Details

sample268.0ms

Algorithm

intervals

Results

194.0ms	148×	body	1280	valid
46.0ms	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	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize25.0ms

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))

rewrite31.0ms

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

Counts

4 → 59

Calls

4 calls:

5.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series168.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

simplify110.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	286	430
1	1077	367
2	4907	367
3	5001	367

prune315.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize34.0ms

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))

rewrite27.0ms

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*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 67

Calls

4 calls:

6.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos phi1) (sin phi2))
41.0ms	(* (cos lambda1) (sin lambda2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify40.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	331	476
1	1299	404
2	5002	404

prune421.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

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))))

rewrite32.0ms

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×	`*-commutative` `sin-cos-mult` `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/`

Counts

4 → 82

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos phi1) (sin phi2))
41.0ms	(* (cos lambda1) (sin lambda2))
49.0ms	(* (sin lambda1) (sin lambda2))
167.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	504	780
1	2385	675
2	5001	675

prune519.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cos-mult`
84×	`sin-mult`
50×	`associate-*r/` `frac-add` `associate-/r/`
49×	`pow1`
48×	`associate-*l/`
44×	`frac-times`
31×	`add-exp-log` `add-cbrt-cube`
27×	`frac-sub`
19×	`pow-prod-down`
15×	`sub-div`
13×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`associate-/l/`
6×	`cube-div` `pow-unpow`
4×	`pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `sin-cos-mult` `add-log-exp` `rem-cube-cbrt`
3×	`cbrt-undiv` `flip3--` `flip3-+` `times-frac` `div-exp` `associate-/r*` `flip--` `flip-+`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `sqr-pow`
1×	`pow2` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 163

Calls

4 calls:

3.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
110.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series936.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
752.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
53.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
64.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify62.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1293	4502
1	5001	4261

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes416.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	45
1	47	45

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.2s	4576×	body	1280	valid
1.7s	1968×	body	640	valid
283.0ms	587×	body	320	valid
90.0ms	672×	body	80	valid
59.0ms	197×	body	160	valid