Details

sample204.0ms

Algorithm

intervals

Results

71.0ms	61×	body	640	valid
47.0ms	96×	body	1280	valid
6.0ms	67×	body	80	valid
5.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
4	20
3	19
2	16
1	12
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ b a)))
3.9b	(cos (+ b a))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

11.0ms	(* r (sin b))
10.0ms	(/ (* r (sin b)) (cos (+ b a)))
11.0ms	(cos (+ b a))

series190.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* r (sin b))
118.0ms	(/ (* r (sin b)) (cos (+ b a)))
26.0ms	(cos (+ b a))

simplify755.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	963
1	219
0	99

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

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` `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 → 86

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
15.0ms	(* r (sin b))
19.0ms	(* (sin b) (sin a))
46.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
63.0ms	(* r (sin b))
66.0ms	(* (sin b) (sin a))
335.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify974.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1926
1	398
0	158

prune815.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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` `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/` `cos-mult` `fma-udef`

Counts

4 → 94

Calls

4 calls:

16.0ms	(* (cos a) (cos b))
1.0ms	(fma (- (sin b)) (sin a) (* (cos a) (cos b)))
21.0ms	(* r (/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))))
12.0ms	(/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos a) (cos b))
124.0ms	(fma (- (sin b)) (sin a) (* (cos a) (cos b)))
302.0ms	(* r (/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))))
206.0ms	(/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))

simplify917.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1486
1	381
0	165

prune856.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `associate-/r` `distribute-rgt-neg-in` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `neg-mul-1` `frac-2neg` `associate-*r/` `distribute-rgt-neg-out` `fma-udef`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (* (sin a) (- (sin b))))
14.0ms	(* (sin a) (- (sin b)))
13.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (sin a) (- (sin b))))))
7.0ms	(/ (sin b) (fma (cos a) (cos b) (* (sin a) (- (sin b)))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(fma (cos a) (cos b) (* (sin a) (- (sin b))))
67.0ms	(* (sin a) (- (sin b)))
384.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (sin a) (- (sin b))))))
188.0ms	(/ (sin b) (fma (cos a) (cos b) (* (sin a) (- (sin b)))))

simplify987.0ms

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1807
1	410
0	170

prune793.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes400.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	21
3	21
2	20
1	16
0	12

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	2845×	body	1280	valid
1.6s	1942×	body	640	valid
779.0ms	2101×	body	80	valid
293.0ms	759×	body	320	valid
86.0ms	354×	body	160	valid