Details

sample192.0ms

Algorithm

intervals

Results

88.0ms	285×	body	80	valid
38.0ms	41×	body	640	valid
23.0ms	19×	body	1280	valid
14.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2013
6	2013
5	1878
4	761
3	231
2	72
1	34
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
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))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`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×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
9.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
29.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
16.0ms	(cos (/ (+ phi2 phi1) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

501.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
570.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
94.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
25.0ms	(cos (/ (+ phi2 phi1) 2))

simplify831.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2005
3	2005
2	1076
1	360
0	144

prune546.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
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)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`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` `hypot-udef` `distribute-lft-in` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 69

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
10.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
53.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
14.0ms	(cos (* 1/2 (+ phi1 phi2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

559.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
604.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
111.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
33.0ms	(cos (* 1/2 (+ phi1 phi2)))

simplify971.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	2002
3	2002
2	1076
1	377
0	158

prune579.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
0.1b	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
0.2b	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
0.3b	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

rewrite438.0ms

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

Counts

4 → 106

Calls

4 calls:

33.0ms	(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
61.0ms	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
288.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
55.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cos (* phi1 1/2)) (cos (* phi2 1/2)))
103.0ms	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
275.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
62.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

simplify959.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	2003
2	2003
1	543
0	216

prune981.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (log1p (expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))))
0.3b	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
0.3b	(log1p (expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))))
0.5b	(expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `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 → 71

Calls

4 calls:

30.0ms	(* (- lambda1 lambda2) (log1p (expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))))
40.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
0.0ms	(log1p (expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))))
1.0ms	(expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))

series785.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(* (- lambda1 lambda2) (log1p (expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))))
83.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
192.0ms	(log1p (expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))))
148.0ms	(expm1 (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))

simplify1.1s

Counts

83 → 83

Iterations

Iter	Nodes
done	2004
3	2004
2	967
1	346
0	153

prune750.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes605.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.1s	8360×	body	80	valid
1.8s	1312×	body	640	valid
1.1s	748×	body	1280	valid
505.0ms	720×	body	320	valid
151.0ms	365×	body	160	valid