Details

sample355.0ms

Algorithm

intervals

Results

63.0ms	94×	body	1280	valid
28.0ms	62×	body	640	valid
7.0ms	11×	body	160	valid
7.0ms	68×	body	80	valid
6.0ms	21×	body	320	valid

simplify30.0ms

Counts

1 → 1

Iterations

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

prune78.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.2b	(cos (+ a b))

rewrite31.0ms

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:

7.0ms	(* r (sin b))
10.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series321.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(* r (sin b))
198.0ms	(/ (* r (sin b)) (cos (+ a b)))
50.0ms	(cos (+ a b))

simplify715.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	883
1	220
0	98

prune404.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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:

7.0ms	(* r (sin b))
18.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
22.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* r (sin b))
142.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
79.0ms	(* (sin a) (sin b))
295.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1821
1	396
0	158

prune731.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize50.0ms

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

rewrite58.0ms

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:

19.0ms	(* (cos a) (cos b))
0.0ms	(fma (sin b) (- (sin a)) (* (cos a) (cos b)))
14.0ms	(/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b))))
22.0ms	(* r (/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b)))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos a) (cos b))
99.0ms	(fma (sin b) (- (sin a)) (* (cos a) (cos b)))
160.0ms	(/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b))))
310.0ms	(* r (/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b)))))

simplify837.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1469
1	381
0	166

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

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` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
13.0ms	(* r (sin b))
18.0ms	(* (sin b) (sin a))
17.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin b) (sin a)))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
45.0ms	(* r (sin b))
75.0ms	(* (sin b) (sin a))
338.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin b) (sin a)))))

simplify830.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1369
1	296
0	130

prune539.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes362.0ms

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	20
2	20
1	18
0	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.2s	2960×	body	1280	valid
1.4s	1897×	body	640	valid
465.0ms	2060×	body	80	valid
252.0ms	707×	body	320	valid
96.0ms	376×	body	160	valid