Details

sample588.0ms

Algorithm

intervals

Results

320.0ms	97×	body	1280	valid
70.0ms	65×	body	640	valid
14.0ms	20×	body	320	valid
14.0ms	63×	body	80	valid
6.0ms	11×	body	160	valid

simplify109.0ms

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize37.0ms

Local error

Found 3 expressions with local error:

4.2b	(cos (+ a b))
0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))

rewrite47.0ms

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×	`associate-/r` `associate-l` `insert-posit16` `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 → 70

Calls

3 calls:

Slowest

18.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(cos (+ a b))
9.0ms	(/ (sin b) (cos (+ a b)))

series326.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

197.0ms	(* r (/ (sin b) (cos (+ a b))))
71.0ms	(/ (sin b) (cos (+ a b)))
58.0ms	(cos (+ a b))

simplify859.0ms

Counts: 79 → 79

prune895.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

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×	`insert-posit16`
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` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

Slowest

102.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(* (sin a) (sin b))

series706.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

326.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
182.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
68.0ms	(* (sin a) (sin b))

simplify1.7s

Counts: 116 → 116

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

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×	`associate-/r/` `cos-mult` `insert-posit16`
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` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

Slowest

48.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms	(* (sin a) (sin b))
8.0ms	(* (sin b) r)

series605.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

331.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
85.0ms	(* (sin a) (sin b))
57.0ms	(* (sin b) r)

simplify2.5s

Counts: 92 → 92

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
5×	`sin-mult`
4×	`cbrt-undiv` `div-exp` `cos-mult` `insert-posit16` `associate-/l/`
3×	`associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

Slowest

29.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))
10.0ms	(* (sin a) (sin b))

series700.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

366.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r))
158.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) r)
103.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* (sin a) (sin b))

simplify896.0ms

Counts: 151 → 151

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes322.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.0s	2941×	body	1280	valid
2.3s	1889×	body	640	valid
432.0ms	2072×	body	80	valid
395.0ms	770×	body	320	valid
190.0ms	328×	body	160	valid