Details

sample176.0ms

Algorithm

intervals

Results

105.0ms	111×	body	1280	valid
37.0ms	71×	body	640	valid
13.0ms	35×	body	320	valid
4.0ms	18×	body	160	valid
2.0ms	21×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	12

prune4.0ms

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: 0.8b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.3b	(sin (- lambda1 lambda2))
4.5b	(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 69

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series153.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(sin (- lambda1 lambda2))
24.0ms	(cos (- lambda1 lambda2))

simplify72.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	365	1011
1	800	787
2	2597	784
3	5002	735

prune313.0ms

Filtered

81 candidates to 55 candidates (67.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	67	14	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	14	82

Merged error: 0.6b

Counts

82 → 14

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
4.3b	(sin (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`sin-sum`
9×	`prod-diff`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l`
2×	`associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
6.0ms	(sin (- lambda1 lambda2))

series297.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
45.0ms	(* (sin lambda1) (sin lambda2))
215.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
21.0ms	(sin (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	394	973
1	1124	794
2	5001	785

prune372.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.1b

Counts

95 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `flip-+` `sin-mult`

Counts

4 → 68

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos lambda1) (sin lambda2))
17.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
44.0ms	(* (sin lambda1) (sin lambda2))
224.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	327	826
1	1159	712
2	5002	704

prune383.0ms

Filtered

80 candidates to 61 candidates (76.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	80	13	93

Merged error: 0.1b

Counts

93 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `pow1/3`
2×	`associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `flip-+`

Counts

4 → 57

Calls

4 calls:

4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))

series529.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
106.0ms	(cbrt (sin lambda2))
100.0ms	(cbrt (sin lambda2))
102.0ms	(cbrt (sin lambda2))

simplify89.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	220	471
1	686	419
2	3245	405
3	5001	405

prune351.0ms

Filtered

69 candidates to 58 candidates (84.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	69	13	82

Merged error: 0.1b

Counts

82 → 13

regimes441.0ms

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	30	22
1	30	22

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.4s	3650×	body	1280	valid
1.2s	2324×	body	640	valid
332.0ms	932×	body	320	valid
86.0ms	378×	body	160	valid
83.0ms	716×	body	80	valid