Details

sample353.0ms

Algorithm

intervals

Results

118.0ms	94×	body	1280	valid
74.0ms	69×	body	640	valid
12.0ms	26×	body	320	valid
8.0ms	57×	body	80	valid
3.0ms	10×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite55.0ms

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:

21.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
12.0ms	(cos (+ a b))

series186.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(* r (/ (sin b) (cos (+ a b))))
43.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify2.4s

Counts

85 → 85

Iterations

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

prune459.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

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

rewrite239.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
156.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
19.0ms	(* (sin a) (sin b))
42.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series655.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
294.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
56.0ms	(* (sin a) (sin b))
168.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1557
1	468
0	186

prune838.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

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

rewrite126.0ms

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:

11.0ms	(* (cos a) (cos b))
53.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
32.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
26.0ms	(/ (* (cos a) (cos b)) (sin b))

series571.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos a) (cos b))
119.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
282.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
116.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5002
2	1297
1	476
0	216

prune795.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.2b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
27.0ms	(* (sin a) (sin b))
114.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
167.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
58.0ms	(* (sin a) (sin b))
334.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify3.0s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
3	4793
2	1626
1	525
0	198

prune835.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes351.0ms

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	15
1	15
0	12

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.2s	2824×	body	1280	valid
1.6s	1836×	body	640	valid
410.0ms	785×	body	320	valid
407.0ms	2216×	body	80	valid
89.0ms	341×	body	160	valid