Details

sample284.0ms

Algorithm

intervals

Results

157.0ms	94×	body	1280	valid
39.0ms	60×	body	640	valid
13.0ms	30×	body	320	valid
11.0ms	65×	body	80	valid
2.0ms	7×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.9b	(cos (+ a b))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

11.0ms	(/ (sin b) (cos (+ a b)))
51.0ms	(* r (/ (sin b) (cos (+ a b))))
23.0ms	(cos (+ a b))

series238.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (sin b) (cos (+ a b)))
162.0ms	(* r (/ (sin b) (cos (+ a b))))
29.0ms	(cos (+ a b))

simplify5.1s

Counts

76 → 76

Iterations

Useful iterations: 4 (3.5s)

Iter	Nodes	Cost
0	116	909
1	249	883
2	634	793
3	1708	785
4	4906	783
done	5000	783

prune276.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (sin a) (sin b))
137.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series722.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
164.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
77.0ms	(* (sin a) (sin b))
361.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify2.7s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1168	1856
3	3375	1715
done	5000	1715

prune657.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`associate-/r/`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 77

Calls

4 calls:

23.0ms	(* (cos a) (cos b))
40.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms	(* (sin a) (sin b))
39.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos a) (cos b))
138.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms	(* (sin a) (sin b))
346.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.5s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	155	1300
1	372	1256
2	1192	1114
3	4114	1027
done	5000	1027

prune525.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`times-frac`
26×	`add-cube-cbrt`
22×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
4×	`cbrt-undiv` `associate-/r/` `associate-/l*`
3×	`flip3--` `associate-l` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `cos-mult` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 121

Calls

4 calls:

36.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
94.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
30.0ms	(/ (* (cos a) (cos b)) (sin b))
36.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
333.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
129.0ms	(/ (* (cos a) (cos b)) (sin b))
167.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify3.4s

Counts

133 → 133

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	195	2342
1	441	2125
2	1076	1923
3	3314	1913
done	5000	1913

prune490.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes256.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	13	15
1	16	13
done	16	13

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.4s	2916×	body	1280	valid
1.6s	1826×	body	640	valid
307.0ms	2134×	body	80	valid
287.0ms	784×	body	320	valid
84.0ms	341×	body	160	valid