Details

sample275.0ms

Algorithm

intervals

Results

74.0ms	89×	body	1280	valid
64.0ms	61×	body	640	valid
11.0ms	26×	body	320	valid
8.0ms	71×	body	80	valid
2.0ms	9×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

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

prune60.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize38.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite52.0ms

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:

10.0ms	(* r (sin b))
16.0ms	(/ (* r (sin b)) (cos (+ a b)))
22.0ms	(cos (+ a b))

series418.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* r (sin b))
307.0ms	(/ (* r (sin b)) (cos (+ a b)))
32.0ms	(cos (+ a b))

simplify2.5s

Counts

62 → 62

Iterations

Iter	Nodes
done	5051
3	2951
2	667
1	216
0	98

prune481.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:

14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
35.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

series631.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
58.0ms	(* r (sin b))
374.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
53.0ms	(* (sin a) (sin b))

simplify2.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1212
1	388
0	153

prune828.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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 a) (cos b) (- (* (sin a) (sin b))))
13.0ms	(* r (sin b))
17.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
12.0ms	(* (sin a) (sin b))

series604.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
70.0ms	(* r (sin b))
325.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
71.0ms	(* (sin a) (sin b))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	933
1	301
0	129

prune697.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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 a) (cos b) (- (* (sin a) (sin b))))
8.0ms	(* (sin b) r)
10.0ms	(/ (* (sin b) r) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
10.0ms	(* (sin a) (sin b))

series584.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
46.0ms	(* (sin b) r)
342.0ms	(/ (* (sin b) r) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
82.0ms	(* (sin a) (sin b))

simplify3.1s

Counts

86 → 86

Iterations

Iter	Nodes
done	5007
3	3799
2	961
1	304
0	129

prune543.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes372.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.8s	2890×	body	1280	valid
1.4s	1831×	body	640	valid
842.0ms	806×	body	320	valid
221.0ms	2128×	body	80	valid
119.0ms	346×	body	160	valid