Details

sample291.0ms

Algorithm

intervals

Results

200.0ms	141×	body	1280	valid
60.0ms	69×	body	640	valid
9.0ms	19×	body	320	valid
3.0ms	23×	body	80	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite81.0ms

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:

26.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
34.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series176.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
83.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(cos (- lambda1 lambda2))
19.0ms	(sin (- lambda1 lambda2))

simplify102.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune514.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))

rewrite109.0ms

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

Counts

4 → 69

Calls

4 calls:

55.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
11.0ms	(* (cos lambda1) (sin lambda2))
30.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))

series260.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
38.0ms	(* (cos lambda1) (sin lambda2))
81.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	339	641
1	1438	552
2	5001	552

prune806.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

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:

11.0ms	(* (cos lambda1) (sin lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
12.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos lambda1) (sin lambda2))
102.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
41.0ms	(* (sin lambda1) (sin lambda2))
91.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify54.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	407	777
1	1866	599
2	5002	599

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
3.2b	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite112.0ms

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` `add-log-exp`
4×	`sin-cos-mult`
3×	`log-prod` `log-pow` `*-commutative` `sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

41.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
13.0ms	(* (sin lambda1) (sin lambda2))
44.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
12.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
46.0ms	(* (sin lambda1) (sin lambda2))
92.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
91.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	355	838
1	1625	649
2	5002	649

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes922.0ms

Accuracy

0% (0.2b 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	39	36
1	39	36

end0.0ms

sample9.5s

Algorithm

intervals

Results

7.1s	4651×	body	1280	valid
1.7s	1944×	body	640	valid
301.0ms	531×	body	320	valid
116.0ms	663×	body	80	valid
71.0ms	211×	body	160	valid