Details

sample802.0ms

Algorithm

intervals

Results

155.0ms	93×	body	1280	valid
54.0ms	61×	body	640	valid
15.0ms	26×	body	320	valid
12.0ms	68×	body	80	valid
3.0ms	8×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite87.0ms

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:

45.0ms	(* r (/ (sin b) (cos (+ a b))))
20.0ms	(/ (sin b) (cos (+ a b)))
19.0ms	(cos (+ a b))

series252.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(* r (/ (sin b) (cos (+ a b))))
67.0ms	(/ (sin b) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	877
1	280
0	126

prune973.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

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

rewrite228.0ms

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:

33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
131.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(* (sin a) (sin b))
34.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series694.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
329.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
56.0ms	(* (sin a) (sin b))
177.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	2020
3	2020
2	1557
1	468
0	186

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

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)))))
51.7b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite78.0ms

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:

24.0ms	(* (sin b) (sin a))
25.0ms	(* (sin b) (sin a))
26.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
1.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series533.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (sin b) (sin a))
83.0ms	(* (sin b) (sin a))
281.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
80.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	2001
3	2001
2	722
1	259
0	125

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
12.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
21.0ms	(* (sin a) (sin b))
9.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
338.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
81.0ms	(* (sin a) (sin b))
177.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.2s

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
3	2000
2	1268
1	372
0	160

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes314.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
2	23
1	21
0	15

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.3s	2814×	body	1280	valid
1.7s	1909×	body	640	valid
486.0ms	790×	body	320	valid
428.0ms	2107×	body	80	valid
197.0ms	383×	body	160	valid