Details

analyze2.6s

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample280.0ms

Algorithm

intervals

Results

169.0ms	121×	body	1280	valid
76.0ms	81×	body	640	valid
12.0ms	23×	body	320	valid
4.0ms	23×	body	80	valid
3.0ms	8×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 11.9b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
4.5b	(cos (- lambda1 lambda2))
4.6b	(sin (- lambda1 lambda2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`cos-diff` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`cos-sum` `sin-sum` `associate-*r/` `sin-diff` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

6.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
5.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series46.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
14.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4919	693
1	4919	693

prune173.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	12	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Merged error: 5.1b

Counts

76 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
4.5b	(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`cos-diff` `associate-r`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`sub-neg` `cos-sum` `associate-*r/`

Counts

4 → 71

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
6.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
5.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series49.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos lambda1) (sin lambda2))
23.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
14.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify51.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5138	755

prune162.0ms

Filtered

59 candidates to 83 candidates (-40.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 0.1b

Counts

95 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
9×	`associate-*r/`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
43.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
9.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify33.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5038	1210

prune172.0ms

Filtered

66 candidates to 97 candidates (-47.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 0.0b

Counts

107 → 10

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))
0.2b	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))
3.1b	(log (pow (exp (sin lambda1)) (sin lambda2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`add-exp-log`
13×	`pow1` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
7×	`log-prod` `associate-r`
6×	`associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`unpow-prod-down` `rem-log-exp` `*-commutative`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`pow-to-exp` `pow-exp` `log-pow` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))
8.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))
4.0ms	(log (pow (exp (sin lambda1)) (sin lambda2)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
56.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))
36.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))
22.0ms	(log (pow (exp (sin lambda1)) (sin lambda2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5392	1190

prune110.0ms

Filtered

69 candidates to 94 candidates (-36.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Merged error: 0.0b

Counts

104 → 11

regimes709.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	126	40
1	126	40

end0.0ms

sample9.3s

Algorithm

intervals

Results

6.9s	4562×	body	1280	valid
1.6s	1976×	body	640	valid
333.0ms	617×	body	320	valid
121.0ms	652×	body	80	valid
70.0ms	193×	body	160	valid

Details

analyze2.6s

sample280.0ms

simplify13.0ms

prune17.0ms

localize25.0ms

rewrite20.0ms

series46.0ms

simplify57.0ms

prune173.0ms

localize34.0ms

rewrite21.0ms

series49.0ms

simplify51.0ms

prune162.0ms

localize34.0ms

rewrite30.0ms

series90.0ms

simplify33.0ms

prune172.0ms

localize43.0ms

rewrite28.0ms

series123.0ms

simplify34.0ms

prune110.0ms

regimes709.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.3s

Profiling