Details

sample314.0ms

Algorithm

intervals

Results

228.0ms	150×	body	1280	valid
48.0ms	59×	body	640	valid
10.0ms	18×	body	320	valid
10.0ms	23×	body	80	valid
2.0ms	6×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	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: 12.6b

Counts

2 → 1

localize24.0ms

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))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

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

series171.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos phi1) (sin phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	443	1004
1	1340	773
2	5001	771

prune400.0ms

Filtered

97 candidates to 62 candidates (63.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	83	14	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	14	98

Merged error: 5.3b

Counts

98 → 14

localize32.0ms

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))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

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

series276.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
127.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify52.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	480	966
1	1668	785
2	5001	784

prune491.0ms

Filtered

98 candidates to 66 candidates (67.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	98	14	112

Merged error: 0.0b

Counts

112 → 14

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×	`expm1-log1p-u` `sin-cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 90

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))))

series635.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
49.0ms	(* (sin lambda1) (sin lambda2))
174.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify91.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	592	1295
1	2847	1150
2	5002	1149

prune561.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	101	15	116

Merged error: 0.0b

Counts

116 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3--` `associate-*l/` `flip--` `unswap-sqr`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `sin-mult`

Counts

4 → 79

Calls

4 calls:

4.0ms	(- (* (cos phi1) (sin phi2)) (* (sin phi1) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2))))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
6.0ms	(* (sin phi1) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(- (* (cos phi1) (sin phi2)) (* (sin phi1) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2))))
131.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
52.0ms	(* (sin lambda1) (sin lambda2))
183.0ms	(* (sin phi1) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	426	1070
1	1783	932
2	5001	932

prune400.0ms

Filtered

91 candidates to 64 candidates (70.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	91	15	106

Merged error: 0.0b

Counts

106 → 15

regimes572.0ms

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	24
1	30	24

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4626×	body	1280	valid
1.5s	1968×	body	640	valid
276.0ms	576×	body	320	valid
89.0ms	633×	body	80	valid
61.0ms	197×	body	160	valid