Details

sample304.0ms

Algorithm

intervals

Results

161.0ms	90×	body	1280	valid
49.0ms	56×	body	640	valid
17.0ms	28×	body	320	valid
16.0ms	72×	body	80	valid
5.0ms	10×	body	160	valid

simplify60.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize18.0ms

Local error

Found 3 expressions with local error:

3.4b	(cos (+ a b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite42.0ms

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*` `insert-posit16` `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 → 56

Calls

3 calls:

Slowest

16.0ms	(* r (sin b))
15.0ms	(/ (* r (sin b)) (cos (+ a b)))
9.0ms	(cos (+ a b))

series246.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

130.0ms	(/ (* r (sin b)) (cos (+ a b)))
64.0ms	(* r (sin b))
51.0ms	(cos (+ a b))

simplify918.0ms

Counts: 65 → 65

prune710.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

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:

Slowest

34.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms	(* (cos a) (cos b))
16.0ms	(* r (sin b))
14.0ms	(* (sin a) (sin b))

series528.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

340.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms	(* (sin a) (sin b))
73.0ms	(* (cos a) (cos b))
43.0ms	(* r (sin b))

simplify1.9s

Counts: 105 → 105

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

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:

Slowest

82.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
39.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms	(* (cos a) (cos b))
11.0ms	(* (sin a) (sin b))

series579.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

308.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
151.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
66.0ms	(* (sin a) (sin b))
55.0ms	(* (cos a) (cos b))

simplify2.2s

Counts: 129 → 129

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
28×	`times-frac`
13×	`add-cbrt-cube` `associate-l` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-r` `prod-diff` `div-inv`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`sub-neg` `fma-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 116

Calls

4 calls:

Slowest

25.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
21.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
20.0ms	(* (/ (cos a) (sin b)) (cos b))
9.0ms	(/ (cos a) (sin b))

series554.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

239.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
132.0ms	(* (/ (cos a) (sin b)) (cos b))
128.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
55.0ms	(/ (cos a) (sin b))

simplify1.7s

Counts: 128 → 128

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes361.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.2s	2953×	body	1280	valid
1.7s	1793×	body	640	valid
743.0ms	2106×	body	80	valid
533.0ms	801×	body	320	valid
128.0ms	349×	body	160	valid