Details

sample713.0ms

Algorithm

intervals

Results

543.0ms	234×	body	10240	exit
67.0ms	285×	body	80	valid
4.0ms	7×	body	160	valid

simplify308.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

308.0ms

(- (* PI l) (* (/ 1 (* F F)) (tan (* PI l))))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize17.0ms

Local error

Found 4 expressions with local error:

8.0b	(/ (tan (* PI l)) (* F F))
2.4b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)

rewrite56.0ms

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`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `tan-quot` `*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `associate-/l/`

Counts

4 → 70

Calls

4 calls:

Slowest

28.0ms	(/ (tan (* PI l)) (* F F))
16.0ms	(tan (* PI l))
5.0ms	(* PI l)
5.0ms	(* PI l)

series328.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

171.0ms	(/ (tan (* PI l)) (* F F))
82.0ms	(tan (* PI l))
45.0ms	(* PI l)
30.0ms	(* PI l)

simplify3.8s

Counts

87 → 82

Calls

87 calls:

Slowest

764.0ms	(+ (/ (* PI l) (pow F 2)) (+ (* 2/15 (/ (* (pow PI 5) (pow l 5)) (pow F 2))) (* 1/3 (/ (* (pow PI 3) (pow l 3)) (pow F 2)))))
368.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
353.0ms	(* (* (* PI PI) PI) (* (* l l) l))
335.0ms	(* (* (* PI PI) PI) (* (* l l) l))
334.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) F) (* (* F F) F)))

prune932.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

2.4b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

4 → 76

Calls

4 calls:

Slowest

17.0ms	(tan (* PI l))
14.0ms	(/ (tan (* PI l)) F)
11.0ms	(* PI l)
10.0ms	(* PI l)

series306.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

156.0ms	(/ (tan (* PI l)) F)
92.0ms	(tan (* PI l))
31.0ms	(* PI l)
27.0ms	(* PI l)

simplify3.0s

Counts

99 → 88

Calls

99 calls:

Slowest

491.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* F F) F))
360.0ms	(* (* (* PI PI) PI) (* (* l l) l))
350.0ms	(* (* (* PI PI) PI) (* (* l l) l))
212.0ms	(* (* (* PI l) (* PI l)) (* PI l))
204.0ms	(* (* (* PI l) (* PI l)) (* PI l))

prune855.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

2.4b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

4 → 76

Calls

4 calls:

Slowest

23.0ms	(/ (tan (* PI l)) F)
16.0ms	(tan (* PI l))
16.0ms	(* PI l)
11.0ms	(* PI l)

series280.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(/ (tan (* PI l)) F)
75.0ms	(tan (* PI l))
39.0ms	(* PI l)
33.0ms	(* PI l)

simplify2.8s

Counts

99 → 88

Calls

99 calls:

Slowest

485.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* F F) F))
324.0ms	(* (* (* PI PI) PI) (* (* l l) l))
275.0ms	(* (* (* PI PI) PI) (* (* l l) l))
203.0ms	(* (* (* PI l) (* PI l)) (* PI l))
186.0ms	(* (* (* PI l) (* PI l)) (* PI l))

prune822.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize67.0ms

Local error

Found 4 expressions with local error:

2.4b	(tan (* PI l))
0.5b	(* (cbrt F) (cbrt F))
0.5b	(cbrt F)
0.5b	(cbrt F)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `tan-quot` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

Slowest

16.0ms	(tan (* PI l))
10.0ms	(* (cbrt F) (cbrt F))
1.0ms	(cbrt F)
1.0ms	(cbrt F)

series959.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

313.0ms	(* (cbrt F) (cbrt F))
296.0ms	(cbrt F)
263.0ms	(cbrt F)
88.0ms	(tan (* PI l))

simplify1.3s

Counts

99 → 86

Calls

99 calls:

Slowest

167.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
148.0ms	(* (cbrt -1) (pow (* F -1) 1/3))
136.0ms	(* (cbrt -1) (pow (* F -1) 1/3))
111.0ms	(* (pow (cbrt -1) 2) (pow (pow F 2) 1/3))
86.0ms	(* (* (* (cbrt F) (cbrt F)) (* (cbrt F) (cbrt F))) (* (cbrt F) (cbrt F)))

prune1.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.3b

regimes467.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch2.0ms

end0.0ms

sample20.9s

Algorithm

intervals

Results

18.3s	7736×	body	10240	exit
2.0s	8931×	body	80	valid
146.0ms	225×	body	160	valid