Details

sample171.0ms

Algorithm

intervals

Results

98.0ms	113×	body	1280	valid
41.0ms	74×	body	640	valid
9.0ms	26×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	29×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b	(sin (- lambda1 lambda2))
2.6b	(cos (- lambda1 lambda2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 69

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms	(sin (- lambda1 lambda2))
13.0ms	(cos (- lambda1 lambda2))

series157.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
107.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify68.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	365	1011
1	800	787
2	2597	784
3	5002	735

prune321.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b	(cos (- lambda1 lambda2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

14.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(cos (- lambda1 lambda2))

series188.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (cos lambda2))
14.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
111.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))

simplify90.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	390	869
1	1061	710
2	3925	707
3	5001	706

prune431.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-cos-mult` `fma-udef` `sin-mult`

Counts

4 → 61

Calls

4 calls:

12.0ms	(* (sin lambda1) (cos lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series252.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (cos lambda2))
46.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
139.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify58.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	239	677
1	714	590
2	2486	588
3	5001	588

prune413.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `associate-r` `associate-l`
2×	`fma-udef`
1×	`rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
3.0ms	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
138.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
142.0ms	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify47.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	201	772
1	539	670
2	1732	668
3	5002	668

prune425.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes535.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	25
1	31	25

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.1s	3484×	body	1280	valid
1.3s	2437×	body	640	valid
333.0ms	964×	body	320	valid
95.0ms	428×	body	160	valid
67.0ms	687×	body	80	valid