Details

sample191.0ms

Algorithm

intervals

Results

111.0ms	114×	body	1280	valid
47.0ms	74×	body	640	valid
9.0ms	22×	body	320	valid
5.0ms	31×	body	80	valid
4.0ms	15×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify71.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	365	1011
1	800	787
2	2597	784
3	5002	735

prune325.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b	(cos (- lambda1 lambda2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

13.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))

series272.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
13.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	458	1104
1	1634	916
2	5001	912

prune475.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (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))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

13.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
8.0ms	(* (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))))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
54.0ms	(* (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)))))))
225.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	430	1173
1	1829	1030
2	5001	1013

prune543.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
1.5b	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`unpow-prod-down` `cube-prod`
6×	`pow-unpow` `associate--l+`
5×	`prod-diff`
4×	`cube-div` `expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`distribute-rgt-in` `cube-mult` `sub-neg` `pow-pow` `distribute-lft-in` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
2×	`pow-to-exp` `flip3--` `cos-mult` `flip--` `sin-mult`
1×	`+-commutative` `flip3-+` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `sum-cubes` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `sub-div`

Counts

4 → 104

Calls

4 calls:

15.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
1.0ms	(pow (cos phi1) 3)
11.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
20.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
34.0ms	(pow (cos phi1) 3)
212.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
219.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify111.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	751	1337
1	3696	1192
2	5001	1185

prune743.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes658.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	47	65
1	47	65

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.6s	3601×	body	1280	valid
1.4s	2316×	body	640	valid
402.0ms	964×	body	320	valid
113.0ms	408×	body	160	valid
113.0ms	711×	body	80	valid