Details

sample256.0ms

Algorithm

intervals

Results

179.0ms	145×	body	1280	valid
53.0ms	68×	body	640	valid
4.0ms	30×	body	80	valid
4.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify9.0ms

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

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: 11.6b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite28.0ms

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:

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

series190.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify105.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune306.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	13	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Merged error: 6.1b

Counts

73 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))

rewrite24.0ms

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` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (sin phi1) (cos 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))

series276.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
126.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	322	653
1	1423	557
2	5001	557

prune379.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 0.1b

Counts

95 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin phi1) (cos phi2))
46.0ms	(* (sin lambda1) (sin lambda2))
123.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
166.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify71.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	491	957
1	2489	828
2	5001	828

prune445.0ms

Filtered

97 candidates to 66 candidates (68.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	95	11	106

Merged error: 0.0b

Counts

106 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b	(pow (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
20.6b	(cbrt (pow (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(pow (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
6.0ms	(cbrt (pow (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))

series810.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
171.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
346.0ms	(pow (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
166.0ms	(cbrt (pow (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))

simplify108.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	626	1683
1	3505	1593
2	5002	1592

prune547.0ms

Filtered

115 candidates to 80 candidates (69.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Merged error: 0.0b

Counts

126 → 12

regimes481.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	27
1	36	27

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.2s	4554×	body	1280	valid
1.5s	1952×	body	640	valid
285.0ms	593×	body	320	valid
99.0ms	683×	body	80	valid
64.0ms	218×	body	160	valid