Details

sample66.0ms

Algorithm

intervals

Results

17.0ms	255×	body	80	valid
14.0ms	40×	body	640	valid
9.0ms	22×	body	1280	valid
5.0ms	26×	body	320	valid
2.0ms	14×	body	160	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	8
1	78	8
2	261	8
3	834	8
4	2600	8
5	5001	8

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.7b	(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 63

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
10.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))

series926.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
443.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
85.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
29.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	328	677
1	1130	579
2	5001	569

prune272.0ms

Filtered

75 candidates to 62 candidates (82.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1))))
4.7b	(cos (* 0.5 (+ phi2 phi1)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `hypot-udef` `flip3--` `distribute-lft-in` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2))
3.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2)) R)
15.0ms	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1))))
3.0ms	(cos (* 0.5 (+ phi2 phi1)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

362.0ms	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2))
448.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2)) R)
85.0ms	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1))))
29.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify35.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	338	697
1	1127	599
2	5001	589

prune247.0ms

Filtered

77 candidates to 60 candidates (77.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
0.1b	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.1b	(* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
0.2b	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`flip3--` `associate-r` `flip--` `sin-mult`
8×	`frac-times` `cos-mult`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `frac-sub` `log1p-expm1-u` `sub-div`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/`
1×	`fma-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

3.0ms	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
12.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
55.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
7.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series17.2s

Counts

4 → 12

Calls

4 calls:

16.8s	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
104.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
241.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
67.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify123.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	964	2565
1	4672	2282
2	5001	2275

prune613.0ms

Filtered

113 candidates to 92 candidates (81.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (+ (* (- lambda1 lambda2) (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (* (- lambda1 lambda2) (* (sin (* 0.5 phi1)) (+ (- (sin (* phi2 0.5))) (sin (* phi2 0.5)))))) (- phi1 phi2)) R)
0.1b	(fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
0.1b	(* (- lambda1 lambda2) (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
0.2b	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
2×	`associate-*l/`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 77

Calls

4 calls:

3.0ms	(* (hypot (+ (* (- lambda1 lambda2) (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (* (- lambda1 lambda2) (* (sin (* 0.5 phi1)) (+ (- (sin (* phi2 0.5))) (sin (* phi2 0.5)))))) (- phi1 phi2)) R)
0.0ms	(fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
10.0ms	(* (- lambda1 lambda2) (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
7.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

series18.8s

Counts

4 → 12

Calls

4 calls:

18.3s	(* (hypot (+ (* (- lambda1 lambda2) (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (* (- lambda1 lambda2) (* (sin (* 0.5 phi1)) (+ (- (sin (* phi2 0.5))) (sin (* phi2 0.5)))))) (- phi1 phi2)) R)
110.0ms	(fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))
243.0ms	(* (- lambda1 lambda2) (fma (cos (* phi2 0.5)) (cos (* phi1 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
68.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))

simplify106.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	810	2354
1	3733	2034
2	5002	2033

prune522.0ms

Filtered

89 candidates to 71 candidates (79.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes367.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	42
1	45	42
2	45	42

end0.0ms

sample1.9s

Algorithm

intervals

Results

584.0ms	8358×	body	80	valid
379.0ms	1224×	body	640	valid
350.0ms	805×	body	1280	valid
171.0ms	755×	body	320	valid
57.0ms	392×	body	160	valid