Details

analyze2.9s (19%)

Algorithm

1×

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

sample298.0ms (1.9%)

Algorithm

1×

intervals

Results

207.0ms	149×	body	1280	valid
55.0ms	71×	body	640	valid
12.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid
1.0ms	4×	body	80	valid

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	95	19
1	95	19

prune11.0ms (0.1%)

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: 13.3b

Counts

2 → 1

localize24.0ms (0.2%)

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

rewrite18.0ms (0.1%)

Algorithm

1×	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:

8.0ms	(* (sin phi1) (sin phi2))
4.0ms	(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)))))

series48.0ms (0.3%)

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))
8.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune186.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	52	14	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	14	67

Merged error: 3.0b

Counts

67 → 14

localize34.0ms (0.2%)

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)
0.2b	(* (sin phi1) (sin phi2))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite15.0ms (0.1%)

Algorithm

1×	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))))))

series79.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (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))))))
9.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (sin phi1) (sin phi2))

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5164	1173

prune199.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	75	15	90

Merged error: 3.0b

Counts

90 → 15

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
30.8b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

5.0ms	(* (sin phi1) (sin phi2))
5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
3.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))

series49.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
9.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))
9.0ms	(* (sin phi1) (sin phi2))

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4978	795
1	4978	795

prune391.0ms (2.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	79	16	95

Merged error: 2.9b

Counts

95 → 16

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.9b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.6b	(log (exp (* (sin phi1) (sin phi2))))

rewrite13.0ms (0.1%)

Algorithm

1×	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	(log (exp (* (sin phi1) (sin phi2))))
2.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series81.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
14.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
10.0ms	(log (exp (* (sin phi1) (sin phi2))))
10.0ms	(* (sin phi1) (sin phi2))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4996	1145
1	4996	1145

prune94.0ms (0.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	71	16	87

Merged error: 2.9b

Counts

87 → 16

regimes1.3s (8.2%)

Accuracy

Total 0.3b remaining (8.6%)

Threshold costs 0.3b (8.6%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	29
1	33	29

end0.0ms (0%)

sample9.4s (60.8%)

Algorithm

1×

intervals

Results

6.7s	4876×	body	1280	valid
1.7s	2056×	body	640	valid
368.0ms	675×	body	320	valid
96.0ms	259×	body	160	valid
25.0ms	129×	body	80	valid
18.0ms	5×	body	2560	valid
2.0ms	1×	body	1280	invalid

Details

analyze2.9s (19%)

sample298.0ms (1.9%)

simplify5.0ms (0%)

prune11.0ms (0.1%)

localize24.0ms (0.2%)

rewrite18.0ms (0.1%)

series48.0ms (0.3%)

simplify58.0ms (0.4%)

prune186.0ms (1.2%)

localize34.0ms (0.2%)

rewrite15.0ms (0.1%)

series79.0ms (0.5%)

simplify48.0ms (0.3%)

prune199.0ms (1.3%)

localize37.0ms (0.2%)

rewrite15.0ms (0.1%)

series49.0ms (0.3%)

simplify37.0ms (0.2%)

prune391.0ms (2.5%)

localize40.0ms (0.3%)

rewrite13.0ms (0.1%)

series81.0ms (0.5%)

simplify69.0ms (0.4%)

prune94.0ms (0.6%)

regimes1.3s (8.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample9.4s (60.8%)

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