Details

sample421.0ms

Algorithm

intervals

Results

212.0ms	59×	body	640	valid
114.0ms	95×	body	1280	valid
15.0ms	32×	body	320	valid
8.0ms	61×	body	80	valid
2.0ms	9×	body	160	valid

simplify23.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite108.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

61.0ms	(* r (/ (sin b) (cos (+ a b))))
13.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(cos (+ a b))

series268.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(* r (/ (sin b) (cos (+ a b))))
72.0ms	(/ (sin b) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify3.6s

Counts

82 → 82

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	659	834
3	1814	830
done	5001	824

prune321.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

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

rewrite200.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
114.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
13.0ms	(* (sin a) (sin b))
43.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
361.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
71.0ms	(* (sin a) (sin b))
146.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.1s

Counts

122 → 122

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1244	1949
3	3754	1826
done	5000	1821

prune650.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin 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))))

rewrite129.0ms

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×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

19.0ms	(* r (sin b))
27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms	(* (sin a) (sin b))
57.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series616.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* r (sin b))
130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(* (sin a) (sin b))
362.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.9s

Counts

98 → 98

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	152	1364
1	370	1324
2	1162	1174
3	4193	1081
done	5000	1078

prune466.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`fma-neg`
6×	`pow1` `div-inv` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 128

Calls

4 calls:

15.0ms	(* (cos a) (cos b))
45.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
29.0ms	(/ (* (cos a) (cos b)) (sin b))
46.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series645.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (cos a) (cos b))
139.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
135.0ms	(/ (* (cos a) (cos b)) (sin b))
297.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify1.7s

Counts

140 → 140

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	216	2544
1	456	2233
2	1294	1954
done	5001	1825

prune589.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes233.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: done (2.0ms)

Iter	Nodes	Cost
0	13	15
1	14	15
done	14	13

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.7s	2939×	body	1280	valid
1.2s	1778×	body	640	valid
343.0ms	2138×	body	80	valid
333.0ms	811×	body	320	valid
91.0ms	335×	body	160	valid