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

sample299.0ms

Algorithm

intervals

Results

209.0ms	158×	body	1280	valid
47.0ms	62×	body	640	valid
10.0ms	19×	body	320	valid
4.0ms	1×	body	2560	valid
4.0ms	11×	body	160	valid
1.0ms	5×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	95	19
1	95	19

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: 16.1b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
2.6b	(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×	`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:

5.0ms	(* (sin phi1) (sin phi2))
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))

series49.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin phi1) (sin phi2))
27.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune169.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	52	14	66
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	54	14	68

Merged error: 3.1b

Counts

68 → 14

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
1.5b	(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 phi1) (sin phi2))
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)))))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
9.0ms	(* (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)))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5166	1173

prune175.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	76	14	90

Merged error: 3.0b

Counts

90 → 14

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
3.0b	(log (pow (exp (sin lambda1)) (sin lambda2)))

rewrite16.0ms

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:

6.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
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)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin phi1) (sin phi2))
45.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2)))))))) R)
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (pow (exp (sin lambda1)) (sin lambda2))))))))
23.0ms	(log (pow (exp (sin lambda1)) (sin lambda2)))

simplify33.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5009	1204

prune166.0ms

Filtered

54 candidates to 75 candidates (-38.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	74	15	89

Merged error: 3.0b

Counts

89 → 15

localize39.0ms

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)))))))))
0.3b	(* (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))))))))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite12.0ms

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)))))))))
6.0ms	(* (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)))))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
45.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
28.0ms	(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)))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4866	1908
1	4866	1908

prune64.0ms

Filtered

40 candidates to 69 candidates (-72.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	67	17	84

Merged error: 3.0b

Counts

84 → 17

regimes1.3s

Accuracy

0% (0.3b 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	31	28
1	31	28

end0.0ms

sample9.0s

Algorithm

intervals

Results

6.5s	4790×	body	1280	valid
1.7s	2108×	body	640	valid
365.0ms	684×	body	320	valid
95.0ms	279×	body	160	valid
24.0ms	134×	body	80	valid
18.0ms	5×	body	2560	valid
1.0ms	1×	body	1280	invalid
1.0ms	1×	body	640	invalid

Details

analyze3.0s

sample299.0ms

simplify6.0ms

prune17.0ms

localize24.0ms

rewrite14.0ms

series49.0ms

simplify57.0ms

prune169.0ms

localize32.0ms

rewrite15.0ms

series74.0ms

simplify47.0ms

prune175.0ms

localize37.0ms

rewrite16.0ms

series94.0ms

simplify33.0ms

prune166.0ms

localize39.0ms

rewrite12.0ms

series97.0ms

simplify71.0ms

prune64.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.0s

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