Details

sample249.0ms

Algorithm

intervals

Results

168.0ms	137×	body	1280	valid
52.0ms	69×	body	640	valid
7.0ms	16×	body	320	valid
3.0ms	24×	body	80	valid
3.0ms	10×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

8.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series185.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune403.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(cos (- lambda1 lambda2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 86

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin lambda2))
129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	462	959
1	1689	784
2	5001	783

prune507.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.1b	(* (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))))

rewrite30.0ms

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`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos lambda1) (sin lambda2))
45.0ms	(* (sin lambda1) (sin lambda2))
134.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
171.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify75.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	524	989
1	2555	869
2	5001	869

prune571.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(expm1 (log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))

rewrite22.0ms

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`
5×	`expm1-log1p-u`
4×	`associate-l` `pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/`
2×	`flip3-+` `frac-add` `cos-mult` `*-commutative` `flip-+` `sin-mult`
1×	`distribute-rgt-in` `log1p-udef` `expm1-log1p` `flip3--` `distribute-lft-in` `log1p-expm1` `flip--` `expm1-udef` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
1.0ms	(expm1 (log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
1.0ms	(log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
186.0ms	(expm1 (log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))))
181.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
181.0ms	(log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))

simplify70.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	471	1104
1	2188	957
2	5002	947

prune468.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes392.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	27
1	35	27

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4642×	body	1280	valid
1.4s	1936×	body	640	valid
264.0ms	559×	body	320	valid
98.0ms	669×	body	80	valid
58.0ms	194×	body	160	valid