Details

sample185.0ms

Algorithm

intervals

Results

66.0ms	264×	body	80	valid
37.0ms	39×	body	640	valid
30.0ms	25×	body	1280	valid
19.0ms	26×	body	320	valid
6.0ms	15×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
6	5440
5	1878
4	761
3	231
2	72
1	34
0	17

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
4.2b	(cos (/ (+ phi2 phi1) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
19.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms	(cos (/ (+ phi2 phi1) 2))

series778.0ms

Counts

3 → 9

Calls

3 calls:

649.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
106.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
23.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.3s

Counts

65 → 65

Iterations

Iter	Nodes
3	3266
2	911
1	306
0	128

prune898.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize41.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
4.2b	(cos (* 1/2 (+ phi1 phi2)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 58

Calls

3 calls:

12.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
49.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
8.0ms	(cos (* 1/2 (+ phi1 phi2)))

series803.0ms

Counts

3 → 9

Calls

3 calls:

636.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
129.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
38.0ms	(cos (* 1/2 (+ phi1 phi2)))

simplify1.5s

Counts

67 → 67

Iterations

Iter	Nodes
3	3393
2	914
1	320
0	141

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))
0.1b	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))) (- phi1 phi2)) R)
0.2b	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
0.2b	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
14×	`-un-lft-identity` `associate-l*`
12×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-cube-cbrt`
8×	`frac-times` `flip3--` `flip--`
7×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `frac-sub` `sub-div`
2×	`sub-neg` `prod-diff` `associate-*l/`
1×	`distribute-lft-out--` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

33.0ms	(* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))
6.0ms	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))) (- phi1 phi2)) R)
41.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
327.0ms	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

series22.0s

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))
21.5s	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))) (- phi1 phi2)) R)
82.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
338.0ms	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

simplify3.2s

Counts

120 → 120

Iterations

Iter	Nodes
2	3703
1	932
0	334

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))
0.2b	(* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))
0.2b	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi2)) (cos (* 1/2 phi1))) (* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))))
48.8b	(fma (- (sin (* 1/2 phi2))) (sin (* 1/2 phi1)) (* (sin (* 1/2 phi2)) (sin (* 1/2 phi1))))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
8×	`frac-times` `flip3--` `flip--` `sin-mult`
6×	`cos-mult`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `sub-div` `unswap-sqr`
2×	`sub-neg` `prod-diff` `associate-*l/`
1×	`fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 98

Calls

4 calls:

31.0ms	(* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))
33.0ms	(* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))
333.0ms	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi2)) (cos (* 1/2 phi1))) (* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))))
0.0ms	(fma (- (sin (* 1/2 phi2))) (sin (* 1/2 phi1)) (* (sin (* 1/2 phi2)) (sin (* 1/2 phi1))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))
74.0ms	(* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))
347.0ms	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi2)) (cos (* 1/2 phi1))) (* (sin (* 1/2 phi2)) (sin (* 1/2 phi1)))))
67.0ms	(fma (- (sin (* 1/2 phi2))) (sin (* 1/2 phi1)) (* (sin (* 1/2 phi2)) (sin (* 1/2 phi1))))

simplify5.8s

Counts

110 → 110

Iterations

Iter	Nodes
3	7455
2	1631
1	456
0	179

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes917.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	39
1	39
0	30

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.1s	8378×	body	80	valid
1.9s	1309×	body	640	valid
1.5s	784×	body	1280	valid
541.0ms	730×	body	320	valid
142.0ms	356×	body	160	valid