Details

sample257.0ms

Algorithm

intervals

Results

85.0ms	91×	body	1280	valid
31.0ms	56×	body	640	valid
10.0ms	25×	body	320	valid
9.0ms	75×	body	80	valid
2.0ms	9×	body	160	valid

simplify99.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ r (cos (+ b a)))
0.2b	(* (sin b) (/ r (cos (+ b a))))
2.3b	(cos (+ b a))

rewrite73.0ms

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` `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 → 73

Calls

3 calls:

9.0ms	(/ r (cos (+ b a)))
31.0ms	(* (sin b) (/ r (cos (+ b a))))
12.0ms	(cos (+ b a))

series314.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ r (cos (+ b a)))
168.0ms	(* (sin b) (/ r (cos (+ b a))))
46.0ms	(cos (+ b a))

simplify888.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1481
1	287
0	124

prune491.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

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

rewrite168.0ms

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` `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 → 110

Calls

4 calls:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(* (sin a) (sin b))
23.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
99.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series921.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
86.0ms	(* (sin a) (sin b))
328.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
381.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2412
1	472
0	184

prune891.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

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

rewrite28.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `cos-mult` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

9.0ms	(* (cos a) (cos b))
0.0ms	(fma (- (sin b)) (sin a) (* (cos a) (cos b)))
8.0ms	(* (sin b) r)
10.0ms	(/ (* (sin b) r) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))

series665.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos a) (cos b))
114.0ms	(fma (- (sin b)) (sin a) (* (cos a) (cos b)))
63.0ms	(* (sin b) r)
415.0ms	(/ (* (sin b) r) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))

simplify1.0s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1463
1	314
0	138

prune609.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos b) (cos a) (* (sin a) (- (sin b))))
0.2b	(/ 1 (fma (cos b) (cos a) (* (sin a) (- (sin b)))))
0.2b	(* (sin a) (- (sin b)))
0.3b	(* (* (sin b) r) (/ 1 (fma (cos b) (cos a) (* (sin a) (- (sin b))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

0.0ms	(fma (cos b) (cos a) (* (sin a) (- (sin b))))
4.0ms	(/ 1 (fma (cos b) (cos a) (* (sin a) (- (sin b)))))
13.0ms	(* (sin a) (- (sin b)))
30.0ms	(* (* (sin b) r) (/ 1 (fma (cos b) (cos a) (* (sin a) (- (sin b))))))

series818.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(fma (cos b) (cos a) (* (sin a) (- (sin b))))
188.0ms	(/ 1 (fma (cos b) (cos a) (* (sin a) (- (sin b)))))
89.0ms	(* (sin a) (- (sin b)))
385.0ms	(* (* (sin b) r) (/ 1 (fma (cos b) (cos a) (* (sin a) (- (sin b))))))

simplify2.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	2691
1	465
0	180

prune691.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes652.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.4s	2928×	body	1280	valid
1.6s	1797×	body	640	valid
884.0ms	2178×	body	80	valid
283.0ms	758×	body	320	valid
125.0ms	339×	body	160	valid