Details

sample251.0ms

Algorithm

intervals

Results

183.0ms	158×	body	1280	valid
42.0ms	66×	body	640	valid
8.0ms	20×	body	320	valid
2.0ms	7×	body	160	valid
1.0ms	5×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b	(cos (- lambda1 lambda2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
9×	`prod-diff`
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×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

15.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms	(cos (- lambda1 lambda2))

series174.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	388	1113
1	1250	911
2	5001	909

prune354.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `cos-mult`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
106.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	434	1553
1	1716	1275
2	5001	1274

prune439.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `cos-mult`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
14.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
106.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	434	1641
1	1720	1351
2	5001	1350

prune491.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
0.6b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
18×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`fma-neg`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`associate-*l/`
2×	`asin-acos` `flip3--` `cos-mult` `*-commutative` `flip--` `sin-mult` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `diff-log` `associate-*r/` `associate--r-` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

37.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))) R)
14.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
14.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))) R)
112.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms	(asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
56.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (expm1 (log1p (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))))

simplify85.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	538	7399
1	1777	4379
2	5002	4349

prune672.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.6b

regimes1.1s

Accuracy

0% (0.5b remaining)

Error of 3.6b against oracle of 3.1b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	27
1	39	27

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.6s	4771×	body	1280	valid
1.6s	2120×	body	640	valid
301.0ms	690×	body	320	valid
83.0ms	280×	body	160	valid
24.0ms	7×	body	2560	valid
20.0ms	132×	body	80	valid