Details

sample165.0ms

Algorithm

intervals

Results

97.0ms	111×	body	1280	valid
37.0ms	74×	body	640	valid
10.0ms	30×	body	320	valid
3.0ms	15×	body	160	valid
3.0ms	26×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	21	12
2	21	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(sin (- lambda1 lambda2))
4.2b	(cos (- lambda1 lambda2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

12.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
3.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series206.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
104.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms	(sin (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))

simplify74.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	249	435
1	795	394
2	2920	393
3	5001	393

prune309.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.0b	(sin (- lambda1 lambda2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`sum-log`
3×	`flip3-+` `associate-r` `associate-l` `flip-+` `sin-mult`
2×	`+-commutative` `sin-sum` `associate-*r/` `frac-add`
1×	`sub-neg` `associate-+l+` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
3.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0ms	(sin (- lambda1 lambda2))

series425.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (sin lambda2))
231.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
127.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms	(sin (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	339	703
1	1406	645
2	5001	628

prune551.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`sum-log`
3×	`flip3-+` `associate-r` `associate-l` `flip-+` `sin-mult`
2×	`+-commutative` `associate-*r/` `frac-add`
1×	`associate-+l+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
12.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
3.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
220.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
124.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify46.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	347	967
1	1389	865
2	5001	848

prune407.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.8b	(log (exp (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sum-log`
6×	`exp-prod`
5×	`pow1`
4×	`add-exp-log` `log-prod` `log-pow` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `rem-exp-log`
2×	`+-commutative` `associate-*r/` `exp-sum` `frac-add` `sin-mult`
1×	`associate-+l+` `rem-log-exp`

Counts

4 → 56

Calls

4 calls:

27.0ms	(exp (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
12.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
3.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
27.0ms	(log (exp (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))

series867.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(exp (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
223.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
127.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
227.0ms	(log (exp (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	311	1121
1	1324	1001
2	5002	981

prune401.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes399.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	45
1	45	45

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.2s	3550×	body	1280	valid
1.2s	2343×	body	640	valid
330.0ms	982×	body	320	valid
93.0ms	409×	body	160	valid
69.0ms	716×	body	80	valid