Details

sample231.0ms

Algorithm

intervals

Results

82.0ms	97×	body	1280	valid
76.0ms	81×	body	2560	valid
27.0ms	275×	body	80	nan
18.0ms	38×	body	640	valid
8.0ms	21×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	6×	body	80	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
6	3394
5	1102
4	438
3	170
2	63
1	23
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.2b	(* 5 (* v v))
0.5b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite66.0ms

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` `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 → 71

Calls

3 calls:

38.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
23.0ms	(* 5 (* v v))
2.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
48.0ms	(* 5 (* v v))
5.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify7.2s

Counts

80 → 80

Iterations

Iter	Nodes
3	6330
2	1269
1	362
0	145

prune624.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* v v) (* v v)) (* v v))
0.0b	(* (+ (* (* v v) (* v v)) (* v v)) 4)
0.1b	(* (* v v) (* v v))
0.5b	(acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
24×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus` `add-cbrt-cube` `add-exp-log`
13×	`pow2`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-l`
4×	`associate-r`
2×	`distribute-lft1-in` `flip3-+` `associate-l/` `-commutative` `flip-+` `unswap-sqr`
1×	`acos-asin` `+-commutative` `sum-log` `swap-sqr`

Counts

4 → 104

Calls

4 calls:

36.0ms	(+ (* (* v v) (* v v)) (* v v))
113.0ms	(* (+ (* (* v v) (* v v)) (* v v)) 4)
20.0ms	(* (* v v) (* v v))
2.0ms	(acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))

series315.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (* (* v v) (* v v)) (* v v))
146.0ms	(* (+ (* (* v v) (* v v)) (* v v)) 4)
59.0ms	(* (* v v) (* v v))
7.0ms	(acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))

simplify14.7s

Counts

116 → 116

Iterations

Iter	Nodes
3	10829
2	1378
1	290
0	107

prune903.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))
1.0b	(sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))
1.0b	(sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))
1.0b	(* (sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))

rewrite26.0ms

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×	`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 → 83

Calls

4 calls:

4.0ms	(acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))
2.0ms	(sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))
1.0ms	(sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))
16.0ms	(* (sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))
29.0ms	(sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))
32.0ms	(sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))
8.0ms	(* (sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (sqrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))

simplify3.3s

Counts

95 → 95

Iterations

Iter	Nodes
5	3983
4	1291
3	571
2	277
1	138
0	72

prune777.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

147×	`pow1`
115×	`sqrt-pow1`
62×	`pow1/3`
61×	`pow-prod-up`
44×	`add-sqr-sqrt`
41×	`pow-prod-down` `pow-sqr`
32×	`cbrt-prod`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`pow-plus`
16×	`pow2` `swap-sqr` `associate-r` `associate-l`
12×	`unswap-sqr`
11×	`pow1/2`
10×	`add-exp-log`
9×	`sqrt-prod`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`prod-exp` `*-commutative` `cbrt-unprod`
1×	`rem-sqrt-square` `rem-square-sqrt` `sqrt-unprod`

Counts

4 → 190

Calls

4 calls:

3.0ms	(sqrt (* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))))
7.0ms	(* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))
6.0ms	(* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))
29.0ms	(* (sqrt (* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))) (sqrt (* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(sqrt (* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1)))))
215.0ms	(* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))
241.0ms	(* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))
165.0ms	(* (sqrt (* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))) (sqrt (* (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))) (cbrt (acos (+ (* (+ (* (* v v) (* v v)) (* v v)) 4) -1))))))

simplify6.2s

Counts

202 → 202

Iterations

Iter	Nodes
4	7697
3	1418
2	537
1	259
0	122

prune2.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes149.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	10
1	10
0	9

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.1s	2970×	body	2560	valid
2.3s	2480×	body	1280	valid
824.0ms	8255×	body	80	nan
668.0ms	1262×	body	640	valid
238.0ms	636×	body	320	valid
118.0ms	430×	body	160	valid
28.0ms	222×	body	80	valid