Details

sample676.0ms

Algorithm

intervals

Results

306.0ms	108×	body	1280	valid
50.0ms	56×	body	640	valid
42.0ms	57×	body	80	valid
12.0ms	25×	body	320	valid
6.0ms	10×	body	160	valid

simplify97.0ms

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize72.0ms

Local error

Found 3 expressions with local error:

1.9b	(cos (+ a b))
0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))

rewrite51.0ms

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×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `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 → 76

Calls

3 calls:

Slowest

18.0ms	(cos (+ a b))
15.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))

series425.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

296.0ms	(* r (/ (sin b) (cos (+ a b))))
83.0ms	(/ (sin b) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify891.0ms

Counts: 85 → 85

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite227.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 114

Calls

4 calls:

Slowest

115.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
54.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(* (sin a) (sin b))

series754.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

397.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
177.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
112.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
68.0ms	(* (sin a) (sin b))

simplify2.0s

Counts: 126 → 126

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`expm1-log1p-u` `cos-mult` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `div-inv` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 126

Calls

4 calls:

Slowest

98.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
53.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))
8.0ms	(* r (sin b))

series602.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

333.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
131.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms	(* r (sin b))
67.0ms	(* (sin a) (sin b))

simplify769.0ms

Counts: 138 → 138

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize51.0ms

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

rewrite101.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

Slowest

34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
31.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(* (sin a) (sin b))
16.0ms	(* r (sin b))

series901.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

473.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
270.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
83.0ms	(* (sin a) (sin b))
75.0ms	(* r (sin b))

simplify2.1s

Counts: 102 → 102

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes375.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.7s	2993×	body	1280	valid
1.6s	1807×	body	640	valid
431.0ms	746×	body	320	valid
396.0ms	2118×	body	80	valid
168.0ms	337×	body	160	valid