Details

sample286.0ms

Algorithm

intervals

Results

208.0ms	150×	body	1280	valid
50.0ms	65×	body	640	valid
8.0ms	19×	body	320	valid
2.0ms	16×	body	80	valid
2.0ms	6×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 14.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite82.0ms

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:

27.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))
13.0ms	(sin (- lambda1 lambda2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

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

prune450.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
5.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
13.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series313.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (cos lambda2))
105.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
144.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	476	857
1	1742	702
2	5001	697

prune489.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sin-cos-mult` `log1p-expm1-u`
3×	`*-commutative` `sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `sin-neg` `cos-mult` `distribute-rgt-neg-out`
1×	`+-commutative` `fma-def` `flip3-+` `unsub-neg` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

5.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
16.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
50.0ms	(* (sin lambda1) (sin lambda2))
108.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
97.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify58.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	461	902
1	2075	718
2	5002	716

prune521.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative` `sin-cos-mult` `sin-mult`
2×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`
1×	`+-commutative` `frac-times` `fma-def` `flip3-+` `associate-*r/` `unsub-neg` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

5.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos lambda1))
16.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
44.0ms	(* (sin lambda1) (sin lambda2))
74.0ms	(* (* (sin phi1) (cos phi2)) (cos lambda1))
101.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	405	767
1	1913	625
2	5001	623

prune454.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes361.0ms

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	40	30
1	40	30

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.3s	4717×	body	1280	valid
1.4s	1883×	body	640	valid
253.0ms	550×	body	320	valid
84.0ms	637×	body	80	valid
65.0ms	213×	body	160	valid