Details

sample329.0ms

Algorithm

intervals

Results

157.0ms	95×	body	1280	valid
34.0ms	48×	body	640	valid
15.0ms	68×	body	80	valid
14.0ms	27×	body	320	valid
6.0ms	18×	body	160	valid

simplify172.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize120.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite140.0ms

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:

56.0ms	(* r (/ (sin b) (cos (+ a b))))
29.0ms	(/ (sin b) (cos (+ a b)))
49.0ms	(cos (+ a b))

series397.0ms

Counts

3 → 9

Calls

3 calls:

241.0ms	(* r (/ (sin b) (cos (+ a b))))
114.0ms	(/ (sin b) (cos (+ a b)))
42.0ms	(cos (+ a b))

simplify6.7s

Counts

85 → 85

Iterations

Iter	Nodes
done	5008
3	3220
2	894
1	282
0	126

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize137.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))))

rewrite411.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

28.0ms	(* (cos a) (cos b))
235.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))
91.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.2s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (cos a) (cos b))
647.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
106.0ms	(* (sin a) (sin b))
351.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.0s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	1577
1	484
0	200

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize152.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 93

Calls

4 calls:

53.0ms	(* (cos a) (cos b))
24.0ms	(* r (sin b))
145.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
63.0ms	(* (sin a) (sin b))

series912.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (cos a) (cos b))
81.0ms	(* r (sin b))
635.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
107.0ms	(* (sin a) (sin b))

simplify8.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	4810
2	1197
1	410
0	170

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize169.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l` `associate-/l*`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `neg-mul-1` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `distribute-frac-neg` `fma-udef` `div-inv` `sin-mult`

Counts

4 → 98

Calls

4 calls:

3.0ms	(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
27.0ms	(* r (sin b))
22.0ms	(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))
57.0ms	(* (sin a) (sin b))

series1.1s

Counts

4 → 12

Calls

4 calls:

202.0ms	(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
107.0ms	(* r (sin b))
661.0ms	(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))
111.0ms	(* (sin a) (sin b))

simplify7.6s

Counts

110 → 110

Iterations

Iter	Nodes
done	5084
3	3792
2	965
1	376
0	176

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes1.1s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify26.0ms

Iterations

Iter	Nodes
done	25
2	25
1	23
0	15

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.9s	2918×	body	1280	valid
1.2s	1912×	body	640	valid
317.0ms	2095×	body	80	valid
288.0ms	705×	body	320	valid
139.0ms	370×	body	160	valid