Details

sample336.0ms

Algorithm

intervals

Results

170.0ms	111×	body	1280	valid
42.0ms	48×	body	640	valid
13.0ms	22×	body	320	valid
12.0ms	67×	body	80	valid
3.0ms	8×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite46.0ms

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:

16.0ms	(* r (sin b))
18.0ms	(/ (* r (sin b)) (cos (+ a b)))
9.0ms	(cos (+ a b))

series239.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* r (sin b))
154.0ms	(/ (* r (sin b)) (cos (+ a b)))
37.0ms	(cos (+ a b))

simplify781.0ms

Counts

65 → 65

Iterations

Iter	Nodes
3	2189
2	582
1	212
0	101

prune620.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

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

rewrite114.0ms

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:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
16.0ms	(* (sin a) (sin b))
62.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* r (sin b))
82.0ms	(* (sin a) (sin b))
315.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	4407
2	1152
1	382
0	157

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite209.0ms

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:

24.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
105.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms	(* (sin a) (sin b))
54.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
378.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
58.0ms	(* (sin a) (sin b))
149.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.6s

Counts

126 → 126

Iterations

Iter	Nodes
3	4651
2	1491
1	464
0	186

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.3b	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

60.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
90.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
11.0ms	(* (sin a) (sin b))
105.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
336.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
63.0ms	(* (sin a) (sin b))
155.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify8.5s

Counts

142 → 142

Iterations

Iter	Nodes
3	4184
2	1551
1	504
0	203

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes298.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.4s	2950×	body	1280	valid
2.1s	1796×	body	640	valid
473.0ms	744×	body	320	valid
428.0ms	2168×	body	80	valid
121.0ms	343×	body	160	valid