Details

sample264.0ms

Algorithm

intervals

Results

193.0ms	150×	body	1280	valid
41.0ms	59×	body	640	valid
9.0ms	18×	body	320	valid
3.0ms	23×	body	80	valid
2.0ms	6×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

Filtered

1 candidates to 0 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: 12.6b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(sin (- lambda1 lambda2))
2.5b	(cos (- lambda1 lambda2))

rewrite21.0ms

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

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos phi1) (sin phi2))
93.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify114.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	286	430
1	1077	367
2	4907	367
3	5001	367

prune318.0ms

Filtered

71 candidates to 50 candidates (70.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 5.3b

Counts

72 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(cos (- lambda1 lambda2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series286.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi1) (sin phi2))
135.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	357	648
1	1484	552
2	5002	552

prune418.0ms

Filtered

81 candidates to 56 candidates (69.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Merged error: 0.0b

Counts

93 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`sin-cos-mult`
3×	`frac-times` `associate-r/` `associate-l/` `*-commutative` `sin-mult`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `frac-add` `cos-mult` `flip--` `flip-+` `associate--r+` `unswap-sqr`
1×	`sub-neg` `diff-log`

Counts

4 → 80

Calls

4 calls:

4.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series640.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
128.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
51.0ms	(* (sin lambda1) (sin lambda2))
172.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify85.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	553	1180
1	2692	1053
2	5002	1053

prune475.0ms

Filtered

92 candidates to 63 candidates (68.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 0.0b

Counts

105 → 13

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
4.3b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `associate-l/` `log-pow` `-commutative` `sin-cos-mult`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `exp-prod` `flip3--` `exp-to-pow` `distribute-lft-in` `rem-log-exp` `flip--` `sin-mult`

Counts

4 → 78

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
50.0ms	(* (sin lambda1) (sin lambda2))
175.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
46.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify63.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	432	950
1	2076	797
2	5002	795

prune423.0ms

Filtered

90 candidates to 64 candidates (71.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	90	13	103

Merged error: 0.0b

Counts

103 → 13

regimes487.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	27
1	35	27

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4626×	body	1280	valid
1.5s	1968×	body	640	valid
276.0ms	576×	body	320	valid
87.0ms	633×	body	80	valid
57.0ms	197×	body	160	valid

Details

sample264.0ms

simplify10.0ms

prune5.0ms

localize34.0ms

rewrite21.0ms

series181.0ms

simplify114.0ms

prune318.0ms

localize34.0ms

rewrite26.0ms

series286.0ms

simplify46.0ms

prune418.0ms

localize34.0ms

rewrite30.0ms

series640.0ms

simplify85.0ms

prune475.0ms

localize43.0ms

rewrite28.0ms

series399.0ms

simplify63.0ms

prune423.0ms

regimes487.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.5s

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