Details

sample272.0ms

Algorithm

intervals

Results

191.0ms	154×	body	1280	valid
49.0ms	67×	body	640	valid
9.0ms	17×	body	320	valid
5.0ms	14×	body	160	valid
1.0ms	4×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize24.0ms

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)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b	(cos (- lambda1 lambda2))

rewrite23.0ms

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×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

14.0ms	(* (* (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)))))
5.0ms	(cos (- lambda1 lambda2))

series173.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify106.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	264	773
1	1022	656
2	4705	656
3	5002	656

prune306.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
1.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite33.0ms

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×	`add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

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

series331.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
110.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
128.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
20.0ms	(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

88 → 88

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	419	1435
1	1667	1158
2	5001	1158

prune413.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
1.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
4.0b	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
28×	`add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`cos-mult`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`log-prod` `log-pow`
2×	`frac-times` `associate-r/` `associate-r` `associate-l` `associate-l/` `*-commutative` `sin-mult`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

14.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
13.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series374.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
129.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
115.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	385	1054
1	1552	834
2	5001	832

prune443.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.6b	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))))
1.6b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
4.0b	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
17×	`add-exp-log`
16×	`add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
5×	`add-log-exp`
4×	`log-pow` `cos-mult`
2×	`rem-log-exp`
1×	`acos-asin` `frac-times` `exp-prod` `exp-to-pow` `associate-r/` `associate-r` `associate-l` `associate-l/` `*-commutative`

Counts

4 → 59

Calls

4 calls:

13.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
1.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
55.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
114.0ms	(log (exp (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	300	1253
1	1076	1024
2	5002	1020

prune373.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

regimes615.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	27
1	38	27

end0.0ms

sample8.9s

Algorithm

intervals

Results

6.3s	4767×	body	1280	valid
1.6s	2060×	body	640	valid
376.0ms	702×	body	320	valid
118.0ms	307×	body	160	valid
42.0ms	11×	body	2560	valid
37.0ms	155×	body	80	valid