Details

sample87.0ms

Algorithm

intervals

Results

27.0ms	268×	body	80	valid
17.0ms	43×	body	640	valid
14.0ms	25×	body	1280	valid
7.0ms	23×	body	320	valid
2.0ms	11×	body	160	valid

simplify57.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize16.0ms

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)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.7b	(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))

series989.0ms

Counts

4 → 12

Calls

4 calls:

394.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
474.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
93.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

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

prune281.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
3.7b	(cos (* 0.5 (+ phi2 phi1)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
3.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
16.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
3.0ms	(cos (* 0.5 (+ phi2 phi1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

544.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
421.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
133.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
28.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify49.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	395	1071
1	1515	866
2	5001	851

prune472.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

3.0ms	(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
12.0ms	(- (* (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)))
48.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (hypot (* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
107.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
69.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
305.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

simplify111.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	868	2672
1	4071	2375
2	5002	2363

prune586.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* lambda2 (sin (* 0.5 phi1)))
5.0ms	(* (cos (* 0.5 phi1)) lambda2)
11.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))
12.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))

series268.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* lambda2 (sin (* 0.5 phi1)))
53.0ms	(* (cos (* 0.5 phi1)) lambda2)
75.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))
93.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))

simplify40.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	281	588
1	1179	482
2	5001	482

prune431.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes399.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	28
1	33	28

end0.0ms

sample2.5s

Algorithm

intervals

Results

836.0ms	8233×	body	80	valid
525.0ms	1285×	body	640	valid
453.0ms	806×	body	1280	valid
235.0ms	740×	body	320	valid
89.0ms	424×	body	160	valid