Details

sample704.0ms

Algorithm

intervals

Results

108.0ms	88×	body	1280	valid
35.0ms	68×	body	640	valid
11.0ms	26×	body	320	valid
7.0ms	68×	body	80	valid
2.0ms	6×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

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

prune59.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize45.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.6b	(cos (+ a b))

rewrite60.0ms

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:

21.0ms	(* r (/ (sin b) (cos (+ a b))))
15.0ms	(/ (sin b) (cos (+ a b)))
20.0ms	(cos (+ a b))

series267.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(* r (/ (sin b) (cos (+ a b))))
50.0ms	(/ (sin b) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify1.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1076
1	284
0	123

prune547.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

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:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
96.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
24.0ms	(* (sin a) (sin b))

series771.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
415.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
144.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
81.0ms	(* (sin a) (sin b))

simplify1.6s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1967
1	467
0	182

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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:

16.0ms	(* (sin b) r)
27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

series601.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin b) r)
143.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
299.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
92.0ms	(* (sin a) (sin b))

simplify2.5s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1966
1	389
0	152

prune881.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin b) r) (+ (- (* (cos b) (cos a)) (* (sin b) (sin a))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
53.5b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r*` `times-frac` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `sin-mult` `distribute-lft-out` `unswap-sqr`
1×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

57.0ms	(/ (* (sin b) r) (+ (- (* (cos b) (cos a)) (* (sin b) (sin a))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
17.0ms	(* (sin b) (sin a))
9.0ms	(* (sin b) (sin a))
0.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series687.0ms

Counts

4 → 12

Calls

4 calls:

496.0ms	(/ (* (sin b) r) (+ (- (* (cos b) (cos a)) (* (sin b) (sin a))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
67.0ms	(* (sin b) (sin a))
55.0ms	(* (sin b) (sin a))
69.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify2.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1595
1	307
0	127

prune670.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes452.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.8s	2888×	body	1280	valid
1.4s	1804×	body	640	valid
317.0ms	782×	body	320	valid
247.0ms	2179×	body	80	valid
122.0ms	347×	body	160	valid