Details

sample82.0ms

Algorithm

intervals

Results

30.0ms	93×	body	2560	valid
22.0ms	87×	body	1280	valid
7.0ms	258×	body	80	nan
5.0ms	32×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	43	7
2	84	7
3	155	7
4	262	7
5	454	7
6	2878	7
7	5001	7
done	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

23.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
15.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series117.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify38.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	349	623
1	1288	567
2	5001	565
done	5001	565

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

23.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0ms	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
19.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
131.0ms	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
32.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	361	749
1	1295	678
2	5001	676
done	5001	676

prune230.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- (* 1.0 1.0) (* (* 5.0 (* v v)) (* 5.0 (* v v)))) (* (- (* v v) 1.0) (+ 1.0 (* 5.0 (* v v))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative` `unswap-sqr`
1×	`acos-asin`

Counts

4 → 73

Calls

4 calls:

18.0ms	(* 5.0 (* v v))
15.0ms	(* 5.0 (* v v))
16.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- (* 1.0 1.0) (* (* 5.0 (* v v)) (* 5.0 (* v v)))) (* (- (* v v) 1.0) (+ 1.0 (* 5.0 (* v v))))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* 5.0 (* v v))
25.0ms	(* 5.0 (* v v))
25.0ms	(* 5.0 (* v v))
8.0ms	(acos (/ (- (* 1.0 1.0) (* (* 5.0 (* v v)) (* 5.0 (* v v)))) (* (- (* v v) 1.0) (+ 1.0 (* 5.0 (* v v))))))

simplify52.0ms

Counts

85 → 85

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	155	484
1	541	408
2	1909	408
3	5002	408
done	5002	408

prune165.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 4.0 (fma v v (pow v 4)) (- 1.0))
0.0b	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.4b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `expm1-log1p` `fma-udef` `expm1-udef`

Counts

3 → 31

Calls

3 calls:

0.0ms	(fma 4.0 (fma v v (pow v 4)) (- 1.0))
0.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
1.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma 4.0 (fma v v (pow v 4)) (- 1.0))
155.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
7.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify166.0ms

Counts

40 → 40

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	70	262
1	177	231
2	677	231
3	4408	231
4	5001	231
done	5001	231

prune109.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes57.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15
done	16	15

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2970×	body	2560	valid
563.0ms	2508×	body	1280	valid
220.0ms	8062×	body	80	nan
208.0ms	1312×	body	640	valid
69.0ms	598×	body	320	valid
33.0ms	412×	body	160	valid
10.0ms	200×	body	80	valid