Details

sample99.0ms

Algorithm

intervals

Results

41.0ms	256×	body	80	valid
30.0ms	264×	body	80	nan

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	14	435
1	21	435
2	23	435
3	27	410
4	29	410
5	30	410
done	30	410

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize61.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
1.0b	(/ (acos (/ (- g) h)) 3.0)
1.0b	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`div-sub` `fma-udef`
1×	`acos-asin` `cbrt-undiv` `acos-neg` `cos-sum` `clear-num` `frac-2neg` `div-exp` `distribute-frac-neg` `div-inv`

Counts

3 → 51

Calls

3 calls:

0.0ms	(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
10.0ms	(/ (acos (/ (- g) h)) 3.0)
4.0ms	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
21.0ms	(/ (acos (/ (- g) h)) 3.0)
179.0ms	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

simplify4.2s

Counts

60 → 60

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	103	21926
1	158	21494
2	304	21414
3	825	21414
4	2502	21414
done	5007	21414

prune417.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (acos (/ (- g) h)) 3.0)
1.0b	(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
1.0b	(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))
1.0b	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-sub`
1×	`acos-asin` `cbrt-undiv` `acos-neg` `cos-sum` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `log1p-expm1` `distribute-frac-neg` `fma-udef` `div-inv` `expm1-udef`

Counts

4 → 63

Calls

4 calls:

12.0ms	(/ (acos (/ (- g) h)) 3.0)
0.0ms	(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
0.0ms	(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))
2.0ms	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (acos (/ (- g) h)) 3.0)
244.0ms	(expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))))
275.0ms	(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))))
145.0ms	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

simplify5.6s

Counts

75 → 75

Iterations

Useful iterations: 2 (563.0ms)

Iter	Nodes	Cost
0	115	30945
1	180	28712
2	321	28632
3	719	28632
4	1662	28632
5	4302	28632
done	5410	28632

prune507.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.0b

localize65.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
1.0b	(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
1.0b	(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))))
1.0b	(/ 1 (sqrt 3.0))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
76×	`times-frac`
51×	`*-un-lft-identity`
45×	`add-cube-cbrt`
41×	`sqrt-prod`
30×	`add-exp-log`
22×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `div-inv` `pow-flip` `associate-/l*`
1×	`frac-times` `cos-sum` `log1p-udef` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `log1p-expm1` `associate-r/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 153

Calls

4 calls:

65.0ms	(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
4.0ms	(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
0.0ms	(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))))
19.0ms	(/ 1 (sqrt 3.0))

series880.0ms

Counts

4 → 10

Calls

4 calls:

109.0ms	(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
335.0ms	(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
436.0ms	(log1p (expm1 (cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))))
0.0ms	(/ 1 (sqrt 3.0))

simplify672.0ms

Iterations

Useful iterations: 1 (205.0ms)

Iter	Nodes	Cost
0	202	70190
1	511	60244