Details

sample63.0ms

Algorithm

intervals

Results

16.0ms	258×	body	80	valid
12.0ms	43×	body	640	valid
10.0ms	25×	body	1280	valid
4.0ms	20×	body	320	valid
1.0ms	10×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize17.0ms

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)))
3.5b	(cos (/ (+ phi1 phi2) 2.0))

rewrite43.0ms

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))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

531.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
407.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
79.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (29.0ms)

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

prune258.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize13.0ms

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))
3.5b	(cos (* 0.5 (+ phi2 phi1)))

rewrite57.0ms

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))
7.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
37.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
10.0ms	(cos (* 0.5 (+ phi2 phi1)))

series988.0ms

Counts

4 → 12

Calls

4 calls:

476.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
383.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
106.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
23.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (39.0ms)

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

prune260.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
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))

rewrite285.0ms

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` `cos-mult` `flip--` `sin-mult`
8×	`frac-times`
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 → 118

Calls

4 calls:

26.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
52.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
29.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
173.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

series479.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
95.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
63.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
275.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

simplify83.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	622	2236
1	2632	2018
2	5002	2016

prune550.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 0.5 phi1)) lambda2)
0.1b	(fma (cos (* 0.5 phi2)) (* (cos (* 0.5 phi1)) lambda2) (* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1)))
0.2b	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))
0.3b	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

17.0ms	(* (cos (* 0.5 phi1)) lambda2)
0.0ms	(fma (cos (* 0.5 phi2)) (* (cos (* 0.5 phi1)) lambda2) (* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1)))
45.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))
47.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))

series409.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos (* 0.5 phi1)) lambda2)
222.0ms	(fma (cos (* 0.5 phi2)) (* (cos (* 0.5 phi1)) lambda2) (* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1)))
61.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))
84.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))

simplify99.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	277	667
1	1047	550
2	4064	550
3	5002	550

prune392.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes410.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	28
1	33	28

end0.0ms

sample1.9s

Algorithm

intervals

Results

537.0ms	8339×	body	80	valid
374.0ms	1318×	body	640	valid
330.0ms	804×	body	1280	valid
150.0ms	727×	body	320	valid
52.0ms	367×	body	160	valid