Details

sample168.0ms

Algorithm

intervals

Results

79.0ms	107×	body	2560	valid
32.0ms	69×	body	1280	valid
17.0ms	46×	body	640	valid
15.0ms	248×	body	80	nan
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	6×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
5	2012
4	467
3	171
2	65
1	25
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.1b	(* 5 (* v v))
0.3b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`times-frac`
15×	`add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `difference-of-squares`
6×	`associate-/r*`
4×	`difference-of-sqr-1`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `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 → 74

Calls

3 calls:

20.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
30.0ms	(* 5 (* v v))
2.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
28.0ms	(* 5 (* v v))
3.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify1.4s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1125
1	378
0	148

prune364.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* v v) 4)
0.0b	(* (* v v) 4)
0.1b	(* (* v v) (* (* v v) 4))
0.4b	(acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1` `add-cbrt-cube` `add-exp-log`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-l` `*-commutative`
2×	`unswap-sqr`
1×	`acos-asin`

Counts

4 → 78

Calls

4 calls:

14.0ms	(* (* v v) 4)
14.0ms	(* (* v v) 4)
54.0ms	(* (* v v) (* (* v v) 4))
289.0ms	(acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))

series125.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* v v) 4)
31.0ms	(* (* v v) 4)
59.0ms	(* (* v v) (* (* v v) 4))
4.0ms	(acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))

simplify3.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
3	2966
2	773
1	204
0	79

prune272.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.3b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
1.0b	(cbrt (* (* (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
1.0b	(* (* (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `acos-asin` `pow3` `pow-sqr`
1×	`cbrt-prod` `pow1/3` `associate-l` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

2.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
2.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
21.0ms	(cbrt (* (* (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
31.0ms	(* (* (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
8.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
10.0ms	(cbrt (* (* (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
48.0ms	(* (* (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

simplify2.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
4	2214
3	824
2	375
1	158
0	61

prune271.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))
1.0b	(sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1)))
1.0b	(sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1)))
1.0b	(* (sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))) (sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))))

rewrite329.0ms

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:

306.0ms	(acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))
2.0ms	(sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1)))
2.0ms	(sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1)))
18.0ms	(* (sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))) (sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))
21.0ms	(sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1)))
31.0ms	(sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1)))
9.0ms	(* (sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))) (sqrt (acos (- (+ (* (* v v) (* (* v v) 4)) (* (* v v) 4)) 1))))

simplify2.8s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
4	1628
3	780
2	328
1	157
0	74

prune388.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

regimes276.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	9

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.9s	2979×	body	2560	valid
1.6s	2468×	body	1280	valid
1.0s	8112×	body	80	nan
463.0ms	1258×	body	640	valid
145.0ms	650×	body	320	valid
111.0ms	422×	body	160	valid
19.0ms	223×	body	80	valid