Details

sample270.0ms

Algorithm

intervals

Results

112.0ms	95×	body	1280	valid
27.0ms	48×	body	640	valid
14.0ms	68×	body	80	valid
10.0ms	27×	body	320	valid
5.0ms	18×	body	160	valid

simplify288.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize234.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite276.0ms

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*` `insert-posit16` `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 → 56

Calls

3 calls:

50.0ms	(* r (sin b))
79.0ms	(/ (* r (sin b)) (cos (+ a b)))
139.0ms	(cos (+ a b))

series765.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(* r (sin b))
578.0ms	(/ (* r (sin b)) (cos (+ a b)))
84.0ms	(cos (+ a b))

simplify5.0s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	2510
2	606
1	223
0	101

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize184.0ms

Local error

Found 4 expressions with local error:

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

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 93

Calls

4 calls:

43.0ms	(* (cos a) (cos b))
29.0ms	(* r (sin b))
126.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
36.0ms	(* (sin a) (sin b))

series942.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (cos a) (cos b))
84.0ms	(* r (sin b))
663.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
99.0ms	(* (sin a) (sin b))

simplify9.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	4810
2	1197
1	410
0	170

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize190.0ms

Local error

Found 4 expressions with local error:

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

rewrite485.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 117

Calls

4 calls:

35.0ms	(* (cos a) (cos b))
296.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
41.0ms	(* (sin a) (sin b))
103.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.1s

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (cos a) (cos b))
627.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
108.0ms	(* (sin a) (sin b))
312.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.1s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	1577
1	484
0	200

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize152.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l` `associate-/l*`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `neg-mul-1` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `distribute-frac-neg` `fma-udef` `div-inv` `sin-mult`

Counts

4 → 98

Calls

4 calls:

1.0ms	(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
39.0ms	(* r (sin b))
45.0ms	(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))
67.0ms	(* (sin a) (sin b))

series1.1s

Counts

4 → 12

Calls

4 calls:

203.0ms	(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
75.0ms	(* r (sin b))
709.0ms	(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))
100.0ms	(* (sin a) (sin b))

simplify8.6s

Counts

110 → 110

Iterations

Iter	Nodes
done	5084
3	3792
2	965
1	376
0	176

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes997.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	25
2	25
1	23
0	15

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.3s	2918×	body	1280	valid
1.1s	1912×	body	640	valid
884.0ms	2095×	body	80	valid
382.0ms	705×	body	320	valid
134.0ms	370×	body	160	valid