Details

sample201.0ms

Algorithm

intervals

Results

48.0ms	96×	body	1280	valid
19.0ms	63×	body	640	valid
5.0ms	70×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
4	20
3	19
2	16
1	12
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite41.0ms

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*` `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 → 53

Calls

3 calls:

8.0ms	(* r (sin b))
11.0ms	(/ (* r (sin b)) (cos (+ a b)))
10.0ms	(cos (+ a b))

series245.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* r (sin b))
149.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify759.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	883
1	220
0	98

prune412.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

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` `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 → 86

Calls

4 calls:

13.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
44.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
57.0ms	(* r (sin b))
61.0ms	(* (sin a) (sin b))
339.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1797
1	396
0	158

prune692.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(expm1 (log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b)))))
0.2b	(/ (* r (sin b)) (expm1 (log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b))))))
0.4b	(log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `associate-r` `associate-l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `pow-prod-down` `log1p-expm1` `-commutative` `div-inv` `associate-/l` `expm1-udef` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

15.0ms	(* r (sin b))
0.0ms	(expm1 (log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b)))))
25.0ms	(/ (* r (sin b)) (expm1 (log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b))))))
1.0ms	(log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b))))

series859.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* r (sin b))
157.0ms	(expm1 (log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b)))))
458.0ms	(/ (* r (sin b)) (expm1 (log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b))))))
175.0ms	(log1p (fma (sin a) (- (sin b)) (* (cos a) (cos b))))

simplify631.0ms

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1038
1	273
0	124

prune640.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
60×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
10×	`associate-r`
6×	`pow1` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l`
2×	`clear-num` `frac-2neg`
1×	`neg-mul-1` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

1.0ms	(fma (cos a) (cos b) (* (sin b) (- (sin a))))
27.0ms	(* (sin b) (- (sin a)))
7.0ms	(/ (fma (cos a) (cos b) (* (sin b) (- (sin a)))) r)
26.0ms	(/ (sin b) (/ (fma (cos a) (cos b) (* (sin b) (- (sin a)))) r))

series864.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(fma (cos a) (cos b) (* (sin b) (- (sin a))))
81.0ms	(* (sin b) (- (sin a)))
184.0ms	(/ (fma (cos a) (cos b) (* (sin b) (- (sin a)))) r)
442.0ms	(/ (sin b) (/ (fma (cos a) (cos b) (* (sin b) (- (sin a)))) r))

simplify1.4s

Counts

151 → 151

Iterations

Iter	Nodes
done	5002
2	3383
1	603
0	244

prune993.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes332.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	26
3	26
2	24
1	22
0	18

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.4s	2945×	body	1280	valid
1.1s	1803×	body	640	valid
360.0ms	773×	body	320	valid
338.0ms	2112×	body	80	valid
83.0ms	367×	body	160	valid