Details

sample238.0ms

Algorithm

intervals

Results

146.0ms	126×	body	1280	valid
57.0ms	81×	body	640	valid
12.0ms	26×	body	320	valid
3.0ms	9×	body	160	valid
3.0ms	14×	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: 0.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.3b	(sin (- lambda1 lambda2))
4.4b	(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:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify68.0ms

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

prune315.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

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)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.4b	(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))

series269.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (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)))))
101.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(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

prune451.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (sin 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)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.7b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

11.0ms	(* (cos phi2) (* (sin 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)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
4.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series252.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cos phi2) (* (sin lambda1) (sin lambda2)))
21.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
43.0ms	(* (sin lambda1) (sin lambda2))
122.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify92.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	244	740
1	794	632
2	3501	631
3	5002	631

prune420.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
0.7b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series581.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(cbrt (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)))
123.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
128.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
123.0ms	(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify46.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	110	490
1	344	408
2	1232	401
3	5001	400

prune388.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes424.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	41
1	36	41

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	3604×	body	1280	valid
1.4s	2371×	body	640	valid
341.0ms	871×	body	320	valid
112.0ms	406×	body	160	valid
108.0ms	748×	body	80	valid