Details

analyze2.9s

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

sample281.0ms

Algorithm

intervals

Results

193.0ms	146×	body	1280	valid
51.0ms	69×	body	640	valid
14.0ms	29×	body	320	valid
3.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	95	19
1	95	19

prune18.0ms

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: 17.1b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.0b	(cos (- lambda1 lambda2))

rewrite16.0ms

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-l`
5×	`cos-diff`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`*-commutative`
1×	`acos-asin` `sub-neg` `cos-sum` `associate-*r/` `cos-mult` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
25.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
8.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify77.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4881	1065
1	4881	1065

prune170.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	56	14	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	14	71

Merged error: 4.6b

Counts

71 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
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)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin 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×	`associate-r`
6×	`associate-*r/`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
3×	`*-commutative`
2×	`sin-mult` `unswap-sqr`
1×	`acos-asin` `flip3-+` `frac-add` `cos-mult` `flip-+`

Counts

4 → 70

Calls

4 calls:

10.0ms	(* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
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)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
10.0ms	(* (sin lambda1) (sin lambda2))
43.0ms	(* (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)))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4960	1541
1	4960	1541

prune187.0ms

Filtered

52 candidates to 82 candidates (-57.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	80	16	96

Merged error: 4.5b

Counts

96 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
0.2b	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
0.6b	(log (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)))))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
42.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
31.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4866	1908
1	4866	1908

prune169.0ms

Filtered

43 candidates to 69 candidates (-60.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	70	15	85

Merged error: 4.5b

Counts

85 → 15

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.6b	(log (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))))
1.0b	(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)))))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`log-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity` `log-pow`
7×	`pow1`
5×	`add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`acos-asin`
2×	`exp-diff` `rem-log-exp`
1×	`log-div` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

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

series83.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
31.0ms	(log (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))))
12.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4963	1828
1	4963	1828

prune83.0ms

Filtered

43 candidates to 64 candidates (-48.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	65	14	79

Merged error: 4.5b

Counts

79 → 14

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	29
1	37	29

end0.0ms

sample8.9s

Algorithm

intervals

Results

6.4s	4776×	body	1280	valid
1.6s	2076×	body	640	valid
364.0ms	722×	body	320	valid
88.0ms	263×	body	160	valid
31.0ms	9×	body	2560	valid
28.0ms	154×	body	80	valid
8.0ms	2×	body	1280	invalid
1.0ms	1×	body	640	invalid

Details

analyze2.9s

sample281.0ms

simplify5.0ms

prune18.0ms

localize24.0ms

rewrite16.0ms

series66.0ms

simplify77.0ms

prune170.0ms

localize31.0ms

rewrite21.0ms

series114.0ms

simplify53.0ms

prune187.0ms

localize36.0ms

rewrite11.0ms

series99.0ms

simplify70.0ms

prune169.0ms

localize41.0ms

rewrite9.0ms

series83.0ms

simplify49.0ms

prune83.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.9s

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