Details

sample168.0ms

Algorithm

intervals

Results

96.0ms	109×	body	1280	valid
42.0ms	71×	body	640	valid
11.0ms	33×	body	320	valid
4.0ms	16×	body	160	valid
3.0ms	27×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

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))))
3.1b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite28.0ms

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:

9.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
5.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
98.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify112.0ms

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

prune362.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

1.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
5.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(cos (- lambda1 lambda2))

series220.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
85.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
104.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify106.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	416	988
1	1146	798
2	4580	796
3	5001	794

prune440.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
6.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
85.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
223.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	362	950
1	1266	805
2	5001	797

prune481.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos phi1) 3)
0.4b	(/ (fma (pow (cos phi2) 3) (pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3) (pow (cos phi1) 3)) (fma (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))) (* (cos phi1) (cos phi1))))
0.6b	(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
1.2b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `unpow-prod-down` `pow-unpow` `cube-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 89

Calls

4 calls:

2.0ms	(pow (cos phi1) 3)
3.0ms	(/ (fma (pow (cos phi2) 3) (pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3) (pow (cos phi1) 3)) (fma (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))) (* (cos phi1) (cos phi1))))
2.0ms	(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
1.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

series2.5s

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (cos phi1) 3)
2.1s	(/ (fma (pow (cos phi2) 3) (pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3) (pow (cos phi1) 3)) (fma (cos phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))) (* (cos phi1) (cos phi1))))
108.0ms	(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
212.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

simplify95.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	572	2270
1	2757	2054
2	5002	2042

prune664.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes542.0ms

Accuracy

0% (0.1b 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	42	51
1	42	51

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.2s	3565×	body	1280	valid
1.2s	2349×	body	640	valid
331.0ms	939×	body	320	valid
104.0ms	416×	body	160	valid
77.0ms	730×	body	80	valid
2.0ms	1×	body	2560	valid