Details

sample245.0ms

Algorithm

intervals

Results

118.0ms	90×	body	2560	valid
54.0ms	84×	body	1280	valid
27.0ms	286×	body	80	nan
19.0ms	39×	body	640	valid
9.0ms	24×	body	320	valid
3.0ms	10×	body	160	valid
1.0ms	9×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
6	3209
5	1064
4	436
3	171
2	65
1	25
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (* 5 (* v v)))
0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.1b	(* 5 (* v v))
0.6b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite48.0ms

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:

11.0ms	(- 1 (* 5 (* v v)))
20.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
13.0ms	(* 5 (* v v))
1.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- 1 (* 5 (* v v)))
90.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
56.0ms	(* 5 (* v v))
6.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify3.4s

Counts

99 → 99

Iterations

Iter	Nodes
3	6416
2	1315
1	404
0	156

prune887.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* v v) (* v v)) (* v v))
0.0b	(* 4 (+ (* (* v v) (* v v)) (* v v)))
0.1b	(* (* v v) (* v v))
0.6b	(acos (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1))

rewrite170.0ms

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-r`
4×	`associate-l` `insert-posit16`
2×	`distribute-lft1-in` `flip3-+` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `+-commutative` `sum-log` `distribute-lft-in` `swap-sqr`

Counts

4 → 110

Calls

4 calls:

21.0ms	(+ (* (* v v) (* v v)) (* v v))
94.0ms	(* 4 (+ (* (* v v) (* v v)) (* v v)))
42.0ms	(* (* v v) (* v v))
10.0ms	(acos (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1))

series321.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (* (* v v) (* v v)) (* v v))
150.0ms	(* 4 (+ (* (* v v) (* v v)) (* v v)))
35.0ms	(* (* v v) (* v v))
5.0ms	(acos (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1))

simplify20.7s

Counts

122 → 122

Iterations

Iter	Nodes
3	13084
2	1775
1	334
0	114

prune860.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4 (+ (* (* v v) (* v v)) (* v v)))
0.0b	(- (/ PI 2) (asin (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1)))
0.1b	(* (* v v) (* v v))
0.6b	(asin (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1))

rewrite114.0ms

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` `add-sqr-sqrt`
9×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
5×	`associate-r`
4×	`associate-l` `insert-posit16`
2×	`asin-acos` `associate-r/` `-commutative` `difference-of-squares` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `distribute-lft1-in` `flip3-+` `times-frac` `flip3--` `diff-log` `swap-sqr` `flip-+` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 114

Calls

4 calls:

69.0ms	(* 4 (+ (* (* v v) (* v v)) (* v v)))
12.0ms	(- (/ PI 2) (asin (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1)))
25.0ms	(* (* v v) (* v v))
6.0ms	(asin (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1))

series219.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* 4 (+ (* (* v v) (* v v)) (* v v)))
44.0ms	(- (/ PI 2) (asin (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1)))
53.0ms	(* (* v v) (* v v))
6.0ms	(asin (+ (* 4 (+ (* (* v v) (* v v)) (* v v))) -1))

simplify25.4s

Counts

126 → 126

Iterations

Iter	Nodes
3	13527
2	1875
1	380
0	139

prune954.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
1.0b	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0b	(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)))))

rewrite28.0ms

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:

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

series67.0ms

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))))
27.0ms	(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
7.0ms	(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))

simplify3.6s

Counts

99 → 99

Iterations

Iter	Nodes
5	6301
4	1753
3	683
2	300
1	148
0	73

prune783.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes174.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	16
1	16
0	13

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.5s	3046×	body	2560	valid
2.3s	2429×	body	1280	valid
944.0ms	7868×	body	80	nan
722.0ms	1263×	body	640	valid
265.0ms	632×	body	320	valid
101.0ms	416×	body	160	valid
30.0ms	214×	body	80	valid