Details

sample254.0ms

Algorithm

intervals

Results

176.0ms	149×	body	1280	valid
41.0ms	67×	body	640	valid
12.0ms	29×	body	320	valid
2.0ms	1×	body	2560	valid
2.0ms	6×	body	160	valid
1.0ms	4×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b	(cos (- lambda1 lambda2))

rewrite31.0ms

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×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

12.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
10.0ms	(cos (- lambda1 lambda2))

series116.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin phi1) (sin phi2))
42.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
20.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	200	661
1	565	569
2	1790	569
3	5001	569

prune295.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.2b	(* (sin lambda1) (sin (- lambda2)))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 65

Calls

4 calls:

14.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
15.0ms	(* (sin lambda1) (sin (- lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (sin phi2))
71.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
47.0ms	(* (sin lambda1) (sin (- lambda2)))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	281	1000
1	916	859
2	2499	835
3	5001	835

prune438.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
0.7b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`log-pow`
3×	`acos-asin` `log-prod` `associate-r` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `rem-exp-log` `sin-mult` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

17.0ms	(* (sin lambda1) (sin (- lambda2)))
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (sin (- lambda2)))
47.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
16.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify104.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	205	1176
1	548	1032
2	1573	996
3	4459	996
4	5001	996

prune445.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2))))))))) R)
0.2b	(* (sin lambda1) (sin (- lambda2)))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
2.8b	(log (exp (* (sin lambda1) (sin (- lambda2)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `sin-neg` `log-pow` `distribute-rgt-neg-out`
2×	`exp-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `log-div` `exp-prod` `exp-to-pow` `rem-log-exp` `log-rec` `sin-mult`

Counts

4 → 62

Calls

4 calls:

7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2))))))))) R)
15.0ms	(* (sin lambda1) (sin (- lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
5.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2))))))))) R)
51.0ms	(* (sin lambda1) (sin (- lambda2)))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
53.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	238	1078
1	713	922
2	2010	910
3	5002	910

prune361.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

regimes609.0ms

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	20
1	32	20

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.8s	4851×	body	1280	valid
1.3s	2068×	body	640	valid
279.0ms	667×	body	320	valid
78.0ms	263×	body	160	valid
36.0ms	9×	body	2560	valid
22.0ms	144×	body	80	valid