Details

sample260.0ms

Algorithm

intervals

Results

192.0ms	165×	body	1280	valid
37.0ms	59×	body	640	valid
9.0ms	22×	body	320	valid
1.0ms	8×	body	80	valid
1.0ms	2×	body	160	valid

simplify7.0ms

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: 17.5b

localize25.0ms

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)
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.7b	(cos (- lambda1 lambda2))

rewrite54.0ms

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:

29.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(* (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)))))
11.0ms	(cos (- lambda1 lambda2))

series159.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
44.0ms	(* (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)))))
16.0ms	(cos (- lambda1 lambda2))

simplify104.0ms

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

prune287.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.4b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `cos-mult`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`frac-times` `associate-*r/` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`acos-asin` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 77

Calls

4 calls:

6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
84.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
15.0ms	(* (sin lambda1) (sin (- lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
193.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
48.0ms	(* (sin lambda1) (sin (- lambda2)))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	481	1482
1	2051	1253
2	5002	1248

prune491.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.3b

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)) (* (sin lambda1) (sin (- lambda2)))))))))
0.3b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`log-pow`
3×	`acos-asin` `log-prod` `associate-r` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `rem-exp-log` `sin-mult` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

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

series128.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
50.0ms	(* (sin lambda1) (sin (- lambda2)))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
44.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

simplify108.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	205	1176
1	548	1032
2	1573	996
3	4459	996
4	5002	996

prune426.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.3b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
34×	`add-exp-log` `add-cbrt-cube`
27×	`pow-prod-down`
18×	`prod-exp` `cbrt-unprod`
7×	`cos-mult`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
4×	`pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `add-log-exp` `rem-cube-cbrt`
3×	`distribute-rgt-neg-out` `sin-mult`
2×	`cube-div` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `associate-r/` `associate-r` `associate-l` `associate-l/` `sin-neg` `*-commutative` `sqr-pow`
1×	`pow2` `swap-sqr` `cube-neg`

Counts

4 → 110

Calls

4 calls:

48.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
10.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
43.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
8.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series275.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
65.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
52.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
54.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify82.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	479	699
1	2440	646
2	5001	646

prune543.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.3b

regimes504.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	47
1	42	47

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.7s	4708×	body	1280	valid
1.4s	2118×	body	640	valid
308.0ms	725×	body	320	valid
95.0ms	314×	body	160	valid
37.0ms	10×	body	2560	valid
19.0ms	126×	body	80	valid