Details

sample174.0ms

Algorithm

intervals

Results

50.0ms	93×	body	1280	valid
19.0ms	57×	body	640	valid
8.0ms	22×	body	320	valid
5.0ms	70×	body	80	valid
2.0ms	14×	body	160	valid

simplify54.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite57.0ms

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	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
12.0ms	(cos (+ a b))

series203.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(* r (/ (sin b) (cos (+ a b))))
43.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify2.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	3116
2	877
1	280
0	126

prune500.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite241.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
129.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
33.0ms	(* (sin a) (sin b))
57.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series689.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
358.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
62.0ms	(* (sin a) (sin b))
160.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1557
1	468
0	186

prune850.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
0.2b	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
49.6b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

26.0ms	(* (sin b) (sin a))
27.0ms	(* (sin b) (sin a))
30.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
1.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin b) (sin a))
86.0ms	(* (sin b) (sin a))
230.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
88.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify2.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	5012
3	2538
2	722
1	259
0	125

prune860.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
23.5b	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
29×	`sin-mult`
20×	`add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down`
16×	`add-sqr-sqrt`
14×	`cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
11×	`frac-times` `associate-*l/`
9×	`times-frac` `prod-exp` `associate-/r/` `cbrt-unprod`
7×	`associate-*r/` `cos-mult` `frac-sub`
4×	`expm1-log1p-u` `associate-r` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `pow1/3` `swap-sqr` `div-exp` `pow3` `rem-cbrt-cube` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 121

Calls

4 calls:

25.0ms	(* (sin a) (sin b))
203.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
68.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
240.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sin a) (sin b))
205.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
73.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
64.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify2.9s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
3	4614
2	1541
1	469
0	204

prune797.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes286.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.0s	2902×	body	1280	valid
1.6s	1902×	body	640	valid
341.0ms	724×	body	320	valid
310.0ms	2112×	body	80	valid
127.0ms	361×	body	160	valid