Details

sample271.0ms

Algorithm

intervals

Results

178.0ms	143×	body	1280	valid
53.0ms	64×	body	640	valid
12.0ms	27×	body	320	valid
3.0ms	19×	body	80	valid
1.0ms	3×	body	160	valid

simplify8.0ms

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

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 13.4b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite25.0ms

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:

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

series203.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos phi1) (sin phi2))
104.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify111.0ms

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

prune409.0ms

Filtered

71 candidates to 50 candidates (29.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 6.8b

Counts

72 → 13

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))

rewrite20.0ms

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` `*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 68

Calls

4 calls:

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

series232.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin lambda1) (cos lambda2))
51.0ms	(* (cos phi1) (sin phi2))
108.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	340	481
1	1343	409
2	5002	409

prune478.0ms

Filtered

80 candidates to 55 candidates (31.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 0.1b

Counts

93 → 12

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

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

series353.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (cos phi1) (sin phi2))
57.0ms	(* (sin lambda1) (sin lambda2))
132.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
113.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	420	777
1	1833	599
2	5001	599

prune540.0ms

Filtered

99 candidates to 57 candidates (42.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	100	11	111

Merged error: 0.1b

Counts

111 → 11

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

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

series359.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
53.0ms	(* (sin lambda1) (cos lambda2))
51.0ms	(* (cos phi1) (sin phi2))
58.0ms	(* (sin lambda1) (sin lambda2))

simplify72.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	506	785
1	2326	680
2	5001	679

prune574.0ms

Filtered

95 candidates to 64 candidates (32.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	96	10	106

Merged error: 0.1b

Counts

106 → 10

regimes707.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	52
1	37	52

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.1s	4555×	body	1280	valid
1.4s	1948×	body	640	valid
282.0ms	565×	body	320	valid
97.0ms	712×	body	80	valid
71.0ms	220×	body	160	valid

Details

sample271.0ms

simplify8.0ms

prune7.0ms

localize27.0ms

rewrite25.0ms

series203.0ms

simplify111.0ms

prune409.0ms

localize40.0ms

rewrite20.0ms

series232.0ms

simplify41.0ms

prune478.0ms

localize41.0ms

rewrite29.0ms

series353.0ms

simplify57.0ms

prune540.0ms

localize41.0ms

rewrite26.0ms

series359.0ms

simplify72.0ms

prune574.0ms

regimes707.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.4s

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