Details

sample77.0ms

Algorithm

intervals

Results

40.0ms	87×	body	1280	valid
12.0ms	53×	body	640	valid
5.0ms	75×	body	80	valid
4.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

14.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series173.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
106.0ms	(/ (* r (sin b)) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify1.7s

Counts

62 → 62

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	96	575
1	207	562
2	572	484
3	2172	482
done	5000	480

prune161.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
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×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))
12.0ms	(* (sin a) (sin b))
30.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(* r (sin b))
47.0ms	(* (sin a) (sin b))
231.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	152	1364
1	370	1324
2	1166	1174
3	4192	1081
done	5002	1078

prune316.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
71.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
228.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
119.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7s

Counts

122 → 122

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1248	1955
3	3717	1826
done	5000	1821

prune398.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

2.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))
14.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
8.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
49.0ms	(* (sin a) (sin b))
229.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
123.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.5s

Counts

106 → 106

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	153	1831
1	326	1797
2	877	1603
3	2438	1599
done	5001	1572

prune349.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes150.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	18	16
2	20	16
done	20	16

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2872×	body	1280	valid
414.0ms	1763×	body	640	valid
132.0ms	796×	body	320	valid
121.0ms	2210×	body	80	valid
50.0ms	361×	body	160	valid