Details

sample575.0ms

Algorithm

intervals

Results

380.0ms	94×	body	1280	valid
52.0ms	30×	body	320	valid
36.0ms	60×	body	640	valid
11.0ms	65×	body	80	valid
3.0ms	7×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.9b	(cos (+ a b))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

26.0ms	(/ (sin b) (cos (+ a b)))
23.0ms	(* r (/ (sin b) (cos (+ a b))))
16.0ms	(cos (+ a b))

series194.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (sin b) (cos (+ a b)))
120.0ms	(* r (/ (sin b) (cos (+ a b))))
29.0ms	(cos (+ a b))

simplify3.5s

Counts

82 → 82

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	666	834
3	1809	830
done	5001	824

prune415.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

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:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))
105.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
163.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
69.0ms	(* (sin a) (sin b))
339.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify2.9s

Counts

122 → 122

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1247	1971
3	3712	1826
done	5000	1821

prune648.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:

1.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
27.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
25.0ms	(* (sin a) (sin b))
29.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))

series781.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
204.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
83.0ms	(* (sin a) (sin b))
378.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))

simplify2.5s

Counts

106 → 106

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	153	1831
1	326	1797
2	888	1607
3	2448	1599
done	5000	1572

prune640.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

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

Counts

4 → 74

Calls

4 calls:

20.0ms	(* r (sin b))
1.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
25.0ms	(* (sin a) (sin b))
25.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* r (sin b))
160.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
61.0ms	(* (sin a) (sin b))
324.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.9s

Counts

86 → 86

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	127	1087
1	273	1071
2	775	921
3	2734	915
done	5000	912

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes179.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	16	18
done	16	18

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.0s	2916×	body	1280	valid
1.0s	1826×	body	640	valid
868.0ms	784×	body	320	valid
374.0ms	2134×	body	80	valid
88.0ms	341×	body	160	valid