Details

sample274.0ms

Algorithm

intervals

Results

196.0ms	152×	body	1280	valid
50.0ms	64×	body	640	valid
11.0ms	25×	body	320	valid
1.0ms	11×	body	80	valid
1.0ms	4×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite31.0ms

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-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

10.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune333.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-cos-mult` `flip-+`

Counts

4 → 69

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series273.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos phi1) (sin phi2))
125.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
86.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	387	676
1	1684	576
2	5002	575

prune466.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult` `sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`associate-*l/` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 89

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
13.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
24.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi1) (sin phi2))
51.0ms	(* (sin lambda1) (sin (- lambda2)))
126.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
174.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	551	1122
1	2584	972
2	5001	970

prune616.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
34×	`add-exp-log` `add-cbrt-cube`
27×	`pow-prod-down`
18×	`prod-exp` `cbrt-unprod`
7×	`cos-mult`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
4×	`pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `add-log-exp` `rem-cube-cbrt`
3×	`distribute-rgt-neg-out` `sin-mult`
2×	`cube-div` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `associate-r/` `associate-r` `associate-l` `associate-l/` `sin-neg` `*-commutative` `sqr-pow`
1×	`pow2` `swap-sqr` `cube-neg`

Counts

4 → 110

Calls

4 calls:

4.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
15.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series300.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
114.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
53.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
63.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify84.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	479	699
1	2440	646
2	5001	646

prune588.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes357.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	56
1	46	56

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.2s	4625×	body	1280	valid
1.4s	1920×	body	640	valid
488.0ms	557×	body	320	valid
91.0ms	677×	body	80	valid
75.0ms	221×	body	160	valid