Details

sample304.0ms

Algorithm

intervals

Results

199.0ms	154×	body	1280	valid
51.0ms	60×	body	640	valid
15.0ms	29×	body	320	valid
5.0ms	1×	body	2560	valid
2.0ms	7×	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: 18.3b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.3b	(* (sin phi1) (sin phi2))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.1b	(cos (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(* (sin phi1) (sin phi2))
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	200	661
1	565	569
2	1790	569
3	5001	569

prune382.0ms

Filtered

67 candidates to 49 candidates (26.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	52	15	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	15	68

Merged error: 3.2b

Counts

68 → 15

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (sin phi1) (sin phi2))
45.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	260	929
1	831	774
2	1930	774
3	3056	774
4	5001	774

prune437.0ms

Filtered

76 candidates to 51 candidates (32.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	76	15	91

Merged error: 3.1b

Counts

91 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.8b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

5.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
27.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
13.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (38.0ms)

Iter	Nodes	Cost
0	179	1561
1	401	1313
2	897	1309
3	1255	1309
4	3512	1305
5	5001	1305

prune355.0ms

Filtered

70 candidates to 46 candidates (34.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	67	18	85

Merged error: 3.1b

Counts

85 → 18

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.7b	(log (exp (* (sin phi1) (sin phi2))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

5.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.0ms	(log (exp (* (sin phi1) (sin phi2))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
43.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
15.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(log (exp (* (sin phi1) (sin phi2))))

simplify127.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	214	980
1	621	826
2	1325	826
3	2037	826
4	4926	826
5	5001	826

prune268.0ms

Filtered

71 candidates to 49 candidates (31.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	71	18	89

Merged error: 3.1b

Counts

89 → 18

regimes2.0s

Accuracy

0% (0.4b 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	32	19
1	32	19

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.9s	4751×	body	1280	valid
1.4s	2078×	body	640	valid
325.0ms	734×	body	320	valid
80.0ms	275×	body	160	valid
34.0ms	10×	body	2560	valid
24.0ms	153×	body	80	valid

Details

sample304.0ms

simplify5.0ms

prune6.0ms

localize28.0ms

rewrite14.0ms

series47.0ms

simplify45.0ms

prune382.0ms

localize35.0ms

rewrite15.0ms

series77.0ms

simplify73.0ms

prune437.0ms

localize34.0ms

rewrite12.0ms

series98.0ms

simplify111.0ms

prune355.0ms

localize35.0ms

rewrite13.0ms

series77.0ms

simplify127.0ms

prune268.0ms

regimes2.0s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.3s

Profiling