Details

sample202.0ms

Algorithm

intervals

Results

86.0ms	98×	body	2560	valid
53.0ms	83×	body	1280	valid
21.0ms	228×	body	80	nan
20.0ms	43×	body	640	valid
6.0ms	16×	body	320	valid
2.0ms	8×	body	160	valid
1.0ms	8×	body	80	valid

simplify573.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	467
3	171
2	65
1	25
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0b	(- 1 (* 5 (* v v)))
0.1b	(* 5 (* v v))
0.5b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
8×	`difference-of-squares`
6×	`associate-/r*` `add-log-exp`
4×	`difference-of-sqr-1` `insert-posit16`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`acos-asin` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

43.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
6.0ms	(- 1 (* 5 (* v v)))
14.0ms	(* 5 (* v v))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
90.0ms	(- 1 (* 5 (* v v)))
36.0ms	(* 5 (* v v))
6.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify781.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	2004
2	1192
1	412
0	156

prune292.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (/ (- 1 (* (* (cbrt (* 5 (* v v))) (cbrt (* 5 (* v v)))) (cbrt (* 5 (* v v))))) (- (* v v) 1)))
31.1b	(cbrt (* 5 (* v v)))
31.1b	(cbrt (* 5 (* v v)))
31.1b	(cbrt (* 5 (* v v)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`acos-asin`

Counts

4 → 39

Calls

4 calls:

2.0ms	(acos (/ (- 1 (* (* (cbrt (* 5 (* v v))) (cbrt (* 5 (* v v)))) (cbrt (* 5 (* v v))))) (- (* v v) 1)))
20.0ms	(cbrt (* 5 (* v v)))
9.0ms	(cbrt (* 5 (* v v)))
9.0ms	(cbrt (* 5 (* v v)))

series1.0s

Counts

4 → 12

Calls

4 calls:

13.0ms	(acos (/ (- 1 (* (* (cbrt (* 5 (* v v))) (cbrt (* 5 (* v v)))) (cbrt (* 5 (* v v))))) (- (* v v) 1)))
374.0ms	(cbrt (* 5 (* v v)))
334.0ms	(cbrt (* 5 (* v v)))
324.0ms	(cbrt (* 5 (* v v)))

simplify678.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	2035
4	1345
3	426
2	164
1	73
0	41

prune258.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.9b	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
0.9b	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0b	(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

rewrite13.0ms

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×	`insert-posit16` `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 → 87

Calls

4 calls:

1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
1.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
10.0ms	(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
28.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
23.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
4.0ms	(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

simplify850.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	2002
3	705
2	321
1	152
0	73

prune341.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ -5 (/ (+ -1 (* v v)) (* v v)))
0.9b	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
0.9b	(sqrt (acos (+ (/ -5 (/ (+ -1 (* v v)) (* v v))) (/ 1 (+ -1 (* v v))))))
1.0b	(* (sqrt (acos (+ (/ -5 (/ (+ -1 (* v v)) (* v v))) (/ 1 (+ -1 (* v v)))))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`times-frac`
26×	`*-un-lft-identity` `add-cube-cbrt`
16×	`sqrt-prod`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
7×	`associate-/r*`
6×	`associate-r` `associate-l`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`sqrt-pow1` `pow1/2` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/l*`
2×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `sqrt-unprod` `associate-/r/` `*-commutative`

Counts

4 → 108

Calls

4 calls:

16.0ms	(/ -5 (/ (+ -1 (* v v)) (* v v)))
1.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0ms	(sqrt (acos (+ (/ -5 (/ (+ -1 (* v v)) (* v v))) (/ 1 (+ -1 (* v v))))))
9.0ms	(* (sqrt (acos (+ (/ -5 (/ (+ -1 (* v v)) (* v v))) (/ 1 (+ -1 (* v v)))))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ -5 (/ (+ -1 (* v v)) (* v v)))
18.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
20.0ms	(sqrt (acos (+ (/ -5 (/ (+ -1 (* v v)) (* v v))) (/ 1 (+ -1 (* v v))))))
60.0ms	(* (sqrt (acos (+ (/ -5 (/ (+ -1 (* v v)) (* v v))) (/ 1 (+ -1 (* v v)))))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

simplify965.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	2004
2	1967
1	479
0	195

prune731.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

regimes177.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.1s	3026×	body	2560	valid
2.2s	2504×	body	1280	valid
1.3s	7787×	body	80	nan
689.0ms	1229×	body	640	valid
230.0ms	627×	body	320	valid
140.0ms	422×	body	160	valid
28.0ms	192×	body	80	valid