Details

sample197.0ms

Algorithm

intervals

Results

71.0ms	99×	body	2560	valid
57.0ms	82×	body	1280	valid
18.0ms	251×	body	80	nan
15.0ms	40×	body	640	valid
5.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	4×	body	80	valid

simplify909.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	944
5	254
4	155
3	84
2	43
1	20
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

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)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
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×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

26.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
26.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

155.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
51.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.9s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1832
1	373
0	145

prune416.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

0.0ms	(fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v)))
14.0ms	(* 4.0 (* v v))
18.0ms	(* 4.0 (* v v))
2.0ms	(acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))

series207.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v)))
28.0ms	(* 4.0 (* v v))
28.0ms	(* 4.0 (* v v))
5.0ms	(acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	831
1	156
0	69

prune414.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))
1.0b	(sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0)))
1.0b	(sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0)))
1.0b	(* (sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))) (sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

1.0ms	(acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))
1.0ms	(sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0)))
1.0ms	(sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0)))
14.0ms	(* (sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))) (sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))
20.0ms	(sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0)))
30.0ms	(sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0)))
8.0ms	(* (sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))) (sqrt (acos (- (fma (* 4.0 (* v v)) (* v v) (* 4.0 (* v v))) 1.0))))

simplify1.9s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	840
1	153
0	75

prune514.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

17.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series832.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
206.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
202.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
196.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify6.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	3624
2	521
1	143
0	65

prune390.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes189.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.0s	3049×	body	2560	valid
1.2s	2440×	body	1280	valid
964.0ms	8164×	body	80	nan
455.0ms	1214×	body	640	valid
133.0ms	629×	body	320	valid
101.0ms	451×	body	160	valid
18.0ms	217×	body	80	valid