Details

sample459.0ms

Algorithm

intervals

Results

244.0ms	91×	body	1280	valid
75.0ms	62×	body	640	valid
17.0ms	75×	body	80	valid
12.0ms	21×	body	320	valid
3.0ms	7×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	21
5	21
4	20
3	18
2	16
1	12
0	8

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize61.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
4.2b	(cos (+ a b))

rewrite71.0ms

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` `insert-posit16` `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 → 76

Calls

3 calls:

20.0ms	(/ (sin b) (cos (+ a b)))
29.0ms	(* r (/ (sin b) (cos (+ a b))))
18.0ms	(cos (+ a b))

series239.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (sin b) (cos (+ a b)))
147.0ms	(* r (/ (sin b) (cos (+ a b))))
34.0ms	(cos (+ a b))

simplify745.0ms

Counts

85 → 85

Iterations

Iter	Nodes
3	2061
2	766
1	276
0	126

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

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` `insert-posit16` `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 → 114

Calls

4 calls:

38.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
48.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
115.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms	(* (sin a) (sin b))

series762.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
191.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
351.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
87.0ms	(* (sin a) (sin b))

simplify1.9s

Counts

126 → 126

Iterations

Iter	Nodes
3	4062
2	1441
1	462
0	186

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
25.6b	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
18×	`sin-mult`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-div` `associate-r` `associate-l`
6×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `associate-*r/` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`cbrt-prod` `pow2` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube`

Counts

4 → 104

Calls

4 calls:

23.0ms	(* (sin a) (sin b))
13.0ms	(* (sin a) (sin b))
66.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
163.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin a) (sin b))
85.0ms	(* (sin a) (sin b))
95.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
67.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify1.1s

Counts

116 → 116

Iterations

Iter	Nodes
3	2969
2	791
1	246
0	115

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
10.6b	(cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
25.6b	(cbrt (* (cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (* (sin a) (sin b))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

648×	`sin-mult`
452×	`frac-times`
316×	`cbrt-div`
290×	`associate-*l/`
192×	`associate-*r/`
82×	`pow1`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `pow2` `pow1/3` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`pow3` `rem-cbrt-cube`

Counts

4 → 295

Calls

4 calls:

82.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
58.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
1.0s	(cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
727.0ms	(cbrt (* (cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (* (sin a) (sin b))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
88.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
76.0ms	(cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
81.0ms	(cbrt (* (cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (* (sin a) (sin b))))

simplify1.2s

Counts

307 → 307

Iterations

Iter	Nodes
2	2298
1	1034
0	541

prune5.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes238.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	23
1	23
0	18

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.6s	2937×	body	1280	valid
1.6s	1855×	body	640	valid
576.0ms	792×	body	320	valid
439.0ms	2099×	body	80	valid
151.0ms	318×	body	160	valid