Details

sample172.0ms

Algorithm

intervals

Results

98.0ms	103×	body	1280	valid
41.0ms	81×	body	640	valid
12.0ms	38×	body	320	valid
3.0ms	13×	body	160	valid
2.0ms	21×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

18.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

series198.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
99.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify113.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	505	1623
1	1430	1236
2	4873	1161
3	5001	1161

prune382.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b	(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
91.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
99.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify109.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	430	956
1	1269	789
2	4435	784
3	5001	779

prune435.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

5.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
4.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
18.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
229.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	402	1025
1	1436	901
2	5002	884

prune492.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (log (exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1)))))
0.2b	(exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1)))
0.7b	(fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1))
0.8b	(log (exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 51

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (log (exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1)))))
1.0ms	(exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1)))
0.0ms	(fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1))
2.0ms	(log (exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (log (exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1)))))
244.0ms	(exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1)))
186.0ms	(fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1))
185.0ms	(log (exp (fma (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi2) (cos phi1))))

simplify138.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 4 (129.0ms)

Iter	Nodes	Cost
0	205	1116
1	440	977
2	1174	957
3	4470	953
4	5001	946

prune339.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes391.0ms

Accuracy

0% (0.1b 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	42	51
1	42	51

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.3s	3634×	body	1280	valid
1.2s	2306×	body	640	valid
332.0ms	953×	body	320	valid
93.0ms	418×	body	160	valid
68.0ms	689×	body	80	valid