Details

sample257.0ms

Algorithm

intervals

Results

186.0ms	148×	body	1280	valid
44.0ms	63×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	20×	body	80	valid
2.0ms	7×	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: 13.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(sin (- lambda1 lambda2))
4.2b	(cos (- lambda1 lambda2))

rewrite33.0ms

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`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series188.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos phi1) (sin phi2))
96.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	443	1004
1	1340	773
2	5001	771

prune432.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.2b	(cos (- lambda1 lambda2))

rewrite34.0ms

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` `*-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-neg` `distribute-rgt-neg-out` `sin-cos-mult`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
6.0ms	(* (cos lambda1) (sin (- lambda2)))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))

series203.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
53.0ms	(* (cos lambda1) (sin (- lambda2)))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	461	812
1	1657	651
2	5001	650

prune558.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 91

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
6.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
22.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
54.0ms	(* (cos lambda1) (sin (- lambda2)))
44.0ms	(* (sin lambda1) (sin lambda2))
174.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify74.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	537	842
1	2541	735
2	5001	735

prune672.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))
0.5b	(pow (* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) 3)
21.5b	(cbrt (pow (* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-*l/` `pow-exp` `sin-cos-mult` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `*-commutative` `fma-udef` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-div` `distribute-lft-in` `pow1/3` `rem-cbrt-cube` `sin-mult` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))
11.0ms	(pow (* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) 3)
3.0ms	(cbrt (pow (* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) 3))

series735.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (sin lambda2))
178.0ms	(* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))
334.0ms	(pow (* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) 3)
177.0ms	(cbrt (pow (* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	374	1048
1	1677	993
2	5003	992

prune585.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes466.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	27
1	36	27

end0.0ms

sample8.1s

Algorithm

intervals

Results

6.0s	4576×	body	1280	valid
1.4s	1968×	body	640	valid
262.0ms	587×	body	320	valid
88.0ms	672×	body	80	valid
58.0ms	197×	body	160	valid