Details

sample201.0ms

Algorithm

intervals

Results

126.0ms	121×	body	1280	valid
41.0ms	68×	body	640	valid
12.0ms	28×	body	320	valid
4.0ms	28×	body	80	valid
3.0ms	11×	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: 0.3b

localize21.0ms

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))))
2.8b	(cos (- lambda1 lambda2))
2.9b	(sin (- 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)))))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series153.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
101.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify66.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (58.0ms)

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

prune307.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
0.5b	(log (exp (cos (- lambda1 lambda2))))
2.8b	(cos (- lambda1 lambda2))
2.9b	(sin (- lambda1 lambda2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `prod-diff`
22×	`cos-sum`
12×	`log-prod`
11×	`log-div` `exp-diff` `sin-sum`
8×	`associate-+r+`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `distribute-rgt-in` `cos-diff` `expm1-log1p-u` `distribute-lft-in` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `exp-prod` `fma-def` `exp-sum`
1×	`+-commutative` `flip3-+` `rem-log-exp` `sum-log` `sin-diff` `flip-+`

Counts

4 → 95

Calls

4 calls:

19.0ms	(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
14.0ms	(log (exp (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series156.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (cos phi1) (* (cos phi2) (log (exp (cos (- lambda1 lambda2))))))
17.0ms	(log (exp (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify92.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	481	1306
1	1054	982
2	3036	952
3	5002	852

prune433.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.9b	(sin (- lambda1 lambda2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
33×	`cos-sum`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`sin-sum`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
1×	`sin-diff`

Counts

4 → 84

Calls

4 calls:

7.0ms	(cos (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series74.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cos (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	235	1339
1	404	983
2	1324	979
3	5002	880

prune403.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.9b	(sin (- lambda1 lambda2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

30×	`prod-diff`
23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`cos-sum`
11×	`sin-sum`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `cos-diff` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--l+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `fma-neg` `diff-log` `sin-diff` `flip--`

Counts

4 → 83

Calls

4 calls:

6.0ms	(- (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
7.0ms	(cos (- lambda1 lambda2))
9.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series171.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
17.0ms	(cos (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify98.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	369	1228
1	847	924
2	3533	915
3	5001	840

prune491.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

regimes369.0ms

Accuracy

0% (0.2b remaining)

Error of 0.9b against oracle of 0.7b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	34
1	37	34

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.6s	3542×	body	1280	valid
1.4s	2399×	body	640	valid
390.0ms	957×	body	320	valid
115.0ms	400×	body	160	valid
110.0ms	702×	body	80	valid