prune79.0ms

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

regimes1.3s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	23
1	36	23

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.0s	4826×	body	1280	valid
1.4s	2022×	body	640	valid
351.0ms	710×	body	320	valid
90.0ms	293×	body	160	valid
48.0ms	15×	body	2560	valid
22.0ms	135×	body	80	valid

Details

sample267.0ms

simplify5.0ms

prune6.0ms

localize23.0ms

rewrite15.0ms

series62.0ms

simplify101.0ms

prune164.0ms

localize32.0ms

rewrite23.0ms

series112.0ms

simplify52.0ms

prune166.0ms

localize38.0ms

rewrite17.0ms

series109.0ms

simplify127.0ms

prune176.0ms

localize35.0ms

rewrite18.0ms

series89.0ms

simplify121.0ms

prune79.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.5s

Profiling