Details

sample263.0ms

Algorithm

intervals

Results

191.0ms	148×	body	1280	valid
45.0ms	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))

rewrite20.0ms

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

series177.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify109.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (7.0ms)

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

prune334.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize36.0ms

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))

rewrite22.0ms

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-neg` `distribute-rgt-neg-out` `sin-cos-mult`

Counts

4 → 68

Calls

4 calls:

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

series210.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos phi1) (sin phi2))
55.0ms	(* (cos lambda1) (sin (- lambda2)))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify40.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	338	504
1	1347	428
2	5001	428

prune445.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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))))

rewrite30.0ms

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/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 83

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
5.0ms	(* (cos lambda1) (sin (- lambda2)))
5.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
55.0ms	(* (cos lambda1) (sin (- lambda2)))
45.0ms	(* (sin lambda1) (sin lambda2))
175.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify69.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	520	808
1	2450	699
2	5001	699

prune567.0ms

Pruning

12 alts after pruning (12 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)

rewrite75.0ms

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:

5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
45.0ms	(/ (* (* (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))))))
9.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
5.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series943.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
758.0ms	(/ (* (* (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))))))
60.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
61.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify67.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1293	4502
1	5001	4261

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes654.0ms

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	69	49
1	93	49
2	94	49
3	94	49

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.1s	4576×	body	1280	valid
1.5s	1968×	body	640	valid
268.0ms	587×	body	320	valid
106.0ms	672×	body	80	valid
57.0ms	197×	body	160	valid