Details

analyze3.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

sample289.0ms

Algorithm

intervals

Results

205.0ms	152×	body	1280	valid
50.0ms	69×	body	640	valid
9.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid
1.0ms	6×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.1b

Counts

2 → 1

localize25.0ms

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))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
2.0b	(cos (- lambda1 lambda2))

rewrite19.0ms

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×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `cos-sum` `sin-mult`

Counts

4 → 54

Calls

4 calls:

4.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
8.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.0ms	(cos (- lambda1 lambda2))

series51.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
10.0ms	(* (sin phi1) (sin phi2))
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify55.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4915	876
1	4915	876

prune188.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	51	15	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	15	67

Merged error: 3.8b

Counts

67 → 15

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.3b	(* (sin phi1) (sin phi2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite17.0ms

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

series79.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
44.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
10.0ms	(* (sin phi1) (sin phi2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4919	1173
1	4919	1173

prune227.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	71	20	91

Merged error: 3.7b

Counts

91 → 20

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
0.3b	(* (sin phi1) (sin phi2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
2.9b	(log (pow (exp (sin lambda1)) (sin lambda2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

series98.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
9.0ms	(* (sin phi1) (sin phi2))
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
24.0ms	(log (pow (exp (sin lambda1)) (sin lambda2)))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5044	1204

prune215.0ms

Filtered

53 candidates to 75 candidates (-41.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	76	19	95

Merged error: 3.7b

Counts

95 → 19

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2))))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`acos-asin`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2))))))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (sin lambda2))
19.0ms	(cbrt (sin lambda2))
19.0ms	(cbrt (sin lambda2))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2))))))))

simplify29.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4851	517
1	4851	517

prune61.0ms

Filtered

36 candidates to 53 candidates (-47.2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	52	20	72

Merged error: 3.7b

Counts

72 → 20

regimes1.6s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	35
1	34	35

end0.0ms

analyze2.8s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

sample8.9s

Algorithm

intervals

Results

6.3s	4760×	body	1280	valid
1.6s	2078×	body	640	valid
380.0ms	731×	body	320	valid
95.0ms	283×	body	160	valid
47.0ms	11×	body	2560	valid
24.0ms	137×	body	80	valid
2.0ms	2×	body	1280	invalid

Details

analyze3.0s

sample289.0ms

simplify3.0ms

prune14.0ms

localize25.0ms

rewrite19.0ms

series51.0ms

simplify55.0ms

prune188.0ms

localize32.0ms

rewrite17.0ms

series79.0ms

simplify44.0ms

prune227.0ms

localize40.0ms

rewrite14.0ms

series98.0ms

simplify42.0ms

prune215.0ms

localize36.0ms

rewrite7.0ms

series73.0ms

simplify29.0ms

prune61.0ms

regimes1.6s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.8s

sample8.9s

Profiling