Details

sample444.0ms

Algorithm

intervals

Results

155.0ms	87×	body	1280	valid
148.0ms	72×	body	640	valid
11.0ms	71×	body	80	valid
7.0ms	15×	body	320	valid
4.0ms	11×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize49.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite66.0ms

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:

18.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
20.0ms	(cos (+ a b))

series234.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* r (sin b))
125.0ms	(/ (* r (sin b)) (cos (+ a b)))
43.0ms	(cos (+ a b))

simplify719.0ms

Counts

65 → 65

Iterations

Iter	Nodes
3	2189
2	582
1	212
0	101

prune656.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

31.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(* r (sin b))
22.0ms	(* (sin a) (sin b))
38.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* r (sin b))
55.0ms	(* (sin a) (sin b))
267.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
3	4407
2	1152
1	382
0	157

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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` `insert-posit16` `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 → 78

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
17.0ms	(* r (sin b))
22.0ms	(* (sin a) (sin b))
23.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
50.0ms	(* r (sin b))
77.0ms	(* (sin a) (sin b))
323.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
3	3888
2	888
1	294
0	133

prune1.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `cos-mult` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

27.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
24.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b)))
27.0ms	(* (sin b) (sin a))
39.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b))

series675.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
283.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b)))
62.0ms	(* (sin b) (sin a))
213.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b))

simplify950.0ms

Counts

161 → 161

Iterations

Iter	Nodes
2	2135
1	660
0	261

prune1.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes354.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
3	20
2	20
1	18
0	12

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.2s	2929×	body	1280	valid
1.9s	1864×	body	640	valid
474.0ms	2146×	body	80	valid
406.0ms	737×	body	320	valid
119.0ms	325×	body	160	valid