Details

sample83.0ms

Algorithm

intervals

Results

33.0ms	98×	body	2560	valid
17.0ms	78×	body	1280	valid
10.0ms	272×	body	80	nan
7.0ms	41×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	4×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	14
1	20	14
2	42	14
3	88	14
4	159	14
5	256	14
6	401	14
7	1139	14
done	5000	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

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))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite20.0ms

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:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify850.0ms

Counts

78 → 78

Iterations

Useful iterations: done (848.0ms)

Iter	Nodes	Cost
0	145	1268
1	345	1223
2	1107	1120
done	5000	1118

prune181.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* 5.0 (* v v))))
0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.5b	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `associate-r` `*-commutative` `unswap-sqr`
1×	`acos-asin` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 69

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
7.0ms	(* 5.0 (* v v))
7.0ms	(* 5.0 (* v v))
0.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series134.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
27.0ms	(* 5.0 (* v v))
25.0ms	(* 5.0 (* v v))
4.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify1.6s

Counts

81 → 81

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	116	1023
1	259	815
2	783	747
3	3929	747
done	5001	747

prune199.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 4.0 (fma v v (pow v 4)))
0.5b	(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

3.0ms	(* 4.0 (fma v v (pow v 4)))
0.0ms	(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

series103.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(* 4.0 (fma v v (pow v 4)))
3.0ms	(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

simplify1.1s

Counts

38 → 38

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	59	471
1	107	459
2	350	399
3	1715	399
done	5001	399

prune88.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (acos (- (* 4.0 (fma v v (pow v 4))) 1.0)))
0.0b	(expm1 (log1p (acos (- (* 4.0 (fma v v (pow v 4))) 1.0))))
0.0b	(* 4.0 (fma v v (pow v 4)))
0.5b	(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`fma-udef`
1×	`distribute-rgt-in` `acos-asin` `log1p-udef` `expm1-log1p` `distribute-lft-in` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

0.0ms	(log1p (acos (- (* 4.0 (fma v v (pow v 4))) 1.0)))
0.0ms	(expm1 (log1p (acos (- (* 4.0 (fma v v (pow v 4))) 1.0))))
3.0ms	(* 4.0 (fma v v (pow v 4)))
0.0ms	(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

series306.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(log1p (acos (- (* 4.0 (fma v v (pow v 4))) 1.0)))
124.0ms	(expm1 (log1p (acos (- (* 4.0 (fma v v (pow v 4))) 1.0))))
99.0ms	(* 4.0 (fma v v (pow v 4)))
3.0ms	(acos (- (* 4.0 (fma v v (pow v 4))) 1.0))

simplify1.3s

Counts

66 → 66

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	80	896
1	130	858
2	377	746
3	1758	746
done	5001	746

prune158.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes42.0ms

Accuracy

0% (0.1b 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	11	24
1	13	24
done	13	24

end0.0ms

sample2.3s

Algorithm

intervals

Results

979.0ms	2937×	body	2560	valid
561.0ms	2545×	body	1280	valid
224.0ms	8079×	body	80	nan
200.0ms	1240×	body	640	valid
77.0ms	648×	body	320	valid
35.0ms	414×	body	160	valid
10.0ms	216×	body	80	valid