Details

sample246.0ms

Algorithm

intervals

Results

156.0ms	138×	body	1280	valid
52.0ms	83×	body	640	valid
16.0ms	27×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	2×	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: 18.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (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)))))
2.1b	(cos (- lambda1 lambda2))

rewrite58.0ms

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:

30.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

series182.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
45.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify40.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (31.0ms)

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

prune337.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

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:

41.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
45.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
116.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	434	1553
1	1716	1275
2	5002	1274

prune453.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

18.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
6.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
51.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
19.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify125.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 4 (44.0ms)

Iter	Nodes	Cost
0	199	2029
1	449	1785
2	1044	1781
3	1438	1781
4	3717	1777
5	5001	1777

prune461.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

26.0ms	(* (* (cos phi1) (cos phi2)) (sin lambda1))
73.0ms	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (* (cos phi1) (cos phi2)) (sin lambda1))
118.0ms	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
75.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	313	1371
1	1404	1151
2	5002	1151

prune360.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

regimes535.0ms

Accuracy

0% (0.3b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.7s	4700×	body	1280	valid
1.5s	2230×	body	640	valid
289.0ms	681×	body	320	valid
79.0ms	260×	body	160	valid
19.0ms	126×	body	80	valid
16.0ms	6×	body	2560	valid