Details

sample278.0ms

Algorithm

intervals

Results

76.0ms	93×	body	1280	valid
30.0ms	57×	body	640	valid
12.0ms	22×	body	320	valid
8.0ms	70×	body	80	valid
4.0ms	14×	body	160	valid

simplify143.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize45.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite124.0ms

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:

52.0ms	(* r (/ (sin b) (cos (+ a b))))
28.0ms	(/ (sin b) (cos (+ a b)))
32.0ms	(cos (+ a b))

series473.0ms

Counts

3 → 9

Calls

3 calls:

257.0ms	(* r (/ (sin b) (cos (+ a b))))
149.0ms	(/ (sin b) (cos (+ a b)))
67.0ms	(cos (+ a b))

simplify5.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	5008
3	3220
2	894
1	282
0	126

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite297.0ms

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:

48.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
153.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
35.0ms	(* (sin a) (sin b))
47.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.1s

Counts

4 → 12

Calls

4 calls:

174.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
569.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
82.0ms	(* (sin a) (sin b))
323.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1544
1	469
0	186

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize126.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
0.2b	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
49.6b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

38.0ms	(* (sin b) (sin a))
34.0ms	(* (sin b) (sin a))
40.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
2.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series793.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (sin b) (sin a))
88.0ms	(* (sin b) (sin a))
529.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
85.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify4.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
3	2558
2	719
1	259
0	125

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

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×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `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 → 90

Calls

4 calls:

39.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
14.0ms	(* (sin b) r)
17.0ms	(* (sin b) (sin a))
80.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series1.1s

Counts

4 → 12

Calls

4 calls:

200.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
77.0ms	(* (sin b) r)
130.0ms	(* (sin b) (sin a))
654.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify7.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4779
2	1184
1	389
0	159

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes858.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.4s	2902×	body	1280	valid
1.1s	1902×	body	640	valid
288.0ms	724×	body	320	valid
254.0ms	2112×	body	80	valid
88.0ms	361×	body	160	valid