Details

sample331.0ms

Algorithm

intervals

Results

128.0ms	89×	body	1280	valid
46.0ms	55×	body	640	valid
17.0ms	31×	body	320	valid
11.0ms	67×	body	80	valid
5.0ms	14×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite57.0ms

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:

26.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
18.0ms	(cos (+ a b))

series217.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(* r (/ (sin b) (cos (+ a b))))
46.0ms	(/ (sin b) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify2.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	3116
2	877
1	280
0	126

prune457.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite257.0ms

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:

35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
22.0ms	(* (sin a) (sin b))
140.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
57.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
77.0ms	(* (sin a) (sin b))
335.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
171.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1551
1	469
0	186

prune941.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
0.3b	(/ (* (cos a) (cos b)) (sin b))
0.3b	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
7×	`fma-neg`
6×	`pow1` `div-inv` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
22.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
12.0ms	(/ (* (cos a) (cos b)) (sin b))
26.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos a) (cos b))
123.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
118.0ms	(/ (* (cos a) (cos b)) (sin b))
248.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1310
1	477
0	216

prune734.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (cos b) (sin b))
0.2b	(fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a)))
0.3b	(/ r (fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`fma-udef`

Counts

3 → 71

Calls

3 calls:

15.0ms	(/ (cos b) (sin b))
0.0ms	(fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a)))
4.0ms	(/ r (fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a))))

series390.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ (cos b) (sin b))
110.0ms	(fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a)))
254.0ms	(/ r (fma (/ (cos a) 1) (/ (cos b) (sin b)) (- (sin a))))

simplify1.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	2263
2	754
1	268
0	141

prune520.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes287.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	35
3	35
2	25
1	21
0	14

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.9s	2893×	body	1280	valid
2.1s	1826×	body	640	valid
890.0ms	765×	body	320	valid
384.0ms	2174×	body	80	valid
168.0ms	343×	body	160	valid