Details

sample290.0ms

Algorithm

intervals

Results

207.0ms	144×	body	1280	valid
47.0ms	61×	body	640	valid
8.0ms	18×	body	320	valid
4.0ms	24×	body	80	valid
3.0ms	9×	body	160	valid

simplify7.0ms

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 (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: 14.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(sin (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))

rewrite19.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune151.0ms

Filtered

72 candidates to 51 candidates (29.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	62	10	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	10	73

Merged error: 6.3b

Counts

73 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(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` `sin-cos-mult`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin phi1) (cos phi2))
24.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	308	486
1	1294	414
2	5002	414

prune139.0ms

Filtered

81 candidates to 56 candidates (30.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 0.1b

Counts

91 → 8

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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` `sin-cos-mult` `cbrt-unprod`
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 → 84

Calls

4 calls:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
45.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	474	790
1	2287	685
2	5001	684

prune150.0ms

Filtered

96 candidates to 64 candidates (33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 0.1b

Counts

104 → 8

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
25.2b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod`
6×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`cube-div` `associate-l` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-*r/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `frac-add` `pow-exp` `cos-mult` `*-commutative` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/3` `associate-*l/` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
12.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
3.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series80.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
43.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
16.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
11.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	469	859
1	2493	741
2	5001	740

prune156.0ms

Filtered

99 candidates to 67 candidates (32.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	99	8	107

Merged error: 0.1b

Counts

107 → 8

regimes510.0ms

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	36	27
1	36	27

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.1s	4571×	body	1280	valid
1.5s	1986×	body	640	valid
263.0ms	539×	body	320	valid
100.0ms	693×	body	80	valid
65.0ms	211×	body	160	valid

Details

sample290.0ms

simplify7.0ms

prune5.0ms

localize24.0ms

rewrite19.0ms

series43.0ms

simplify104.0ms

prune151.0ms

localize37.0ms

rewrite20.0ms

series46.0ms

simplify42.0ms

prune139.0ms

localize34.0ms

rewrite25.0ms

series71.0ms

simplify62.0ms

prune150.0ms

localize37.0ms

rewrite26.0ms

series80.0ms

simplify70.0ms

prune156.0ms

regimes510.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.6s

Profiling