Details

sample67.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
18.0ms	252×	body	80	nan

simplify54.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (21.0ms)

Iter	Nodes	Cost
0	14	16
1	21	16
2	25	16
3	29	15
4	32	15
5	33	15
done	33	15

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
0.9b	(/ (acos (/ (- g) h)) 3.0)
1.0b	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

0.0ms	(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
6.0ms	(/ (acos (/ (- g) h)) 3.0)
20.0ms	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0))
15.0ms	(/ (acos (/ (- g) h)) 3.0)
134.0ms	(cos (fma (/ 2.0 3.0) PI (/ (acos (/ (- g) h)) 3.0)))

simplify3.5s

Counts

60 → 60

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	103	842
1	153	818
2	275	740
3	538	740
4	1224	740
5	3602	740
done	5000	740

prune236.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (acos (/ (- g) h)) (sqrt 3.0))
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	(/ 1 (sqrt 3.0))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`acos-neg` `acos-asin` `frac-times` `cos-sum` `sqrt-pow1` `pow1/2` `associate-r/` `distribute-frac-neg` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 185

Calls

4 calls:

14.0ms	(/ (acos (/ (- g) h)) (sqrt 3.0))
76.0ms	(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
2.0ms	(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
8.0ms	(/ 1 (sqrt 3.0))

series579.0ms

Counts

4 → 10

Calls

4 calls:

78.0ms	(/ (acos (/ (- g) h)) (sqrt 3.0))
147.0ms	(* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))
354.0ms	(cos (fma (/ 2.0 3.0) PI (* (/ 1 (sqrt 3.0)) (/ (acos (/ (- g) h)) (sqrt 3.0)))))
0.0ms	(/ 1 (sqrt 3.0))

simplify4.5s

Counts

195 → 195

Iterations

Useful iterations: done (4.5s)

Iter	Nodes	Cost
0	220	3077
1	478	2682
2	1293	2278
3	3613	2180
done	5000	2168

prune841.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (acos (/ (- g) h)) 3.0)
0.9b	(expm1 (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0))))
1.0b	(log1p (expm1 (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))
1.0b	(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

7.0ms	(/ (acos (/ (- g) h)) 3.0)
0.0ms	(expm1 (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0))))
0.0ms	(log1p (expm1 (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))
3.0ms	(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (acos (/ (- g) h)) 3.0)
205.0ms	(expm1 (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0))))
225.0ms	(log1p (expm1 (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))
168.0ms	(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))

simplify3.7s

Counts

75 → 75

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	115	1134
1	169	1072
2	281	964
3	445	964
4	686	964
5	1021	964
6	2093	964
done	5001	964

prune355.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))
0.0b	(fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0))
0.9b	(/ (acos (/ (- g) h)) 3.0)
1.0b	(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

10.0ms	(log (exp (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))
1.0ms	(fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0))
16.0ms	(/ (acos (/ (- g) h)) 3.0)
3.0ms	(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(log (exp (cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))))
55.0ms	(fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0))
20.0ms	(/ (acos (/ (- g) h)) 3.0)
175.0ms	(cos (fma PI (/ 2.0 3.0) (/ (acos (/ (- g) h)) 3.0)))

simplify3.7s

Counts

81 → 81

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	130	1269
1	188	1200
2	331	1082
3	626	1082
4	1407	1082
5	4278	1082
done	5000	1082

prune375.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes230.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	37
1	24	37
done	24	37

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.6s	8144×	body	80	nan
1.1s	8000×	body	80	valid