Details

sample85.0ms

Algorithm

intervals

Results

30.0ms	277×	body	80	valid
18.0ms	49×	body	640	valid
9.0ms	19×	body	1280	valid
6.0ms	21×	body	320	valid
2.0ms	12×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

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)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite19.0ms

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))

series920.0ms

Counts

4 → 12

Calls

4 calls:

364.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
440.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
88.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

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

prune278.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

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))
3.6b	(cos (* 0.5 (+ phi2 phi1)))

rewrite24.0ms

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

series1.1s

Counts

4 → 12

Calls

4 calls:

512.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
395.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
121.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
26.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (38.0ms)

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

prune272.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.1b	(* (cos (* phi2 0.5)) (cos (* 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` `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:

12.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
6.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
7.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
44.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

series514.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
55.0ms	(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
61.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))
295.0ms	(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) (- lambda1 lambda2))

simplify78.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (61.0ms)

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

prune537.0ms

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

rewrite34.0ms

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:

4.0ms	(* lambda2 (sin (* 0.5 phi1)))
5.0ms	(* (cos (* 0.5 phi1)) lambda2)
11.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))
11.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))

series247.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* lambda2 (sin (* 0.5 phi1)))
49.0ms	(* (cos (* 0.5 phi1)) lambda2)
86.0ms	(* (sin (* 0.5 phi2)) (* (sin (* 0.5 phi1)) lambda1))
69.0ms	(* (sin (* 0.5 phi2)) (* lambda2 (sin (* 0.5 phi1))))

simplify37.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (8.0ms)

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

prune419.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes347.0ms

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

sample2.5s

Algorithm

intervals

Results

932.0ms	8397×	body	80	valid
502.0ms	1350×	body	640	valid
385.0ms	784×	body	1280	valid
192.0ms	704×	body	320	valid
80.0ms	371×	body	160	valid