Details

sample201.0ms

Algorithm

intervals

Results

117.0ms	110×	body	1280	valid
45.0ms	75×	body	640	valid
13.0ms	32×	body	320	valid
8.0ms	15×	body	160	valid
3.0ms	24×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite43.0ms

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

series135.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
92.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify67.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (59.0ms)

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

prune684.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.7b

localize35.0ms

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	(* (cos lambda1) (sin (- lambda2)))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))

rewrite41.0ms

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×	`associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sin-neg` `sum-log` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms	(* (cos lambda1) (sin (- lambda2)))
12.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms	(cos (- lambda1 lambda2))

series165.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
48.0ms	(* (cos lambda1) (sin (- lambda2)))
90.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms	(cos (- lambda1 lambda2))

simplify105.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	404	909
1	1169	743
2	4635	741
3	5001	739

prune952.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.4b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-neg` `distribute-rgt-neg-out` `fma-udef` `sin-mult`

Counts

4 → 61

Calls

4 calls:

14.0ms	(* (cos lambda1) (sin (- lambda2)))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
14.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series213.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos lambda1) (sin (- lambda2)))
19.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
40.0ms	(* (sin lambda1) (sin lambda2))
110.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify71.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	269	717
1	854	623
2	3268	622
3	5002	622

prune927.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.4b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.5b	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `associate-r` `associate-l`
2×	`fma-udef`
1×	`rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
11.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
6.0ms	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
46.0ms	(* (sin lambda1) (sin lambda2))
113.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
112.0ms	(log (exp (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))))

simplify51.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	224	787
1	569	683
2	1792	681
3	5001	681

prune763.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes1.3s

Accuracy

0% (0.2b 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	35	26
1	35	26

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.8s	3527×	body	1280	valid
1.5s	2404×	body	640	valid
385.0ms	922×	body	320	valid
116.0ms	427×	body	160	valid
108.0ms	720×	body	80	valid