Details

sample269.0ms

Algorithm

intervals

Results

199.0ms	152×	body	1280	valid
43.0ms	61×	body	640	valid
5.0ms	11×	body	320	valid
4.0ms	27×	body	80	valid
2.0ms	5×	body	160	valid

simplify18.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(sin (- lambda1 lambda2))
2.7b	(cos (- lambda1 lambda2))

rewrite43.0ms

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

Counts

4 → 86

Calls

4 calls:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune413.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.8b

localize35.0ms

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))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(cos (- lambda1 lambda2))

rewrite39.0ms

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

Counts

4 → 87

Calls

4 calls:

14.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series289.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
48.0ms	(* (sin phi1) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	477	989
1	1849	806
2	5001	802

prune579.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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*`
6×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `sin-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (sin phi1) (cos phi2))
17.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
42.0ms	(* (sin phi1) (cos phi2))
99.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
113.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	368	836
1	1642	658
2	5001	658

prune587.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
2.3b	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
30×	`add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`associate-r` `associate-l` `sin-cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `log-pow` `*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `sin-mult`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
2.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series363.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
101.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
114.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
105.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	389	900
1	1742	711
2	5001	711

prune534.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes462.0ms

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	44	37
1	44	37

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4616×	body	1280	valid
1.4s	1919×	body	640	valid
251.0ms	550×	body	320	valid
107.0ms	699×	body	80	valid
62.0ms	216×	body	160	valid