Details

sample1.2s

Algorithm

intervals

Results

975.0ms	234×	body	10240	exit
73.0ms	285×	body	80	valid
4.0ms	7×	body	160	valid

simplify261.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

260.0ms

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize19.0ms

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)

rewrite66.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 78

Calls

4 calls:

Slowest

20.0ms	(* PI l)
16.0ms	(tan (* PI l))
16.0ms	(/ (tan (* PI l)) (* F F))
10.0ms	(* PI l)

series311.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

166.0ms	(/ (tan (* PI l)) (* F F))
85.0ms	(tan (* PI l))
37.0ms	(* PI l)
22.0ms	(* PI l)

simplify3.5s

Counts

95 → 90

Calls

95 calls:

Slowest

403.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
365.0ms	(* (* (* PI PI) PI) (* (* l l) l))
327.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) F) (* (* F F) F)))
299.0ms	(+ (/ (* 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)))))
296.0ms	(* (* (* PI PI) PI) (* (* l l) l))

prune764.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

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)

rewrite42.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 84

Calls

4 calls:

Slowest

21.0ms	(/ (tan (* PI l)) F)
8.0ms	(tan (* PI l))
5.0ms	(* PI l)
5.0ms	(* PI l)

series291.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(/ (tan (* PI l)) F)
83.0ms	(tan (* PI l))
41.0ms	(* PI l)
22.0ms	(* PI l)

simplify3.2s

Counts

107 → 96

Calls

107 calls:

Slowest

517.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* F F) F))
322.0ms	(* (* (* PI PI) PI) (* (* l l) l))
315.0ms	(* (* (* PI PI) PI) (* (* l l) l))
265.0ms	(* (* (/ (tan (* PI l)) F) (/ (tan (* PI l)) F)) (/ (tan (* PI l)) F))
255.0ms	(* (* (* PI l) (* PI l)) (* PI l))

prune895.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

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)

rewrite61.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 84

Calls

4 calls:

Slowest

23.0ms	(/ (tan (* PI l)) F)
16.0ms	(tan (* PI l))
10.0ms	(* PI l)
10.0ms	(* PI l)

series306.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(/ (tan (* PI l)) F)
90.0ms	(tan (* PI l))
39.0ms	(* PI l)
36.0ms	(* PI l)

simplify3.0s

Counts

107 → 96

Calls

107 calls:

Slowest

439.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* F F) F))
344.0ms	(* (* (* PI PI) PI) (* (* l l) l))
290.0ms	(* (* (* PI PI) PI) (* (* l l) l))
212.0ms	(* (* (* PI l) (* PI l)) (* PI l))
207.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))

prune899.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize53.0ms

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)

rewrite23.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `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 → 82

Calls

4 calls:

Slowest

12.0ms	(* (cbrt F) (cbrt F))
8.0ms	(tan (* PI l))
1.0ms	(cbrt F)
1.0ms	(cbrt F)

series987.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

311.0ms	(cbrt F)
294.0ms	(* (cbrt F) (cbrt F))
292.0ms	(cbrt F)
89.0ms	(tan (* PI l))

simplify1.4s

Counts

107 → 94

Calls

107 calls:

Slowest

184.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
152.0ms	(* (pow (cbrt -1) 2) (pow (pow F 2) 1/3))
131.0ms	(* (cbrt -1) (pow (* F -1) 1/3))
124.0ms	(* (cbrt -1) (pow (* F -1) 1/3))
91.0ms	(* (* (* (cbrt F) (cbrt F)) (* (cbrt F) (cbrt F))) (* (cbrt F) (cbrt F)))

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.3b

regimes661.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample20.5s

Algorithm

intervals

Results

17.1s	7736×	body	10240	exit
2.8s	8931×	body	80	valid
117.0ms	225×	body	160	valid