Details

sample416.0ms

Algorithm

intervals

Results

146.0ms	105×	body	1280	valid
66.0ms	16×	body	320	valid
55.0ms	58×	body	640	valid
21.0ms	71×	body	80	valid
3.0ms	6×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	21
5	21
4	20
3	18
2	16
1	12
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize39.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

17.0ms	(* r (/ (sin b) (cos (+ a b))))
14.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(cos (+ a b))

series234.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(* r (/ (sin b) (cos (+ a b))))
66.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify953.0ms

Counts

85 → 85

Iterations

Iter	Nodes
3	2409
2	802
1	276
0	126

prune892.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 114

Calls

4 calls:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
111.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
33.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))

series640.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
306.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
155.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
75.0ms	(* (sin a) (sin b))

simplify3.7s

Counts

126 → 126

Iterations

Iter	Nodes
3	4837
2	1494
1	464
0	186

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
0.2b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

9.0ms	(* (cos a) (cos b))
17.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
58.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
23.0ms	(* (sin b) (sin a))

series565.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos a) (cos b))
102.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
347.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
59.0ms	(* (sin b) (sin a))

simplify21.2s

Counts

103 → 103

Iterations

Iter	Nodes
3	5347
2	1287
1	422
0	174

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
0.2b	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
0.2b	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
0.2b	(* (sin b) (sin a))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 114

Calls

4 calls:

37.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
40.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
82.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
22.0ms	(* (sin b) (sin a))

series771.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
293.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
321.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
50.0ms	(* (sin b) (sin a))

simplify3.7s

Counts

126 → 126

Iterations

Iter	Nodes
3	3586
2	1303
1	463
0	191

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes266.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.6s	2928×	body	1280	valid
1.7s	1851×	body	640	valid
501.0ms	2209×	body	80	valid
426.0ms	715×	body	320	valid
150.0ms	298×	body	160	valid