Details

sample257.0ms

Algorithm

intervals

Results

187.0ms	165×	body	1280	valid
43.0ms	63×	body	640	valid
7.0ms	17×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	4×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b	(cos (- lambda1 lambda2))

rewrite23.0ms

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`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

11.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms	(cos (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
47.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	388	1113
1	1250	911
2	5001	909

prune357.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite16.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sin-mult`
2×	`pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `sin-neg` `distribute-rgt-neg-out` `frac-sub` `flip--` `sub-div`

Counts

4 → 70

Calls

4 calls:

5.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify119.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	343	1224
1	1150	1071
2	4777	1026
3	5001	1025

prune487.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
0.4b	(log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
5.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))

rewrite11.0ms

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`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `log1p-udef` `log1p-expm1` `sin-neg` `distribute-rgt-neg-out` `sin-mult`

Counts

4 → 63

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
0.0ms	(log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin lambda1) (sin (- lambda2)))
61.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
126.0ms	(log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	254	1199
1	739	1038
2	2611	1032
3	5001	1028

prune502.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* R (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))))
0.4b	(log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
5.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))))

rewrite11.0ms

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`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `log1p-udef` `log1p-expm1` `sin-neg` `distribute-rgt-neg-out` `sin-mult`

Counts

4 → 63

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
3.0ms	(* R (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))))
0.0ms	(log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))))

series231.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (sin (- lambda2)))
43.0ms	(* R (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))))
121.0ms	(log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (expm1 (log1p (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	246	1199
1	744	1038
2	2623	1032
3	5002	1028

prune426.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

regimes742.0ms

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	22
1	37	22

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.9s	4787×	body	1280	valid
1.4s	2033×	body	640	valid
303.0ms	711×	body	320	valid
86.0ms	304×	body	160	valid
41.0ms	11×	body	2560	valid
25.0ms	157×	body	80	valid