Details

sample147.0ms

Algorithm

intervals

Results

34.0ms	253×	body	80	valid
34.0ms	56×	body	640	valid
21.0ms	24×	body	1280	valid
14.0ms	33×	body	320	valid
6.0ms	21×	body	160	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1728
4	730
3	231
2	72
1	34
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
4.4b	(cos (/ (+ phi2 phi1) 2.0))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
11×	`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` `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 → 85

Calls

4 calls:

0.0ms	(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
14.0ms	(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
57.0ms	(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
22.0ms	(cos (/ (+ phi2 phi1) 2.0))

series2.7s

Counts

4 → 12

Calls

4 calls:

1.1s	(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
872.0ms	(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
717.0ms	(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
54.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify4.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5010
3	4195
2	1125
1	432
0	190

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize48.0ms

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))
4.4b	(cos (* 0.5 (+ phi2 phi1)))

rewrite139.0ms

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:

1.0ms	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
15.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
99.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
18.0ms	(cos (* 0.5 (+ phi2 phi1)))

series2.2s

Counts

4 → 12

Calls

4 calls:

1.0s	(hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2))
807.0ms	(* (hypot (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2)) (- phi1 phi2)) R)
325.0ms	(* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))
77.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify4.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	4244
2	1120
1	443
0	202

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite591.0ms

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:

110.0ms	(- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1))))
14.0ms	(* (hypot (* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
342.0ms	(* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) (- lambda1 lambda2))
115.0ms	(* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))

series3.3s

Counts

4 → 12

Calls

4 calls:

200.0ms	(- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1))))
2.4s	(* (hypot (* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
592.0ms	(* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) (- lambda1 lambda2))
123.0ms	(* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))

simplify4.7s

Counts

129 → 129

Iterations

Iter	Nodes
done	5004
2	3451
1	897
0	331

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (expm1 (log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))))) (- lambda1 lambda2))
0.2b	(* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))
0.2b	(expm1 (log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1))))))
0.4b	(log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

49.0ms	(* (expm1 (log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))))) (- lambda1 lambda2))
124.0ms	(* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))
1.0ms	(expm1 (log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1))))))
2.0ms	(log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

710.0ms	(* (expm1 (log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))))) (- lambda1 lambda2))
114.0ms	(* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))
264.0ms	(expm1 (log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1))))))
290.0ms	(log1p (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))))

simplify4.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
3	3458
2	1032
1	444
0	205

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.5s	8281×	body	80	valid
1.6s	1342×	body	640	valid
1.0s	805×	body	1280	valid
451.0ms	697×	body	320	valid
125.0ms	336×	body	160	valid