Details

sample69.0ms

Algorithm

intervals

Results

16.0ms	264×	body	80	valid
12.0ms	24×	body	1280	valid
11.0ms	39×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	16×	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: 3.9b

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)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite46.0ms

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)
26.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series980.0ms

Counts

4 → 12

Calls

4 calls:

386.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
475.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
91.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (29.0ms)

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

prune265.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

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))
2.8b	(cos (* 0.5 (+ phi2 phi1)))

rewrite58.0ms

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))
8.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
38.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
10.0ms	(cos (* 0.5 (+ phi2 phi1)))

series1.2s

Counts

4 → 12

Calls

4 calls:

557.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
449.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
125.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
27.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify46.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

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

prune269.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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

rewrite289.0ms

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:

25.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
54.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
177.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
27.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
108.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
316.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))
68.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify80.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	622	2233
1	2632	2015
2	5001	2014

prune548.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (cbrt (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3))) (- lambda1 lambda2))
0.2b	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
0.3b	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
28.3b	(cbrt (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
8×	`cbrt-prod` `associate-r`
7×	`flip3--` `flip--`
6×	`frac-times` `associate-l` `sin-mult`
5×	`cube-div`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `associate-*l/` `prod-exp` `cos-mult` `frac-sub` `cbrt-unprod`
2×	`cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `associate-r/` `pow-exp` `-commutative` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 121

Calls

4 calls:

186.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (cbrt (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3))) (- lambda1 lambda2))
29.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
18.0ms	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
13.0ms	(cbrt (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3))

series549.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (cbrt (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3))) (- lambda1 lambda2))
63.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
98.0ms	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
69.0ms	(cbrt (pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3))

simplify84.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	635	2194
1	2739	1898
2	5001	1891

prune536.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes324.0ms

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	29	18
1	29	18

end0.0ms

sample2.2s

Algorithm

intervals

Results

760.0ms	8514×	body	80	valid
373.0ms	1285×	body	640	valid
325.0ms	806×	body	1280	valid
156.0ms	726×	body	320	valid
51.0ms	361×	body	160	valid